UTILIZATION-BASED DELAY GUARANTEE TECHNIQUES AND THEIR APPLICATIONS. A Dissertation SHENGQUAN WANG

Transcription

1 UTILIZATION-BASED DELAY GUARANTEE TECHNIQUES AND THEIR APPLICATIONS A Dssertaton by SHENGQUAN WANG Submtted to the Offce of Graduate Studes of Texas A&M Unversty n partal fulfllment of the requrements for the degree of DOCTOR OF PHILOSOPHY December 2006 Major Subject: Computer Scence

2 UTILIZATION-BASED DELAY GUARANTEE TECHNIQUES AND THEIR APPLICATIONS A Dssertaton by SHENGQUAN WANG Submtted to the Offce of Graduate Studes of Texas A&M Unversty n partal fulfllment of the requrements for the degree of DOCTOR OF PHILOSOPHY Approved by: Char of Commttee, Commttee Members, Head of Department, We Zhao Rccardo Bettat Jennfer Welch Janxn Zhou Valere E. Taylor December 2006 Major Subject: Computer Scence

3 ABSTRACT Utlzaton-Based Delay Guarantee Technques and Ther Applcatons. (December 2006) Shengquan Wang, B.S., Anhu Normal Unversty; M.S., Shangha Jao Tong Unversty; M.S., Texas A&M Unversty Char of Advsory Commttee: Dr. We Zhao Many real-tme systems demand effectve and effcent delay-guaranteed servces to meet tmng requrements of ther applcatons. We note that a system provdes a delay-guaranteed servce f the system can ensure that each tas wll meet ts predefned end-to-end deadlne. Admsson control plays a crtcal role n provdng delayguaranteed servces. The major functon of admsson control s to determne admssblty of a new tas. A new tas wll be admtted nto the system f the deadlne of all exstng tass and the new tas can be met. Admsson control has to be effcent and effcent, meanng that a decson should be made qucly whle admttng the maxmum number of tass. In ths dssertaton, we study a utlzaton-based admsson control mechansm. Utlzaton-based admsson control maes an admsson decson based on a smple resource utlzaton test: A tas wll be admtted f the resource utlzaton s lower than a pre-derved safe resource utlzaton bound. The challenge of obtanng a safe resource utlzaton bound s how to perform delay analyss offlne, whch s the man focus of

4 v ths dssertaton. For ths, we develop utlzaton-based delay guarantee technques to render utlzaton-based admsson control both effcent and effectve, whch s further confrmed wth our data. We develop technques for several systems that are of practcal mportance. We frst consder wred networs wth the Dfferentated Servces model, whch s wellnown as ts supportng scalable servces n computer networs. We consder both cases of provdng determnstc and statstcal delay-guaranteed servces n wred networs wth the Dfferentated Servces model. We wll then extend our wor to wreless networs, whch have become popular for both cvlan and msson crtcal applcatons. The varable servce capacty of a wreless ln presents more of a challenge n provdng delay-guaranteed servces n wreless networs. Fnally, we study ways to provde delayguaranteed servces n component-based systems, whch now serve as an mportant platform for developng a new generaton of computer software. We show that wth our utlzaton-based delay guarantee technque, component-based systems can provde effcent and effectve delay-guaranteed servces whle mantanng such advantages as the reusablty of components.

5 v DEDICATION To MY PARENTS, and MY SISTERS.

6 v ACKNOWLEDGMENTS I would le to express my deep apprecaton to my advsor, Dr. We Zhao, for hs ntroducng me to the feld of computer scence. I am greatly ndebted to hm for hs constant nspraton, encouragement, patence, and gudance throughout my Ph.D. studes, whch were essental to the completon of ths dssertaton. Hs broad vson and deep nsght have always been the source of nspraton for me n my professonal growth. I would le to than Dr. Rccardo Bettat, for hs great contrbuton n the development of my research and hs nvolvement on my advsory commttee. Throughout my Ph.D. studes, I have benefted tremendously from the ntensve nteracton wth hm on many research projects, n partcular, at the system level. Many thans go to Dr. Jennfer Welch for servng on my advsory commttee. I apprecate her deep nsght n the area of dstrbuted algorthms. I would le to than Dr. Janxn Zhou for hs nvolvement on my advsory commttee, n partcular n my fnal defense. Apprecaton s due to Dr. Martn Wortman for hs nvolvement on my advsory commttee n the begnnng and hs nsghtful comments on my research proposal. It s also my great pleasure to acnowledgement many professors and researchers wth whom I had the honor to now and wor wth. Among them, I am especally grateful to Dr. Janer Chen. Hs senstvty on research and sncerty on teachng have been a great source of nspraton. I would le to than Mr. Wlls Mart for hs support

7 v for my graduate assstantshp, Dr. Donald Fresen for hs nd advce relatng to many academc ssues, and Dr. Walter Daugherty, Dr. Du L, Dr. Andreas Klappenecer, and Dr. Steve Lu for ther frendshp and encouragement. Many thans also go to my fellow former and current graduate students n the Real-Tme Systems group. I have benefted greatly from worng wth Dr. Dong Xuan, Mr. Zhbn Ma, Mr. Rpal Nathuj, Dr. Nan Zhang, and Dr. Sangg Rho. I have also had many helpful dscussons wth Dr. Chengzh L, Dr. Byung-yu Cho, Dr. Yong Guan, Dr. Xnwen Fu, Dr. Shu Jang, Dr. Soohyun Cho, Dr. Ye Zhu, Mr. Bryan Graham, Mr. We Yu, and Mr. Youngwoo Ahn. I would le to express my apprecaton to Ms. Elena Catelena, Ms. Larsa Archer, and Ms. Kathy Flores for ther frendshp and help durng my Ph.D. studes. In partcular, I would le to than Ms. Archer for her selfless help n polshng most of my wrtngs. Fnally, I owe a specal debt of grattude to my parents and my ssters. Wthout ther tremendous sacrfces and great love, I would not have the chance to pursue an advanced educaton,.e., my graduate studes abroad.

8 v TABLE OF CONTENTS Page ABSTRACT... DEDICATION...v ACKNOWLEDGMENTS...v TABLE OF CONTENTS... v LIST OF FIGURES... x LIST OF TABLES... x CHAPTER I INTRODUCTION.... Overvew....a. Delay-Guaranteed Servce....b. Admsson Control Utlzaton-Based Delay Guarantee Technques and ther Applcatons Organzaton of ths Dssertaton...6 CHAPTER II RELATED WORK...7. Delay-Guaranteed Technques Delay Guarantees n Wred Networs wth Dfferentated Servces Model Delay Guarantees n Wreless Networs Delay Guarantees n Component-Based Systems... CHAPTER III DETERMINISTIC DELAY GUARANTEES IN WIRED NETWORKS WITH THE DIFFERENTIATED SERVICES MODEL...3. Overvew Models a. Networ Models b. Traffc Models A QoS Archtecture for Dfferentated Servces...9

9 x Page 4. Utlzaton-Based Delay Analyss a. Man Result b. Specal Cases Dervng the Delay Formula a. General Delay Formula b. Removng the Dependency on Indvdual Traffc Constrant Functons c. Removng the Dependency on the Number of Flows on Each Input Ln Prorty Assgnment a. Outlne of Algorthms b. Detals of Algorthms Performance Evaluaton a. Experment b. Experment Dscusson...47 CHAPTER IV STATISTICAL DELAY GUARANTEES IN WIRED NET- WORKS WITH THE DIFFERENTIATED SERVICES MODEL Overvew Models Statstcal Delay Guarantees a. Statstcal Delay Analyss b. Utlzaton-Based Statstcal Delay Analyss c. Verfcaton of Utlzaton Bound Performance Evaluaton...6 CHAPTER V STATISTICAL DELAY GUARANTEES IN WIRELESS NETWORKS Overvew Models a. Wreless Ln Model b. Stochastc Servce Curve of a Wreless Ln Statstcal Delay Analyss n a Wreless Networ a. Statstcal Delay Analyss b. Utlzaton-Based Statstcal Delay Analyss Performance Evaluaton a. MUU Comparson b. Admsson Probablty Comparson...85

10 x Page CHAPTER VI DELAY GUARANTEES IN COMPONENT-BASED SYSTEMS..88. Overvew Component-Based Resource Overlays Buldng Real-Tme Applcatons a. Applcaton Model b. Servce Guarantees wth Admsson Control Buldng Real-Tme Components a. Servce Implementaton b. Servce Optmzaton c. Servce Adaptaton A Real-Tme Component-Based System Archtecture Implementaton of a Real-Tme Component-Based System a. EJB and JBoss Applcaton Server b. Real-tme Infrastructure c. Implementaton of Real-Tme Component-Based System Performance Evaluaton a. Admsson Probablty versus Tas Arrval Rate b. Admsson Probablty versus Number of Components c. Admsson Control Latency...3 CHAPTER VII SUMMARY...5 REFERENCES...6 APPENDIX A PROOF OF THEOREM III APPENDIX B PROOF OF THEOREM III APPENDIX C PROOF OF COROLLARY III APPENDIX D PROOF OF COROLLARY III APPENDIX E PROOF OF THEOREM IV APPENDIX F SERVICE OPTIMIZATION...39 VITA...42

11 x LIST OF FIGURES Page Fgure III-. Networ Model...5 Fgure III-2. A Leay Bucet n Edge Router and the Traffc Constrant Functon for a Shaped Class- Flow...8 Fgure III-3. Computaton of Y q,...23 Fgure III-4. The Arrval Curve, the Servce Curve and the Worst-case Delay...29 Fgure III-5. Algorthm One-to-Many...38 Fgure III-6. Procedure ParttonSet...40 Fgure III-7. MUU Computaton...43 Fgure III-8. MCI Networ Topology...44 Fgure III-9. MUU for Randomly Generated Networs...46 Fgure IV-. Senstvty of MUU to Delay Volaton Probablty...63 Fgure IV-2. Admsson Probablty Comparson of Determnstc Model and Statstcal Model...64 Fgure V-. A Ground-space-ground Wreless Communcaton System...68 Fgure V-2. Wreless Ln Framewor...69 Fgure V-3. Flud Verson of Fnte-State Marov Model of a Wreless Channel...70 Fgure V-4. Approxmaton Model of a Wreless Ln...7 Fgure V-5. The Stochastc Servce Curve for a Wreless Ln...74 Fgure V-6. MUU Comparson...84 Fgure V-7. Admsson Probablty Comparson...86

12 x Page Fgure VI-. A Component Archtecture...89 Fgure VI-2. A Component-Based Resource Overlay...93 Fgure VI-3. Servce Optmzaton...0 Fgure VI-4. Servce Adaptaton...03 Fgure VI-5. System Archtecture...04 Fgure VI-6. Real-Tme Servce...08 Fgure VI-7. The Experment Testbed... Fgure VI-8. Comparson of Admsson Probablty vs. Tas Arrval Rate...2 Fgure VI-9. Comparson of Admsson Probablty vs. Number of Components...3 Fgure VI-0. Admsson Control Latency...4 Fgure A-. The Detaled Illustraton of Arrval Curve F ( I + d )...28 p, p, Fgure B-. Worst-case Arrval Curve ɶ ( I + d )...3 F p, p,

13 x LIST OF TABLES Page Table III-. An Example of Prorty Assgnment Table...37 Table III-2. The Comparson of MUU for Dfferent Relatve Burstness...45 Table IV-. Senstvty of MUU to Delay Volaton Probablty...63 Table VI-. A Real-Tme Servce Interface Specfcaton...92

14 CHAPTER I INTRODUCTION. Overvew.a. Delay-Guaranteed Servce Many real-tme systems, such as Voce over IP, mltary command and control systems, and ndustral control systems, demand effectve and effcent delay-guaranteed servces to meet tmng requrements of ther applcatons. We note that a system provdes a delay-guaranteed servce f the system can ensure that each (computatonal or communcaton) tas wll meet ts predefned end-to-end deadlne []. For nstance, n telecommuncaton systems, Voce over IP s a typcal real-tme applcaton [2]. Customers can use IP telephones to communacte wth one another va the Internet, a servce s much cheaper than the tradtonal telephone servces. As more customers recognze the beneft, partcularly durng busy callng perods. When many customers use the servce at the same tme, phone calls wll compete for ln bandwdth, cause networ congestons, and consequently experence long delays. Once delays exceed a certan threshold, the qualty of calls wll become ntolerable. In ndustral/mltary command and control systems, radar sgnal processng and tracng s another typcal real-tme applcaton [3]. In these types of systems, some processors wll sample and dgtze the echo sgnal from radars. Then some processors wll analyze the data, nterface wth the dsplay system and also generate command to control the radars, Ths dssertaton follows the style and format of IEEE/ACM Transactons on Networng.

15 2 n order to trac objects n ts coverage. Because t s a msson-crtcal applcaton, tmng requrement s extremely mportant..b. Admsson Control In order to provde delay-guaranteed servces for real-tme applcatons, we have to ntroduce nto real-tme systems resource management schemes such as admsson control, pacet schedulng, and other sgnalng protocols. Admsson control s one of the most mportant of these. The major functon of admsson control s to determne admssblty of a new tas. A new tas wll be admtted nto the system f the deadlne of all exstng tass and the new tas can be met. Admsson control mechansms have been nvestgated extensvely n lterature [4], [5], [6], [7], [8], [9], [0]. Among them are two major mechansms: delay-based admsson control and utlzaton-based admsson control. The delay-based admsson control mechansm [4], [5], [6] s an approach that performs delay tests at admsson tme: For each tas admsson request, the admsson control needs to explctly compute delays for all exstng tass and the new tas to chec whether delay-guaranteed servces can be met or not. In utlzatonbased admsson control, the utlzaton s defned as the porton of resource on average. The utlzaton-based admsson control mechansm [7], [8], [9], [0] maes an admsson control decson based on a pre-defned safe resource utlzaton bound: For each tas admsson request, as long as the used resource utlzaton plus the requested resource utlzaton are not beyond the pre-defned safe resource utlzaton bound that s computed offlne, the servce guarantee can be provded.

16 3 Rapdly growng worload demands and the contnuous growth of the system sze n real-tme systems are placng enormous processng demands n admsson control, n partcular wthn the systems burdened wth numerous of tass. There are two prmary goals n the desgn of admsson control mechansms for such nd of systems. On the one hand, admsson control has to be effcent, meanng that an admsson decson should be made as qucly as possble, requrng the admsson control mechansm to be lghtweght. On the other hand, admsson control should be effectve, meanng that a system should admt as many tass as possble n order to acheve hgh resource utlzaton. Delay-based admsson control and utlzaton-based admsson control are qute dfferent n achevng these two goals: Delay-based admsson control s not effcent. The admsson control needs to explctly compute delays of all exstng tass and the new tas at the admsson tme, whch s usually computatonally expensve n systems wth a large number of tass. Why s t necessary to compute the delays for all exstng tass? As we now, once a new tas s admtted nto the system, t wll nterfere wth many exstng tass snce they compete for the same resource. In the worst-case, all exstng tass can be affected. Therefore, the admsson control has to ensure that all exstng tass wll stll meet ther deadlne requrements once the new tas s admtted. Despte the fact that t s not effcent, delay-based admsson control s very effectve. Utlzaton-based admsson control nvolves only a smple utlzaton test and elmnates the delay computaton at the admsson tme. Utlzaton-based

17 4 admsson control renders the admsson control very effcent. However, t tends not to be effectve, snce t does not tae nto account of the dynamcs of tass n the admsson process. In our wor, we adopt the utlzaton-based admsson control mechansm; ts effcency renders t very sutable for systems loaded wth a large number of tass. In ths dssertaton, we ntend to show that utlzaton-based admsson control can be both effcent and effectve wth our proposed utlzaton-based delay guarantee technques. 2. Utlzaton-Based Delay Guarantee Technques and Ther Applcatons Resource management s essental to provdng delay-guaranteed servces. Dfferent systems may have dfferent nds of resources or dfferent characterstcs of resources. For nstance, n wred networs, the ey resource s ln bandwdth and the ln bandwdth s constant. In wreless networs, the ey resource s stll ln bandwdth, but the ln bandwdth mght be varable. In software component systems, the ey resource wll not be ln bandwdth, but CPU cycles. In ths dssertaton, we wll focus on development of utlzaton-based delay guarantee technques for these practcal systems. ) We frst consder determnstc delay-guaranteed servces n wred networs wth the Dfferentated Servce model. The Dfferentated Servce model s well-nown for ts advantage of beng able to support scalable servces for aggregated traffc n computer networs. We develop a utlzaton-based delay

18 5 guarantee technque to provde hard delay-guaranteed servces for real-tme applcaton n these systems. 2) We then extend the wor on the Dfferentated Servces model from determnstc delay-guaranteed servces to statstcal delay-guaranteed servces. Statstcal delay-guarantee recognzes the fact that many applcatons can tolerate a small percentage of mssng deadlnes, hence renderng the utlzaton-based admsson control more effectve than the determnstc one. 3) We also extend our wor from wred networs to wreless networs. Wreless networs contnue to experence a surge n popularty for both cvlan and msson crtcal applcatons. However, the capacty of a wreless ln may vary dramatcally, mang delay-guarantee partcularly challengng. We address how to develop a utlzaton-based delay guarantee technque n wreless networs. 4) Fnally, we study how to provde delay-guaranteed servces n componentbased systems, whch now serve as an mportant platform for developng a new generaton of computer software. We show that wth our utlzaton-based delay guarantee technque, component-based systems can effcently and effectvely provde delay-guaranteed servces whle mantanng ther other advantages such as reusablty of components.

19 6 3. Organzaton of ths Dssertaton The rest of ths dssertaton s organzed as follows: In Chapter II, we revew the related wor. In Chapter III, we focus on developng a utlzaton-based delay guarantee technque to provde determnstc delay-guaranteed servce n wred networs wth the Dfferentated Servces model. In Chapter IV, we consder to extend the wor n Chapter III to statstcal delay-guaranteed servces. How to provde delay guarantees n wreless networs s addressed n Chapter V. In Chapter VI, we study ways to provde delayguarantees n component-based systems. Fnally, we conclude ths dssertaton research wth a bref summary n Chapter VII.

20 7 CHAPTER II RELATED WORK. Delay-Guaranteed Technques Developng delay-guaranteed technques are always the central focus of the realtme systems communty and also n our research group. In [], Zhao studed a heurstc approach to schedulng hard real-tme tass wth resource requrements n dstrbuted systems. In [2], Bettat presented the end-to-end schedulng to meet deadlnes n dstrbuted systems. L [3] concentrated on the technques for the analyss of the networ traffc and ts applcatons n the networ management. Cho [4] focused on resource management for scalable Qualty of Servce. Wu [5] performed general schedulablty bound analyss n real-tme systems. In our wor, we adopt utlzaton-based admsson control mechansm to provde delay-guaranteed servces n real-tme systems. In ts basc form, utlzaton-based admsson control was frst proposed [6] for preemptve schedulng of perodc tass on a smple processor. A number of utlzaton-based tests are nown for () centralzed systems such as 69% (and the extensons) for the Rate/Deadlne Monotonc scheduler [6], [7], [8], [9], [20], [2], 00% for Earlest Deadlne Frst scheduler [6], and the general schedulablty bound analyss for statc-prorty scheduler [5], [22], () multprocessor parallel systems ncludng some mportant utlzaton bound results [23], [24], [25], [26], or () dstrbuted systems such as 33% for the Tmed Toen protocol over Fber Dstrbuted Data Interface (FDDI) networs [27], [28], [29], [30].

21 8 2. Delay Guarantees n Wred Networs wth the Dfferentated Servces Model A good survey on recent wor n Dfferentated Servces has been llustrated n [3]. Nchols et al. [32] proposed the premum servce model, whch provded the equvalent of a dedcated ln between two access routers. It provded Dfferentated Servces n prorty-drven schedulng networs wth two prortes, n whch the hgh prorty was reserved for premum servce. The algorthm n [33] provded both guaranteed and statstcal rate and delay bounds, and addressed scalablty through traffc aggregaton and statstcal multplexng. Stoca and Zhang [34] descrbed an archtecture to provde guaranteed servce wthout per-flow state management by usng the Dynamc Pacet State (DPS) technque. However, the pacet headers had to be changed to mplement ther proposed technque. Our wor s based on the statc-prorty schedulng algorthm that s relatvely smple and wdely supported. The utlzaton-based admsson control mechansm s not new to networs. The flud-flow model n the Integrated Servces model, for example, allowed varous forms of utlzaton based admsson control [35]. Such approaches cannot be used n a Dfferentated Servces model, however, because they rely on guaranteed-rate schedulers, whch need to mantan the flow nformaton. A utlzaton-based delay analyss has been studed most recently n [36] for the case of aggregate schedulng. Lower bounds on the worst-case delay have been derved. These bounds are a functon of the networ utlzaton, the maxmum hop count of any flow, and shapng parameters at the entrance to the networ. However, only Frst-In Frst-Out (FIFO) schedulng s under consderaton. Also, delay bounds are not tght, but ndependent of the networ

22 9 topology. In our wor, we derve a better delay bound n statc-prorty schedulng networs. A smlar wor on the utlzaton-based delay guarantee technque was also studed n [7], where t was assumed that prortes were assgned on a class-by-class bass. In our wor, by relaxng ths assumpton, the prorty assgnment s not constraned by class membershp and flows from a class can be assgned dfferent prortes. The problem presented n our wor s more general and challengng. Whle utlzaton-based admsson control sgnfcantly reduces the admsson control overhead, excessve flow establshment actvty can stll add substantal stran to the admsson control components. In [9], an endpont admsson control mechansm was proposed to reduce resource allocaton overhead at the admsson tme by approprately preallocatng resources. Ths mechansm supplements our wor. Statstcal delay-guaranteed servce has been studed va dfferent statstcal envelopes, such as envelopes of boundng moment generatng functons [37], exponentally bounded envelopes [38], [39], and envelopes consstng of famles of boundng dstrbutons [40], [4]. Statstcal envelopes were also appled to resource allocaton for nter-class resource sharng [42] and vdeo-on-demand servces [43]. Much wor has been done to generalze schedulablty condtons for a determnstc servce to a statstcal framewor. Several researchers made statstcal extensons to determnstc servce models. In [44], a rate-varance envelope was ntroduced, whch descrbed the varance of the arrvals of a flow as a functon of a tme perod of length. In [45], arrvals on a flow were assumed to be characterzed by the rate-varance envelope and a longterm arrval rate. Then, applyng the central lmt theorem argument, a bound for the

23 0 probablty of a delay bound volaton was derved for a statc-prorty scheduler. In [46], the authors used a rate-varance envelope as a smple way to capture the second-moment propertes of temporally correlated traffc flows, and to descrbe how qucly the ratedstrbuton becomes concentrated at the mean rate wth ncreasng nterval-length (a ey factor for computng deadlne volaton probabltes). However, these approaches can not be appled to the Dfferentated Servces framewor, snce ther delay computaton reles on the run-tme nformaton of flow dstrbuton. Our wor ntends to solve ths problem. 3. Delay Guarantees n Wreless Networs The dffculty of provsonng delay-guaranteed servces n wreless networs stems from the need to explctly consder both the wreless channel transmsson characterstcs and the underlyng error control mechansms. There s a large volume of lterature dealng wth the representaton and analyss of wreless channel models, and most of these models drectly characterze the fluctuatons of sgnals and provde an estmate of the performance characterstcs, such as symbol error rate vs. sgnal-to-nose rato [47]: The classcal two-state Glbert-Ellott model [48], [49] for burst nose channels, whch characterzed error sequences, had been wdely used and analyzed. In [50], a multple-state quas-statonary Marov channel model was used to characterze the wreless non-statonary channel. In [5], [52], a fnte-state Marov channel was llustrated wth multple states representng the recepton at dfferent sgnal-to-nose levels. A flud verson of the Glbert-Ellott model was used n [53] to perform delay

24 analyss and pacet-dscard performance as well as the effectve capacty for servce guarantee support over a wreless ln wth automatc repeat request (ARQ) and forward error correcton (FEC). In our wor, our utlzaton-based delay guarantee technque can be appled to any of these wreless ln models. At the same tme, we do not assume a partcular traffc pattern, such as the ON/OFF traffc model used n [53]. Instead, we use rate-varance envelopes [44], a smple and general traffc characterzaton. Ths methodology maes our approach applcable to any partcular stuaton. 4. Delay Guarantees n Component-Based Systems Component standards specfy wdely-accepted nterfaces that allow ndependent components from dfferent supplers (thrd partes) to be plugged together and to nteroperate across language, compler, and platform barrers. The best nown examples of such standards are OMG s CORBA [54], Mcrosoft s COM+ [55], and Sun Mcrosystems Enterprse JavaBeans (EJB) [56]. Although component-based models deal successfully wth functonal attrbutes, they provde lttle support for real-tme servces. Exstng standards such as CORBA, COM+, and EJB are unsutable for real-tme applcatons because they do not address ssues of tmelness and predctablty of servce, whch s a basc requrement of real-tme systems [57]. The Real-Tme, Embedded, and Specalzed Systems (RTESS) Platform Tas Force of the OMG proposed a specfcaton for a real-tme CORBA [58], [59]. At the same tme, there s no specfcaton for a real-tme EJB or a real-tme COM+ yet. The TAO project [60]

25 2 provded a CORBA mplementaton that guaranteed that tass across components preserve prorty levels and that overhead n servcng a tas request was statcally predctable. Ths made the ensung system amenable to the same statc schedulablty analyss used n tradtonal real-tme systems. After the archtectural desgn phase was completed, a TAO soluton would be consdered for the AOCS software. In [6], an approach was proposed for run-tme fast software component mgraton (lghtweght mgraton and proactve resource dscovery) for applcaton survvablty n dstrbuted real-tme systems. In [62], the authors proposed to use component-based technques for developng embedded systems software,.e., software for resource-constraned systems, and the VEST toolt amed at provdng a rch set of dependency checs based on the concept of aspects to support dstrbuted embedded system development va components. However, most of these real-tme extensons use tradtonal approaches to provde delay-guaranteed servces, wthout addressng the reusablty n terms of both functonal and delay-guaranteed servces. Our wor ntends to solve ths problem.

26 3 CHAPTER III DETERMINISTIC DELAY GUARANTEES IN WIRED NETWORKS WITH THE DIFFERENTIATED SERVICES MODEL * In the followng two chapters, we wll develop utlzaton-based delay guarantee technques n wred networs wth the Dfferentated Servces model. In ths chapter, we frst focus on provdng determnstc delay-guaranteed servces for real-tme applcatons n such nd of systems.. Overvew In computer networs, a flow s a communcaton tas. Tradtonally, archtectures for provdng delay guarantees over computer networs rely on detaled per-flow nformaton. In the IETF Integrated Servces archtecture [64], for example, each flow s controlled both by admsson control at admsson tme and by pacet schedulng durng the flow lfetme. At the flow establshment tme, the necessary resources must be allocated to the new flow f the admsson request s approved. Durng the flow lfetme, the flow s polced to ensure that the abnormal behavor of a flow does not affect other flows. Ths necesstates that nformaton about each flow s ept by each node along the path for admsson control and pacet forwardng. It s agreed upon that Integrated Servces do not scale. Hgh-speed routers are requred to mantan state and perform schedulng decsons for large numbers of flows. *Reprnted wth permsson from Provdng Absolute Dfferentated Servces for Real-Tme Applcatons n Statc-Prorty Schedulng Networs [63] by S. Wang, D. Xuan, R. Bettat, and W. Zhao, IEEE/ACM Trans. Networng, Vol. 2, pp , Aprl Copyrght 2006 by IEEE.

27 4 In addton, as the number of flows ncreases, the run-tme overhead ncurred n flow establshment and tear-down ncreases as well. The Integrated Servces archtecture therefore cannot provde scalable Qualty-of-Servce (QoS) guaranteed servces (such as delay-guaranteed servces), and the lac of scalablty s due to overhead, both at the flow establshment tme and durng the flow lfetme. The Dfferentated Servces model s a proposed standard amed at supportng scalable servces over the Internet through aggregaton of flows nto servce classes [65]. Networ nodes n Dfferentated Servces need not mantan per-flow nformaton. Snce each router only guarantees that servce agreements are locally mantaned on a per-class bass, end-to-end guarantees are dffcult to provde. In ths chapter, we wll focus on wred networs wth the Dfferentated Servces model that uses the utlzaton-based admsson control mechansm to provde end-to-end delay-guaranteed servces. The challenge of usng the utlzaton-based admsson control mechansm n the Dfferentated Servces framewor s how to verfy whether a utlzaton bound s safe n provdng delay-guaranteed servces at the system confguraton tme. Obvously, the verfcaton wll have to rely on a delay analyss method. We wll follow the approach proposed by Cruz [66] for analyzng delays. Cruz's approach must be adapted to be applcable n a flow-dstrbuton-unaware envronment however. The delay analyss proposed n [66] depends on the nformaton about flow dstrbuton,.e., the number of flows at nput lns and the traffc characterstcs (e.g., the average rate and burst sze) of flows. In our case the delay analyss s done at the system confguraton tme when the nformaton on flow dstrbuton s not yet avalable. We wll develop a utlzaton-based

28 5 delay guarantee technque that allows us to analyze delays wthout dependng on the dynamc nformaton about flow dstrbuton. We also assume that real-tme applcatons have the determnstc deadlne requrement (we wll extend our wor nto statstcal guarantee n the next chapter). We also use statc-prorty schedulers at all routers. Statc-prorty schedulng algorthm s wdely supported on the Internet. The most mportant feature of ths schedulng algorthm s that t s very effcent. Snce statc-prorty schedulng only mantans prortes nformaton, t has lttle overhead, whch s very mportant n the networs loaded wth a large number of flows. 2. Models 2.a. Networ Models Fgure III-. Networ Model In our Dfferentated Servces archtecture, there are two types of routers (as shown n Fgure III-): Edge routers are located at the boundary of the networ and provde

29 6 support for traffc polcng (e.g., leay bucet); Core routers are nsde the networ. A router s connected to other routers, or hosts, through ts nput and output lns. For the purpose of delay computaton, we follow standard practce and model a router as a set of servers, one for each router component, where pacets can experence delays. Pacets are typcally queued at the output buffers, where they compete for the output ln bandwdth. We therefore model a router as a set of output ln servers. All other servers (nput buffers, non-blocng swtch fabrc, wres, etc.) can be elmnated from the delay analyss by approprately subtractng constant delays that have been ncurred from the deadlne requrements of the traffc. Consequently, the networ can be modeled as a graph where the output ln servers are nodes and are connected through ether lns n the networ or paths wthn routers, whch both mae up the set of edges n the graph. We assume Server s of capacty C,, j =,, L. j C and has L nput ln servers wth capactes 2.b. Traffc Models We call a stream of pacets between a sender and a recever a flow. Pacets of a flow are transmtted along a sngle flow route, whch we model as a sequence of servers. Followng the Dfferentated Servces model, flows are parttoned nto classes. QoS requrements and traffc specfcatons of flows are defned on a class-by-class bass. We use M to denote the total number of classes n the networ. We assume that at each server, a certan porton of bandwdth s reserved for each class traffc separately. Let α In the followng, f the context s clear, we wll use ln server or server to refer to output ln server.

30 7 denote the porton of bandwdth reserved for class- traffc at Server. We assume statc-prorty schedulers wth support for P dstnct prortes n the routers. The bandwdth assgned to class- traffc at Server s further parttoned nto portons α p,, one for each class- traffc wth prorty p at that server. We note that P = q= q (the queston of how much bandwdth to assgn to each prorty traffc α α, wll be dscussed n Secton 6). In order to approprately characterze traffc both at the ngress router and wthn the networ, we use a general traffc descrptor n form of traffc functons and ther tme-ndependent counterpart, constrant traffc functons [66]: Defnton III-. For a traffc flow, ts traffc at a specfc pont s characterzed by a traffc functon f(t) whch s defned as the amount of the traffc of the flow passng through the pont durng tme nterval [0,t). The functon F(I) s called the traffc constrant functon of f(t) f f ( t + I) f ( t) F( I), (III-) for any t>0 and I>0. Ths defnton s also appled to aggregated traffc flows. We assume that the source traffc of a flow n Class s controlled by a leay bucet wth burst sze σ and average rate ρ. Defne H ( ) I as the source traffc constrant functon for any class- traffc flow, whch s constraned at the entrance to the networ by H ( I) σ + ρ I. (III-2)

31 8 A leay bucet and the traffc constrant functon for a shaped class- flow are llustrated n Fgure III-2. Fgure III-2. A Leay Bucet n Edge Router and the Traffc Constrant Functon for a Shaped Class- Flow Snce the QoS requrement of traffc (n our case, end-to-end deadlne) s specfed on a class-by-class bass, we can use characterstc parameters σ, ρ, D to represent class- traffc, where D s defned as the end-to-end deadlne requrement of any class pacet. A queue s stable n the sense of bounded queue length and bounded delay for customers f the long-term average rate of the nput traffc s smaller than the capacty [37]. A networ s sad to be stable f all the data pacets experence bounded delays wthn the networ [69]. As long as the utlzaton of all ndvdual lns s less than 00% (ths can be acheved by admsson control), the stablty can be guaranteed [70]. In ths wor, we perform the delay analyss n a stable networ. We use the local worst-case delay suffered by any pacet wth prorty p at Server. d p, to denote

32 9 3. A QoS Archtecture for Dfferentated Servces In ths secton, we propose an archtecture to provde delay-guaranteed servces n wred networs wth the Dfferentated Servces model and statc-prorty schedulers. Ths archtecture conssts of three major modules: Utlzaton Bound Verfcaton: In order to allow for a utlzaton-based admsson control to be used at the admsson tme, safe utlzaton bounds at all servers must be determned durng the system confguraton tme. Usng a utlzaton-based delay computaton method, a delay upper bound s determned for each prorty traffc at each server. Ths module then verfes whether the end-to-end delay bound n each feasble flow route of the networ satsfes the deadlne requrement, as long as the bandwdth usage on the flow route s wthn a pre-defned threshold the safe utlzaton bound. Ths s also the pont when prortes are assgned wthn classes and when bandwdth s assgned to classes and to prortes. We wll dscuss bandwdth and prorty assgnment algorthm later. Utlzaton-Based Admsson Control: Once safe utlzaton levels have been verfed at the system confguraton tme, the admsson control only needs to chec whether the necessary bandwdth s avalable along the flow route of the new flow. Once a new flow arrves, each server along the flow route wll be checed to see whether there s suffcent bandwdth avalable. If ths s satsfed at all servers along the flow route, then the new flow wll be admtted and the avalable bandwdth of all servers along the flow route wll be

33 20 decreased by the requested bandwdth; otherwse, the new flow wll be bloced. Once the flow termnates, the bandwdth requested by the flow wll be released at each server along the flow route. Pacet Forwardng: In a router, pacets are transmtted accordng to ther prortes, whch can be derved from the (possbly extended) class dentfer n the header. Wthn the same prorty, pacets are served n FIFO order. Out of the above three modules, the frst module, utlzaton bound verfcaton, s the most mportant. Utlzaton-based admsson control wors around a utlzaton bound. Whether ths utlzaton bound s safe or not needs to be verfed at the system confguraton tme. We propose to realze ths crtcal functon n three steps: () We frst obtan a general delay formula whch depends on dynamc flow nformaton. () We then remove ths dependence to obtan a utlzaton-based delay formula. () Fnally, we verfy whether or not ths utlzaton bound s safe by applyng the utlzaton-based delay formula. Of the three steps lsted prevously, Step () s relatvely straghtforward once we have the utlzaton-based delay formula. We can apply the delay formula to chec, under the gven utlzaton bound, whether the end-to-end delay bound n each feasble flow route satsfes the deadlne requrement. Accordngly, we wll focus on Step () and Step ().

34 2 4. Utlzaton-Based Delay Analyss In ths secton, we wll present a new utlzaton-based delay computaton formula, whch s ndependent of the dynamc nformaton of flow dstrbuton. 4.a. Man Result Snce statc-prorty schedulng does not provde flow separaton, the local delay at a server depends on detaled nformaton (number and traffc characterstcs) of other flows both at the server under consderaton and at servers upstream. Therefore, all the flows currently establshed n the networ must be nown n order to compute delays. Delay formulas for ths type of system have been derved for a varety of schedulng algorthms [67]. Whle such formulas could be used (albet expensvely) for flow establshment at the admsson tme, they are not applcable for delay computaton durng the system confguraton tme, as they rely on the dynamc nformaton of flow dstrbuton. In the absence of such nformaton, the worst-case delays must be determned assumng a worst-case combnaton of flows. Fortunately, the followng theorem gves an upper bound on ths worst-case delay wthout havng to exhaustvely enumerate all nds of flow dstrbutons. In the followng dscusson, we wll rely heavly on the followng vector notaton: If the symbol a denotes some value specfc to class- traffc, then the notaton a denotes an M -dmensonal vector a, a,, a. We wll 2 M ( ) use the operator " for the nner product and the operator " for the vector norm,.e., a b M a b a M a =, =. = =

35 22 Theorem III-. The worst-case delay d p, suffered by any pacet wth prorty p at Server can be bounded as d p ϖ ( α Z ), (III-3) p, q= q, q, q, α p, where ϖ q, = c c, α α q, q, q < q = p, (III-4) p α p = = α p, q q,, (III-5) c L j= C = C, (III-6) j, Z σ = +, (III-7) ρ q, Y q, Y σ = +, (III-8) q, max d q. s ρ R Sq, s R and S q, s the set of all sub-routes used by class- traffc wth prorty q upstream from Server. The excepton s that d p, = 0 as c = α p, = or ˆ α p = 0., Dervaton of (III-3) wll be dscussed n Secton 5. At ths pont, we would le to mae the followng observatons about Theorem III-: Usually a delay suffered at a server would depend on the state of the server,.e., the number of flows that are admtted and pass through the server. We note that (III-3) s ndependent from ths nd of nformaton. The values of σ, ρ,

36 23 α q,, and c are avalable at the tme when the system s (re-)confgured. Hence, the delay computaton formula s nsenstve to the flow dstrbuton nformaton. We defne σ ρ as the relatve burstness of class- traffc. The relatve burstness of class- traffc s the tme requred for class- traffc to get to burst sze σ at the average rate ρ. The delay formula depends on the relatve burstness and the bandwdth allocaton. As σ ρ or α q, ncreases, d p, ncreases. Fgure III-3. Computaton of Y q, We note that d p, n (III-3) depends on Y q,. By (III-3), Y q, s the maxmum of the worst-case aggregated delays experenced by all class- pacets wth prorty q upstream from Server (see Fgure III-3). Consder any class-

37 24 traffc wth prorty n the networ as shown n Fgure III-3. There are 4 flow routes gong through Server 6 ( 5 8, 2 8, 7 8, and 4 8 ), therefore Y, 6 = max{d, 5 d, d, 4 + +, d, 2 + d, 4, d, 7 + d, 3 + d, 5, d + d + d + d. The value of }, 4, 9, 3, 5 Y q,, n turn, depends on the delays experenced at some servers other than Server. Then we have a crcular dependency. Hence, the delay values depend on each other and must be computed smultaneously. Defne V as the set of all ln servers n the networ. Recall that there are P avalable prortes n total, then we use the ( P V )-dmensonal vector d to denote the upper bounds of the delays suffered by the traffc wth all prortes at all servers: d = ( d, d,, d, d, d,, d,, d, d,, d ). (III-9),, 2, V 2, 2, 2 2, V P, P, 2 P, V Defne the rght hand sde of (III-9) as Φ ( d ), and defne p, Φ ( d ) = ( Φ, ( d),φ, 2( d),,φ, V ( d ), Φ 2, ( d),φ 2, 2( d ),,Φ 2, V ( d ),, Φ ( d ),Φ ( d),,φ ( d )). P, P, 2 P, V (III-0) The queung delay bound vector d can then be determned by teratvely solvng the followng vector equaton: d = Φ ( d ). (III-)

38 25 Once the worst-case delay bound for any pacet wth any prorty at each server s obtaned, the end-to-end worst-case delay for pacets wth prorty p on flow route R can be computed as d = d. e2e p, R R p, The worst-case delay bound suffered by a pacet wth specfc prorty s only affected by the traffc wth equal or hgher prortes. 2 The best-effort traffc has the lowest prorty, and wll not affect the delay suffered by any real-tme traffc, whch has hgher prortes. 4.b. Specal Cases In some specal cases, delay formulas ndependent of networ topology can be derved. Ths s the case, for example, n a networ wth a sngle real-tme class traffc assgned a sngle prorty n a networ of dentcal ln servers and dentcal allocatons of bandwdth to the class on all servers. In ths case, we smplfy the notaton to let σ = σ, ρ = ρ, Y = Y,, C = C, α = α, and L = max{ L }. If we loosen the bound on Y, we wll have an explct delay formula as shown n the followng corollary: Corollary III-. Let d be the maxmum of worst-case delays suffered by all realtme class pacets across all ln servers n the networ. If α <, h + ( 2)( L) (III-2) then 2 Here we gnore blocng due to non-preempton of pacets.

39 26 d σ ( h ) ρ. r (III-3) Therefore, the end-to-end delay e2e d can be bounded by d e2e h σ ( h ) ρ, r (III-4) where L r = α, L α (III-5) and h s the length of the longest flow route n the networ. These delay formulas do not depend on the networ topology except for the length h of the longest flow route. We note that a very smlar result was derved usng a dfferent approach n [36]. The proof of Corollary III- s gven n Appendx C. In a gven networ, f we represent flows between servers as drected lns between servers and there are no loops n the resultng graph, ths networ s called feedforward networ [40]. If a ln server s hops away from the farest source n the resultng graph, we defne t as layer- ln server. In Fgure III-3, there are 5 flow routes, 5 8, 2 8, 7 8, 4 8, and 8 7. The longest flow route s 4 8, thus h = 6. Ths networ s feedforward snce there s no loop n the resultng drected graph. We fnd that Servers 4, 5, 7, and 2 are all at Layer, Servers 8 and are both at Layer 2, Servers 3 and 4 are both at Layer 3, and Servers 5, 6, 8, and 7 are at Layer 4, 5, 6, and 7, respectvely.

40 27 In a feedforward networ, traffc s progressvely pushed forward along the drected lns though the networ wthout loops; therefore, we can get a tghter delay bound that s ndependent of the networ topology as follows: Corollary III-2. Let d ˆ be the maxmum of worst-case delays suffered by any real-tme class pacet at layer- ln servers, then we have the followng delay bound: dˆ r( r ) σ ρ +, (III-6) and the end-to-end delay e2e d can be bounded by d e2e hˆ σ (( r + ) ), (III-7) ρ where r s defned n (7) and ĥ s the number of layers n the feedforward networ ( ĥ h ). Generally, f ĥ s not much greater than h, the delay bound n (9) s much tghter than the bound n (6). In Fgure III-3, h = 6, hˆ = 7, L = 3, f σ = 640 bts, ρ = 32, 000 bps, α = 20%, then ( 2)( = 0. 27, + ) h L hˆ σ h σ (( r + ) ) ρ = 0. 03s and ( ) ρ =. s. The r h proof of Corollary III-2 s gven n Appendx D. 5. Dervng the Delay Formula In ths secton, we dscuss how to derve the delay formula gven n (III-3). We wll start wth a formula for delay computaton that depends on flow dstrbuton, whch we call general delay formula. We wll descrbe how to remove ts dependency on nformaton about flow dstrbuton.

41 28 5.a. General Delay Formula We aggregate flows nto groups. All class- flows wth prorty p gong through Server from Input Ln j form the group G p, j,, and all flows wth prorty p gong through Server from nput ln j form the group G,,. We use F,, ( I ) and p j p j F,, ( I ) to express the traffc constrant functon for group p j G p, j, and group G,, respectvely. The constrant functon F,, ( I ) can be formulated as the summaton p j p j of the constrant functons of ndvdual flows,.e., Fp, j, ( I ) = Fx ( I), x G (III-8) p, j, where Fx ( I ) s the constrant functon for flow x n of group G p, j, s constraned by G p, j,. Further, the aggregate traffc M F ( I ) = mn{ C I, F ( I )}, p, j, j, p, j, = (III-9) where C j, s the capacty of the j th nput ln of Server. In a stable networ, the worst-case delay d p, suffered by any prorty- p pacet at Server can then easly be formulated n terms of the aggregated traffc constrant functons and the servce capacty C of the server accordng to [67]: where d = max( F ( I + d ) C I ), (III-20) p, p, p, C I < I p,

42 29 p L F ( I + d ) = F ( I + d ) + F ( I), p, p, q, j, p, p, j, q= j= j= L (III-2) p L I = mn{ I > 0 : F ( I ) C I}. (III-22) p, q, j, q= j= (III-20) ndcates how long a newly-arrvng pacet wth prorty p can be delayed at Server n a stable networ. It descrbes the maxmum worst-case delay suffered by a pacet due to delay by hgher-prorty pacets that arrved before or durng the tme the pacet s queued, and same-prorty pacets queued before the arrval of the pacet. Fgure III-4. The Arrval Curve, the Servce Curve and the Worst-case Delay. In (III-20), Fp, ( I + d p, ) and C I form an arrval curve and a servce curve, respectvely; and I p, denotes the maxmum busy nterval of the traffc wth prorty no lower than p at Server. In other words, Server never processes pacets wth prorty equal to or hgher than p for more than I p, consecutve tme unts. The arrval

43 30 curve Fp, ( I + d p, ), the servce curve C I, and the worst-case delay n Fgure III-4. 3 To get the value of d p, d p, are llustrated, we frst need to fnd the pont where the worst-case delay n (III-20) s acheved. Ths allows us to gnore the maxmum operator n (III-20). Assume the arrval curve F ( I + d ) s dfferentable almost everywhere for I > 0. p, p, Defne s( I ) as the pece-wse slope (average rate) of the arrval curve F ( I + d ) at p, p, nterval I,.e., d Fp, ( I + d p, ) di s( I) =. As we now, the arrval curve F ( I + d ) s an p, p, ncreasng and concave functon. From Fgure III-4, we now that the worst-case delay s maxmzed at the pont from whch the slope of the aggregate traffc functon becomes smaller than C. Substtutng (III-8) and (III-9) nto (III-20), we observe that the above delay formula depends on flow dstrbuton. Suppose that the group G p, j, has n p, j, flows. In fact, (III-20) depends on n p, j,, the number of flows n G p, j,, and on the traffc constrant functons Fx ( I ) of the ndvdual flows. Ths nd of dependency on the dynamc system status must be removed n order to perform delay computatons at the system confguraton tme. In the followng, we descrbe how we frst elmnate the dependency on the traffc constrant functons. Then we elmnate the dependency on the number of flows on each 3 Here, we slghtly abuse the terms curve and functon.

44 3 nput ln. The result s a delay formula that can be appled wthout nowledge about flow dstrbuton. 5.b. Removng the Dependency on Indvdual Traffc Constrant Functons We now show that the aggregated traffc functon F,, ( I ) can be bounded by replacng the ndvdual traffc constrant functons Fx ( I ) wth a common upper bound, whch s ndependent of nput ln j. The delay at each server can now be formulated wthout relyng on traffc constrant functons of ndvdual flows. The followng theorem n fact states that the delay for each flow on each server can be computed by usng the constrant traffc functons at the entrance to the networ only. Theorem III-2. The aggregated traffc of the group p j G p, j, s constraned by F p, j, ( I ) = n C I, I τ j, p, j, ( η + ρi), I > τ p, j, p, p, j, (III-23) where τ p, j, n p, j, η p, =, C n p, j, ρ j, (III-24) η = σ + ρ Y, (III-25) p, p, and the worst-case delay d p, suffered by any prorty- p pacet at Server can be bounded by

45 32 d p, U V W p, p, p,, (III-26) X p, where p U = n η, (III-27) p, q, q, q= V = C n ρ, p, p q, (III-28) q= X = C n ρ, p, p q, (III-29) q= and W p, n = C j, p, j, p, n η p, j, ρ (III-30) s defned as the pont whch satsfes that s( I) > C as I < W p, and s( I) C as I W p,. In (III-27)-(III-30), n L q, nq, j, j= =. (III-3) The proof of Theorem III-2 s gven n Appendx A. The delay computaton usng (III-26) stll depends on the number of flows on all nput lns. In the next subsecton, we descrbe how to remove ths dependency.

46 33 5.c. Removng the Dependency on the Number of Flows on Each Input Ln As we descrbed earler, admsson control at run tme maes sure that the utlzaton of Server allocated to flows of Class wth prorty q does not exceed α q,. In other words, the followng nequalty always holds: n ρ α C. (III-32) q, q, The number of flows on each nput ln s, therefore, subject to the followng constrant: q, q, C. (III-33) n α ρ To maxmze the rght hand sde of (III-26), we should maxmze U p, and mnmze V p,, X p,, and W p,. Under the constrant of (III-33), these parameters can be bounded for all possble dstrbuton as the followng theorem shows: n q, j, of numbers of actve flows on all nput lns, Theorem III-3. If the worst-case queung delay s experenced by any prorty- p pacet at Server, then, U p, p ( α q, Z q, ) C, (III-34) q= V p, p ( ) C, α q, (III-35) q= X p, p ( α q, ) C, (III-36) q= and

47 34 W p, α Z c α p, p,. p, (III-37) where U p,, V p,, X p,, W p, are defned n (III-27)-(III-30), Z p, s defned n (III-5),.e., Z σ q, = + Yq,, and ρ c s defned n (III-8),.e., c = C j,. C L j= The proof of Theorem III-3 s gven n Appendx B. If we substtute all the bounds n (III-34) nto (III-37), then, after some algebrac manpulaton, we have q= p p ( α ) q= q, ( α q, q, α p, p, ) q= c α p, d p, p Z Z. ( α q, ) (III-38) (III-3) follows after some defntons of parameters n (III-38). Hence, Theorem III- s proved. 6. Prorty Assgnment The delay computaton formulas descrbed n the prevous secton allow assgnment of prortes to flows ndependently of ther classes. Wth approprate prorty assgnment algorthms n place, networ resources can utlzed much more effectvely. Ideally, the prorty assgnment would be done durng the admsson control for a new flow, where resource usage can be taen nto consderaton. Ths would, however, render the admsson control procedure sgnfcantly more expensve. We, therefore, follow the procedure we used earler for delay computaton and perform the prorty assgnment off-lne, that s, durng the system confguraton tme.

48 35 In order to assgn prortes to flows off-lne, we must classfy and aggregate flows usng nformaton (n addton to class membershp) that s avalable before run tme. For a networ wth fxed routers, flows can be classfed at each server by ther class dentfcaton, the source and the destnaton. In the followng, we use class and flow route (n form of source and destnaton address) nformaton to assgn prortes, wth all flows n the same class and wth the same source and destnaton havng the same prorty. Ths approach has two advantages over more dynamc ones. Frst, the prorty assgnment can be done before the admsson tme and, thus, does not burden the admsson control procedure at the tme of flow establshment. Second, the statc-prorty schedulers need no dynamc nformaton at the admsson tme, as the prorty mappng for each pacet s fully defned by ts class dentfcaton and ts source and destnaton dentfcatons. No addtonal felds n pacet headers are needed. 6.a. Outlne of Algorthms Mappng wth ncreasng complexty can be used to assgn prortes to flows: Algorthm One-to-One: All flows n a class are assgned the same prorty. Flows n dfferent classes are mapped nto dfferent prortes. A smple deadlne-based mappng can be used to assgn prortes to classes, wth the earlest deadlne gettng the hghest prorty. The advantage of ths method s ts smplcty. Obvously, ths does not tae nto account more detaled nformaton, such as topology. We use ths mappng as the baselne for comparson wth other approaches.

49 36 Algorthm One-to-Many: Classes may be parttoned nto sub-classes for prorty assgnment purposes, wth flows from a class assgned dfferent prortes. Flows n dfferent classes, however, may not share a prorty. In Subsecton 6.b, we present a verson of ths algorthm. Ths algorthm can recognze the dfferent requrements of flows n a class and assgn them dfferent prortes, hence, mprovng the networ performance. The algorthm s stll relatvely smple, but t may use too many prortes snce t does not allow prortes to be shared by flows from dfferent classes. Algorthm Many-to-Many: The prorty assgnment s not constraned by class membershp, and flows from dfferent classes can be assgned the same prorty. Gven ts generalty, ths mappng can acheve better performance than the prevous two algorthms. 6.b. Detals of Algorthms We wll frst focus on Algorthm One-to-Many. We wll then show that Algorthms One-to-One and Many-to-Many are a specal case and generalzaton of Algorthm Oneto-Many, respectvely; hence, there wll be no need to present the other two algorthms n detal. The purpose of the statc prorty assgnment algorthm s to generate a prorty assgnment table, whch s then used by admsson control and, s loaded nto routers for schedulng purposes. The prorty assgnment table (see Table III- for an example)

50 37 conssts of entres of type class, source, destnaton, prorty. The prorty assgnment then maps from the frst three felds n the entry to the prorty feld. Table III-. An Example of Prorty Assgnment Table Class Source Destnaton Prorty Node 2 Node 3 2 Node 4 Node Node 6 Node Algorthm III- n Fgure III-5 shows our One-to-Many prorty assgnment algorthm. The nput of ths algorthm s the networ server graph, flow routes, characterstc parameters σ, ρ, D for each flow class, and the networ bandwdth α for each class at Server. We need no nowledge about the exact amount of traffc or the number of flows. The value for the α can be pre-determned for dfferent class traffc by some polces. The algorthm wll return the prorty assgnment table and bandwdth allocaton α p, for each class- traffc wth prorty p at Server or return FAILURE as the output.

51 38 Algorthm III- Algorthm One-to-Many Input: Networ server graph, flow routes, characterstc parameters σ, ρ, D Output: for each flow class, assgned networ bandwdth α, =,, M. Prorty assgnment table and bandwdth allocaton α p,, or FAILURE f no such bandwdth allocaton can be found. : ntalze the prorty assgnment table by fllng the proper class ID, source ID, and destnaton ID, and ntalze the prorty felds to undefned ; 2: for from M down to 2.: combne all entres of type, src, dst, p of Class nto subset S and push subset S onto Stac SS ; 3: p 0 (ntal value of prorty) 4: whle Stac SS s not empty 4.: p p + ; 4.2: f p > P (no more prortes avalable) 4.2.: return FAILURE ; 4.3: pop a subset S from Stac SS ; assgn p to the prorty feld of all the entres n S ; use delay formula (III-3) to update the end-to-end delay of flows represented by entres n S ; 4.4: f all per-hop laxtes of entres n S 0 then 4.4.: contnue; 4.5: else f S conssts of a sngle entry 4.5.: return FAILURE ; 4.6: else call ParttonSet( S ) and obtan two subsets: S x, nto Stac SS ; 5: return the current prorty assgnment table and α p,. S y ; push S y and S x Fgure III-5. Algorthm One-to-Many

52 39 The algorthm uses a stac to store subsets of entres of whch the prorty felds are to be assgned. Entres n each subset can potentally be assgned to the same prorty. The subsets are ordered n the stac n accordance to ther real-tme requrements. Gven an entry, src, dst, p n a subset, assume that the flow route from src to dst s R wth length h( R ), then we defne ts per-hop laxty as ( e2e, src, dst, p p, R ) phl = D d, (III-39) h( R) where D s the end-to-end deadlne requrement and d, s the computed worst-case e 2 e p R end-to-end delay along route R. If the per-hop laxty s less than 0, pacets may mss ther deadlne. The subset wth entres that represent flows wth the smallest laxty s at the top of the stac. After ts ntalzaton, the algorthm wors teratvely. At each teraton, the algorthm frst checs whether enough unused prortes are avalable. If not, the program stops and declares FAILURE" (Step ). Otherwse, a subset s popped from the stac. The algorthm then assgns the best (hghest) avalable prorty to the entres n the subset f the deadlnes of the flows represented by those entres can be met. However, f some of the deadlne tests cannot be passed, Procedure ParttonSet (as shown n Algorthm III-2 n Fgure III-6) s called to partton the entres n the subset nto two subsets based on ther per-hop laxty. The dea here s that f we assgn a hgher prorty to entres wth lttle laxty, we may pass the deadlne tests for all entres. Ths s realzed by pushng two new subsets nto the stac n the proper order and by lettng the future teraton deal wth the prorty assgnment. Procedure ParttonSet also assgns

53 40 bandwdth to traffc wth dfferent prortes n the same class. The procedure splts bandwdth accordng to the rato of the cardnalty of the parttoned subset over the one of the orgnal subset. For example, n ths procedure, f S s parttoned nto S x and S y, Sx then α p, wll be splt nto α S p, and S y α S p,. In our experments, we use partton by the half number of entres" (case () n Step 2),.e., S = S = S. x y 2 Algorthm III-2 Procedure ParttonSet(S) Input: subset S Output: subsets S x and S y, and bandwdth re-allocaton : compute the per-hop laxty for each entry n subset S ; 2: sort subset S n the ncreasng order of per-hop laxtes; 3: partton S nto S x and S y (for any entry sx Sx correspondng per-hop laxty as phl( s x ) and phl( s y ) () S = S = S, or () x y 2 α p, and sy S y, defne ther ), such that phl( s ) < phl ( s) phl( s ), where phl( s ) s the mean value of per-hop x laxtes n S, or () phl( s ) < 0 phl( s ) ; x Sx Sx 4: splt α p, nto, and S α p y y α S p,. Fgure III-6. Procedure ParttonSet The program terates untl ether t exhausts all the subsets n the stac, n whch case a successful prorty assgnment has been found and the program returns the assgnment table, or t must declare FAILURE". The latter happens when ether the

54 4 program runs out of prortes, or t cannot meet the real-tme requrements for a sngle entry n a subset. Because the sze of a subset s splt at every teraton step, the worst-case tme complexty of the algorthm s n the order of O( M log V ) n the number of delay computatons. We wll show that ths algorthm does perform reasonably well n spte of ts low tme complexty. Algorthm One-to-One s a specal case of Algorthm One-to-Many presented n Algorthm III-. For Algorthm One-to-One, no subset partton s allowed (otherwse entres n one class wll be assgned to dfferent prortes a volaton of the One-to- One prncple). Thus, f we modfy the code n Algorthm III- so that t returns FAILURE" whenever a falure on a deadlne test s found (Step ), t becomes the code for Algorthm One-to-One. On the other hand, we can generalze Algorthm One-to-Many to become Algorthm Many-to-Many. Recall that Algorthm Many-to-Many allows the prortes to be shared by flows n dfferent classes. Note that sharng a prorty s not necessary unless the prortes have been used up. Followng ths dea, we can modfy the code n Algorthm III- so that t becomes the code for Algorthm Many-to-Many: At Step, when t s dscovered that all the avalable prortes have been used up, do not return FAILURE", but assgn the entres wth the prorty that has just been used. In the case the deadlne test fals, assgn these entres wth a hgher prorty (untl the hghest prorty has been assgned).

55 42 7. Performance Evaluaton In ths secton, we evaluate the performance of the systems that use our new delay analyss technques and prorty assgnment algorthms dscussed n the prevous sectons. Recall that we use a utlzaton-based admsson control n our study: As long as the ln utlzaton along the flow route of a flow does not exceed a gven bound, the end-to-end deadlne of the flow s guaranteed. The value of ths bound, therefore, gves a good ndcaton of how many flows can be admtted by the networ. We defne the maxmum usable utlzaton (MUU) to be the summaton of the bandwdth portons that can be allocated to real-tme traffc n all classes, and use ths metrc to measure the performance of the systems. For a gven networ and a gven prorty assgnment algorthm, the value for the MUU s obtaned by performng a bnary search n conjuncton wth the prorty assgnment algorthm dscussed n Secton 6. Fgure III-7 llustrates the detaled flow chart for MUU Computaton. Gven a networ server graph, flow routes, and characterstc parameters for each class flow (burst, average rate, deadlne), we assume that all lns have the same utlzaton, and bandwdth s allocated for dfferent classes traffc by a gven rato pre-determned by polces. For any nput of ln utlzaton P q= q u = u = α,, we calculate the worstcase delay wth our delay analyss methods. Then, we can verfy whether or not the utlzaton s safe to mae end-to-end delays meet the deadlne requrements. Usng the bnary searchng method, we can obtan the maxmum usable utlzaton (MUU) (The

56 43 condton of stop?" n Fgure III-7 could be u 2 u s less than the gven nfntesmal number or the teraton number s beyond the gven lmt?"). Fgure III-7. MUU Computaton. To llustrate the performance of our algorthms for dfferent settngs, we descrbe two experments. In the frst experment, we use a fxed networ topology and compare the performance of the three algorthms presented n Secton 6 and measure how the algorthms perform for traffc wth varyng burstness. In the second experment, we measure how the three algorthms behave for networs wth dfferent topologes. In the followng, we descrbe the setup for the two experments and dscuss the results.

57 44 7.a. Experment The underlyng networ topology n ths experment s the classcal MCI networ topology as shown n Fgure III-8. All lns n the networ have a capacty of 00 Mbps. All ln servers n the smulated networ use a statc-prorty scheduler wth 8 prortes. Fgure III-8. MCI Networ Topology We assume that there are three classes of traffc: 640 bts, 32, 000 bps, 50 ms,, 280 bts, 64, 000 bps, 00 ms, and, 920 bts, 96, 000 bps, 50 ms, where each trple defnes σ, ρ, and the end-to-end deadlne requrement for the class. 2 3 We assume that α : α : α = : 0. 0 : 0. 20, whch s pre-determned by some polcy before hand governng the operaton of the networ. Any par of nodes n the smulated networs may request a flow n any class. All the traffc wll be routed along shortest paths n terms of the number of hops from source to destnaton. The results of these smulatons are depcted n the frst data row of Table III-2. In the subsequent rows of the table, the same expermental results are depcted for hgher-burstness traffc. In each row, the relatve burstness σ ρ s quadrupled.

58 45 As expected, Table III-2 shows that the MUU ncreases sgnfcantly wth more sophstcated assgnment algorthms. The performance mprovement of algorthms Oneto-Many and Many-to-Many over One-to-One remans constant for traffc wth wdely dfferent relatve burstness. Table III-2. The Comparson of MUU for Dfferent Relatve Burstness σ MUU ρ One-to-One One-to-Many Many-to-Many 0.02 s s s s In Table III-2, we see that the traffc burstness heavly mpacts on the MUU. In fact, for very bursty traffc, the MUU can get qute low. We would le to pont out that, even for very bursty traffc, suffcent amounts of bandwdth can stll be desgnated for real-tme traffc. 7.b. Experment 2 In the second experment, we eep the setup of Experment, except we do not vary the relatve burstness of the traffc. Instead, we vary the networ topology. We randomly generate networ topologes wth GT-ITM [8] usng the Waxman 2 method descrbed there to generate edges. We classfy the generated topologes accordng to

59 46 ther sze n number of nodes, and ther dameter. Performance data are collected based on a sample of 50 networs per number of nodes (overall 550 networs). Fgure III-9. MUU for Randomly Generated Networs Fgure III-9 dsplays the mean values for MUU for small networs (dameter of the networs s less than or equal to 6) and for larger networs. We can mae the followng observatons: We found that Algorthm Many-to-Many can always acheve the hghest MUU among the three algorthms, and Algorthm One-to-Many can acheve hgher mean MUU than Algorthm One-to-One, n the networs wth the same number of nodes. For example, when the number of nodes s 5, for the case of

60 47 Dameter 6, the mean MUU of Algorthm Many-to-Many s 0. 6% hgher than that of Algorthm One-to-Many, and s 26. 7% hgher than that of Algorthm One-to-One. These observatons can be explaned by the fact that Algorthm Many-to-Many has the hghest flexblty n assgnng prortes among the three algorthms. The dameter of the networ has an obvous mpact on the performance of all prorty assgnment algorthms. For example, when the number of nodes s 5, the MUU of Algorthm One-to-Many n the case of Dameter 6, s 7. 4% hgher than that n the case of Dameter 6. Ths s due to the fact that flows n bg networs (n the sense of dameter) usually suffer larger end-to-end delay than n small networs. 8. Dscusson In ths chapter, we use a worst-case delay analyss, whch follows Cruz s wor [66] on worst-case delay analyss. One of our man contrbutons s the scalable delay analyss technque, whch maes offlne delay computaton possble and allows the adaptaton of utlzaton-based admsson control mechansm to be adopted. To acheve ths, we have to remove flow-dstrbuton nformaton from the delay analyss, whch n turn, maes the worse-case delay bound more loose. Generally speang, the looser the worse-case delay bound, the lower the acheved maxmum usable utlzaton. By the expermental data, however, the utlzaton assgned to real-tme traffc s stll very feasble,.e., the delay bound s acceptable. For example, as relatve burstness s s,

61 48 up to 70% utlzaton can be assgned to real-tme traffc by Algorthm Many-to-Many. On the other hand, the resdue bandwdth wll not be wasted, and can therefore be fully utlzed by best-effort traffc (whch s assgned the lowest prorty). Consderng both run-tme delay computaton and offlne delay computaton, we fnd that there s a trade-off between computatonal complexty and maxmum usable utlzaton. Run-tme delay computaton has more run-tme admsson overhead and, subsequently, larger usable utlzaton than offlne delay computaton. In our model, the dstrbuton of flow arrvals s unnown (we only now the characterstc parameters σ, ρ, D for each class flow). An adaptaton method can be adopted to acheve a balance n the trade-off. One possble way s that the utlzaton can be confgured dynamcally. Durng the reconfguraton, all end-to-end delays need to be recomputed and all deadlne requrements must be met. More expensve computaton may be requred but should provde a hgher maxmum usable utlzaton.

62 49 CHAPTER IV STATISTICAL DELAY GUARANTEES IN WIRED NETWORKS WITH THE DIFFERENTIATED SERVICES MODEL In ths chapter, we extend our wor on determnstc delay-guaranteed servces and am at showng how statstcal delay-guaranteed servces can be provded n a Dfferentated Servces framewor.. Overvew Although many real-tme applcatons requre a hard deadlne,.e., a determnstc delay-guaranteed servce, there are stll a consderable number of real-tme applcatons that requre less rgorous tmng constrants, whch are often specfed n statstcal terms. Whle determnstc delay-guaranteed servces provde a very smple model to the applcaton, they tend to heavly overcommt resources because they account for the worst-case scenaro, whch mostly results n sgnfcant portons of networ resources (bandwdth etc.) beng wasted [82]. Statstcal delay-guaranteed servces, on the other hand, sgnfcantly ncrease the effcency of networ usage by allowng ncreased statstcal multplexng of the underlyng networ resources. Ths comes at the expense of pacets occasonally beng dropped or excessvely delayed. In ths chapter, we wll show how such statstcal guarantees can be provded n a Dfferentated Servces framewor. Our approach s based on rate-varance envelopes [44] [46], a smple and general traffc characterzaton. Such envelopes descrbe the varances of the flow rates as a

63 50 functon of the nterval length. The results on deadlne volaton probablty derved n [44] depend on detaled nformaton about the flow dstrbuton. In ths chapter, we wll develop flow-dstrbuton-unaware versons of these results, and develop a method that allows us to analyze delays and determne safe utlzaton bounds wthout dependng on the dynamc status of the flow dstrbuton. Ths wll provde the bass for a scalable admsson control for statstcal delay guarantees n a Dfferentated Servces framewor. 2. Models We consder the same networ model as n the determnstc case. The dfference s that a stochastc traffc model should be ntroduced. We model the traffc arrval for a flow as a stochastc arrval process f = {f(t), t 0}, where random varable f(t) denotes the ncomng traffc amount of the flow passng through a specfc pont durng tme nterval [0,t). We assume that the stochastc process s statonary and ergodc. The traffc arrvals for any two dfferent flows are stochastcally ndependent at the edge of the networ and jtter controllers n the core routers preserve ndependence throughout the networ core. The traffc arrval can be bounded ether determnstcally or statstcally as follows: Defnton IV-. The functon F(I) s called a determnstc traffc constrant functon of the traffc arrval f f ( t + I) f ( t) F( I), (IV-) for any t>0 and I>0. Ths s a smlar dfnton to Defnton III-. Defnton IV-2. The dstrbuton B(I) forms a statstcal traffc envelop of the traffc arrval f, for any t>0 and I>0,

64 5 where X st Y means P{X > Z} P{Y > Z} for any Z. f ( t + I) f ( t) B( I ), (IV-2) Snce f s statonary, we can defne a stochastc arrval traffc rate durng a tme nterval I as st f ( t + I ) f ( t) R( I ) =. I. (IV-3) We wll be usng the rate-varance envelope technque n [46] to provde statstcal delay-guaranteed servces. The rate-varance envelope RV ( I) = var( R( I)) descrbes the varance of the arrval rate for the ncomng flow over an nterval of length I [46]. It s used as a smple way to capture the second-moment propertes of temporally correlated traffc flows. We consder a smple relatonshp between prorty and class that all flows n the same class are assgned the same prorty. We assume that a class- flow s controlled by a leay bucet wth a bursty sze σ and an average rate ρ. In the followng, we use the notaton G, j to denote the group of flows of Class from Input Ln j of a server (for smplcty, we also gnore the server ndex). We also use F, j ( I ), B, j ( I ), and RV, j ( I ) to specfy the determnstc traffc constrant functon, the statstcal traffc envelop, and rate-varance envelope appled to the group of flows G, j respectvely.

65 52 3. Statstcal Delay Guarantees By statstcal delay-guaranteed servces, we mean that an occasonal mssed deadlne or aborted executon s consdered tolerable. A statstcal delay guarantee can be defned as a bound on the probablty of exceedng a deadlne as follows: P{ d > D} ε, (IV-4) where the delay d suffered by a pacet s a random varable, D s the gven deadlne, and ε s the gven volaton probablty, whch s generally small. We wll see that statstcal delay-guaranteed servces may sgnfcantly ncrease the effcency of networ usage by allowng ncreased statstcal multplexng of the underlyng resources. We adopt utlzaton-based admsson control. Durng system (re-)confguraton, a safe utlzaton bound s determned, whch s then used for the utlzaton test at the admsson tme. As long as the bandwdth usage on the flow route of a new flow does not exceed the safe utlzaton bound, the performance guarantees of all flows wll be acheved. The value for ths utlzaton bound depends on the networ topology, the traffc characterstcs, and performance requrements of flows. The challenge of usng any utlzaton-based admsson control method s to verfy whether a utlzaton bound s safe or not at the system confguraton tme. Two crtcal ssues have to be addressed: Statstcal Delay Analyss: The man challenge for statstcal delay analyss s how to clearly descrbe the traffc arrval process. The strong assumptons on the stochastc propertes of traffc streams are nherently dffcult for the networ to enforce or polce. Consequently, f a partcular applcaton does not

66 53 conform to the chosen stochastc model, no guarantees can be made. Moreover, f admtted to the networ, such a stream could adversely affect the performance of other applcatons f t s statstcally multplexed wth them. In ths paper, we wll use an approach prevously developed n [44] to conduct the statstcal delay analyss, whch can cover a wde range of traffc. Utlzaton-Based Statstcal Delay Analyss: The deadlne volaton probablty derved n [44] depends on the nformaton about flow dstrbuton,.e., the number of flows at nput lns and the traffc characterstcs (e.g., the average rate and the burst sze) of flows. In our case, the delay analyss s done at the system confguraton tme, when nformaton about flow dstrbuton s not avalable and only the safe utlzaton bound s nown. Hence, t s necessary to derve a utlzaton-based formula. We wll apply an approach smlar to that used n Chapter III for determnstc delay-guaranteed servce to solve ths. 3.a. Statstcal Delay Analyss In statstcal delay-guaranteed servce, all nput traffc conforms to a set of random processes. Suppose these processes are ndependent. If we now the mean value and the varance of each ndvdual traffc random varable, and the number of flows s large enough, then by the Central Lmt Theorem, we can approxmate the random process of the combned flows. The Central Lmt Theorem states that the summaton of a set of ndependent random varables converges n dstrbuton to a random varable that has a

67 54 Normal Dstrbuton. 4 Actually, usng rate-varance envelopes, the traffc arrval rate of each ndvdual flow s a random varable, and the mean rate and the rate-varance of each ndvdual flow can be determned usng determnstc traffc models. The followng theorem can be found n [44]: Theorem IV-. Consder a statc-prorty scheduler wth L nput lns and ln capacty C such that the traffc wth Class has an random varable delay d and an assocated deadlne D. Suppose that the group of flows G, j has mean rate φ, j and ratevarance envelope RV, ( I). Wth applcaton of a Gaussan approxmaton over j ntervals, the deadlne volaton probablty for a random pacet wth Class s approxmately bounded by L L P{ d > D } max P{ ( B ( I + D ) + B ( I )) ID } q, j, j I < β C q= j= j= 2 ( C( I + D ) µ ( I )) max exp( ), I < β 2π 2 2 σ ( I) (IV-5) where L L (IV-6) µ ( I) = ( I + D ) φ + I φ, q, j, j q= j= j= L L q, j, j q= j= j= (IV-7) σ ( I ) = ( I + D ) RV ( I + D ) + I RV ( I ), and 4 In [44], the author expermentally found the normal dstrbuton approxmaton to be hghly accurate n predctng the performance of a buffered prorty multplexer.

68 55 = mn{ I : F ( I) C I, I > 0}. (IV-8) β q, j q= j= L By ths theorem, the deadlne volaton probablty for any random pacet can be computed approxmately. In the above formula, the fnal queston s how we obtan the values of mean rate and rate-varance envelope. In [44], two methods are presented for obtanng the rate-varance envelope: Adversaral Mode: The traffc arrval process conforms to a bnomal dstrbuton, where the rate-varance envelope s upper bounded. Non-adversaral Mode: The traffc arrval process conforms to a weghted unform dstrbuton, where the rate-varance envelope s approxmated but non-worst-case. Therefore, gven the aggregated arrval traffc constrant functon F, j ( t) of all n, j flows, we can specfy the mean rate and the rate-varance envelope as a functon of n, j etc. By Theorem III-2, the aggregated arrval traffc constrant functon F, ( t) s gven as follows j F, j C I, I τ, ( I ) = n, ( σ + ρ I), I > τ, j j j (IV-9) where τ, j n, jσ =. C n ρ, j (IV-0) Therefore, we have the followng theorem: Theorem IV-2. Gven the same condton as Theorem IV-, the mean rate φ, j s

69 56 φ = n ρ, (IV-), j, j and the rate-varance envelope s upper bounded by Adversaral Mode 2 RV, j ( I) ( n, j ) ρ σ ; (IV-2) I Non-adversaral Mode 2 RV ( ) ( )., I n j 2, ρ σ (IV-3) I j The proof of Theorem IV-2 s gven n Appendx E. At ths pont, the only undetermned s the number of flows on each ln. In the followng subsectons, we descrbe how we elmnate the dependency on the number of flows on each ln. The result s a delay formula that can be appled wthout nowledge of the flow dstrbuton. 3.b. Utlzaton-Based Statstcal Delay Analyss As we descrbed earler, admsson control at run tme maes sure that the ln utlzaton allocated to each class of flows s not exceeded. The total number of Class from all nput lns s therefore subject to the followng constrant: N of flows α =, (IV-4) L N n, j C j= ρ where α s the rato of the ln bandwdth allocated to traffc of Class. Wth ths constrant, by (IV-), (IV-2) and (IV-3), the mean rate and the rate-varance can be upper-bounded. Therefore, the deadlne volaton probablty can be upper-bounded

70 57 wthout relyng on the run-tme nformaton of flow dstrbuton. Ths s shown by the followng theorem: Theorem IV-3. Consder a statc prorty scheduler wth L nput lns and ln capacty C such that the traffc wth Class has an random varable delay d and an assocated deadlne D. Suppose that the group of flows G, j has a statstcal envelope B, j ( I). Then the deadlne volaton probablty for a random pacet of Class s bounded by Adversaral Mode P{ d > D } exp( mn ( I )); 2π 2 ξ I <β (IV-5) Non-adversaral Mode P{ d > D} exp( 6 mn ( I)) 2π ξ, (IV-6) I <β where ξ ( η I + η D ) =, 2 ( I) ζ I + ζ D (IV-7) σ β =, (IV-8) η q αq q= ρq and η = α, p p q= q (IV-9)

71 58 ζ p = σ (IV-20) p 2 q ( αq ). q= ρq In (IV-9) and (IV-20), the value for p s ether or. Ths s the man result of ths paper. We observe that the formula does not depend on the flow dstrbuton. Hence t can be used for utlzaton bound verfcaton at confguraton tme. In the followng, we wll gve the proof. The basc dea s that usng nequalty (IV-4), the nformaton about the flow dstrbuton wll be removed. Proof: Substtutng (IV-), (IV-2) and (IV-3) nto (IV-6) and (IV-7), we have L L (IV-2) C( I + D ) µ ( I ) = I ( C n ρ ) + D ( C n ρ ), q, j q q, j q q= j= q= j= and Adversaral Mode L L I = I nq, j q q + D nq, j q q q= j= q= j= (IV-22) σ ( ) ( ) ρ σ ( ) ρ σ ; Non-adversaral Mode σ ( ) = ( ( ) ρ σ + ( ) ρ σ ). L L I I nq, j q q D nq, j q q 2 q= j= q= j= (IV-23) By (IV-4), we have L nq, j ρq αq C, (IV-24) j= and L 2 2 q ( q, j ) ρq σ q ( αq ), (IV-25) j= ρq n C σ therfore

72 59 Adversaral Mode µ 2 ( C( I + D ) ( I)) ξ 2 ( I ); 2 σ ( I ) 2 (IV-26) Non-adversaral Mode ( C( I + D ) µ ( I)) 2 2 σ ( I ) 2 6 ξ ( I), (IV-27) where ξ ( I) s defned n (IV-7). As an llustratve example, we apply the above theorem n the case of two classes: sngle real-tme class traffc and best effort traffc. Suppose that α = α, σ = σ, ρ = ρ, d = d, D = D, ξ ( I ) = ξ( I), and β = β, for real-tme class traffc. Smplfyng the formula, we can get the followng corollary: Corollary IV-. In the case of a sngle real-tme class, the deadlne volaton probablty for a random real-tme class traffc pacet s bounded by Adversaral Mode P { > D } exp( mn ( )); 2π 2 I <β (IV-28) Non-adversaral Mode P{ d > D} exp( 6 mn ( I)) 2π, I <β (IV-29) where 2 (( α) I + D) ξ ( I ) =, (IV-30) α I 2 σ ρ

73 60 and α σ β =. α ρ (IV-3) Defne the rght hand sde of (IV-28) and (IV-29) as ε and ε 2. We can fnd that D ξ ( I ) reaches ts mnmum at I = I0 = α. By the property of functon ξ ( I ) D f β I0,.e., α σ ρ, then, we fnd α D ε = exp( 2 ), 2 (IV-32) 2π α σ ρ α D ε = exp( 24 ); 2 (IV-33) 2π α σ ρ D f β < I0,.e., α < σ ρ, then α D ε = + (IV-34) 2 exp( ( α ) ), 3 σ 2π 2 α ρ α D ε = + (IV-35) 2 exp( 6 ( α ) ). 3 σ 2π α ρ By the above formulas, we now that as qucly approach zero. α decrease to below D σ, ε and ε 2 wll ρ For the determnstc model, by Theorem 4 n [8], a bandwdth rato formula can be derved as follows: D α =. (IV-36) σ ρ

74 6 Therefore, the bandwdth rato value n the determnstc model s a crtcal pont to the one n statstcal model. Below ths value, the deadlne volaton probablty s qute small and qucly approaches zero. 3.c. Verfcaton of Utlzaton Bound Havng derved the utlzaton-based statstcal delay formula, we can verfy the utlzaton bound, and obtan the MUU, the maxmum of total utlzaton bound for all classes. Under the condton that the probablstc delay guarantee can be met, we can compute the MUU. For a gven deadlne volaton probablty ε and deadlne D along route R, we can splt D nto { D : R}, and the delay guarantee s met when (IV-37) P d > D P d > D ε. 2 { e e } ( { }) R R By Theorem IV-3, for the adversaral mode and the non-adversaral mode, substtutng (IV-5) and (IV-6) nto (IV-37) respectvely, we solve the nequaltes and get the maxmum value of α, for =, 2,, M. The MUU s M α =. 4. Performance Evaluaton In ths secton, we evaluate the performance of the approaches dscussed n the prevous sectons. We wll frst defne the performance metrcs, and then descrbe the system confguraton and present the performance results. We are nterested n two metrcs:

75 62 MUU: The summaton of the bandwdth portons that can be allocated to realtme traffc n all classes. We use ths metrc to measure the performance of the systems. Admsson Probablty: Ths s the probablty that a flow s admtted n a stable system (all pacets have bounded delays). The hgher the admsson probablty, the better the networ resources are beng used. We assume that the traffc belongs to a sngle real-tme class. We smulate voce traffc, wth bursts of 640 bts, an average rate of 32 bt/sec. We assume that the deadlne s 5msec. We assume that requests for flow establshment form a Posson process wth rate λ, and that flow lfetmes are exponentally dstrbuted wth an average of 80 seconds. The real system would support best-effort traffc as well, whch would not affect the results of ths evaluaton, and s therefore omtted n these experments. The MUU can be computed by (IV-5) and (IV-6) usng smple bnary search. The admsson probablty of systems we consder can be analyzed by queung theory and fxed pont method [7]. In the followng, we report performance results and mae observatons. Although we only present a lmted number of cases n ths dssertaton, we fnd that the conclusons we draw here generally hold for many other cases we have evaluated. Data on senstvty of utlzaton to deadlne volaton probablty are gven n Fgure IV- and Table IV-. From Fgure IV- and Table IV-, we have the followng observatons:

76 63 Fgure IV-. Senstvty of MUU to Delay Volaton Probablty Table IV-. Senstvty of MUU to Delay Volaton Probablty ε MUU determnstc adversaral non-adversaral As expected, the value of the MUU for both adversaral and non-adversaral model ncreases as the deadlne volaton probablty ncreases. Ths means that the hgher the deadlne volaton probablty, the hgher MUU we can reach for both adversaral and non-adversaral models. A hgher deadlne volaton

77 64 probablty allows for larger bandwdth allocatons and, therefore, hgher MUU. Both statstcal models can acheve hgher or equal value of the MUU than the determnstc model. Snce the determnstc model does not allow deadlne volatons, more resources need to be reserved, whch decreases MUU. The non-adversaral models acheve much hgher MUU than determnstc ones for any deadlne volaton probablty. Non-adversaral models are much closer to real traffc models, and explot avalable statstcal multplexng gan more effectvely [44]. Fgure IV-2. Admsson Probablty Comparson of Determnstc Model and Statstcal Model

78 65 Data on senstvty of admsson probablty s gven n Fgure IV-2. Note that the curve for determnstc model and the curve for statstcal model (adversaral, ε = 0. 00) overlaps. From ths fgure, we mae the followng observatons: Admsson probablty s senstve to the flow arrval rate λ for all models. Admsson probablty decreases as λ ncreases n all models. The reason s obvous: A large λ value mples a large number of flows n the system. Snce the bandwdth s lmted, some flows are not allowed to enter the networ, therefore, the admsson probablty decreases. Dfferent models have dfferent senstvtes to λ n terms of admsson probablty. The statstcal models always acheve hgher admsson probabltes than the determnstc model. Non-adversaral models always acheve hgher admsson probabltes than adversaral models. Ths s because of the achevable utlzaton. The hgher ths utlzaton s, the hgher the admsson probablty wll be.

79 66 CHAPTER V STATISTICAL DELAY GUARANTEES IN WIRELESS NETWORKS * In ths study, we extend our former wor on utlzaton-based delay-guaranteed servces n wred networs to wreless networs.. Overvew The convenence of wreless communcatons has led to a growng use of wreless networs for both cvlan and msson crtcal applcatons. Many of these nds of applcatons requre delay-guaranteed communcatons. Wreless networs, however, are substantally dfferent from ther wred counterparts, and technologes developed for wred networs cannot be drectly adopted: In most wred networ models for real-tme systems, the communcaton lns are assumed to have a fxed capacty over tme. Ths assumpton may be nvald n wreless (rado or optcal) envronments, where ln capactes can be temporarly degraded due to fadng, attenuaton, and path blocage. For example, n a dgtal cellular rado transmsson envronment, rado wave reflecton, refracton, and scatterng, may cause the transmtted sgnal to reach the recever by more than one path. Ths gves rse to the phenomenon nown as multpath fadng [73]. Also, moble termnals exhbt tme varatons n ther sgnal level due to moton [52]. These characterstcs of wreless lns all result n performance degradaton. In order to *Reprnted wth permsson from Real-Tme Guarantees n Wreless Networs, [72] by S. Wang, R. Nathuj, R. Bettat and W. Zhao, n Resource Management n Wreless Networng, M. Carde, I. Carde and D.-Z. Du (Eds.), Dordrecht, The Netherlands, Sprnger, Copyrght 2006 wth nd permsson of Sprnger Scence and Busness Meda.

80 67 mprove the performance of wreless lns, error control schemes are used. Common error control methods used n wreless communcatons nclude forward error correcton (FEC), automatc repeat request (ARQ) and ther hybrds [74] [75]. The dffculty of provsonng real-tme guarantees n wreless networs stems from the need to explctly consder both the channel transmsson characterstcs and the error control mechansms put n place to allevate the channel errors. 2. Models In order to provde delay-guaranteed servces, one needs both a traffc model, whch s the descrpton of the worload carred on lns, and an approprate descrpton of the underlyng wreless lns. For the traffc model, we adopt the same model used n Chapter IV. We use F( I ) for the determnstc traffc constrant functon of the traffc arrval, and B( I ) as the statstcal traffc envelope of the traffc arrval. We wll also descrbe traffc arrvals usng the rate-varance envelope [44], whch descrbes the varance of the traffc arrval rate durng a tme nterval. To descrbe the underlyng communcaton nfrastructure n terms of channels and protocols, approprate models are needed. In the followng, we wll focus on the wreless ln model and descrbe servce capacty wth the wreless ln model. 2.a. Wreless Ln Model We consder a wreless networ that conssts of a number of wreless lns, each of whch connects two wreless nodes. Ths nd of networ s used wdely n msson-

81 68 crtcal systems rangng from terrestral-based nfrastructures to satellte envronments. Fgure V- shows an example of a wreless networ that falls nto our networ model. Fgure V-. A Ground-space-ground Wreless Communcaton System To guarantee an end-to-end delay, delay characterstcs on each wreless ln need to be analyzed. Thus, n the rest of ths secton, we wll mostly dscuss models related to wreless lns n our networs. Underlyng wreless lns are physcal wreless channels. For the purpose of delay guarantees, a wreless channel model descrbes the channel error statstcs and ts effect on channel capacty. A large number of such models have been descrbed and evaluated n the lterature, based on the Raylegh Fadng Channel, or (by addng a lne-of-sght component) the Rcan Fadng Channel [73]. Typcal channel error statstcs models, such as the bnary symmetrc channel, are modeled as fnte-state Marov models, and can be used to represent tme-varyng Rcan (and other) channels n a varety of settngs [76], [77], [78].

82 69 In addton to the physcal channel, the formulaton of a ln model has to account for error control schemes used at the ln layer. In the followng, we frst consder the framewor of the wreless ln, and then lay out a more detaled descrpton of our Marov ln model. The framewor and descrpton wll largely follow the approach presented by Krunz and Km n [53]. We wll extend ther two-state Marov model to a more general fnte-state Marov model. Fgure V-2. Wreless Ln Framewor We consder a hybrd ARQ/FEC error control scheme (Fgure V-2) and assume a stop-and-wat (SW) scheme for ARQ: The sender transmts a codeword to the recever and wats for an acnowledgement. If a postve acnowledgement (ACK) s receved, the sender transmts the next codeword. If a negatve acnowledgement (NAK) s receved, however, the same codeword s retransmtted. NAK s are trggered at the recever by an error detector, typcally based on some form of a cyclc redundancy chec. The FEC capablty n the hybrd ARQ/FEC mechansm s characterzed by three parameters: the number of bts n a code bloc ( n ), the number of payload bts ( ), and

83 70 the maxmum number of correctable bts n a code bloc ( r ). Note that n counts the payload bts and the extra party bts. Assumng that an FEC code can correct up to r bts and that bt errors n a gven channel state are ndependent, the probablty P ( p ) that a pacet contans a non-correctable error, gven a bt error rate p, s gven by [53] nc n n j n j Pnc ( p) = p ( p). (V-) j= r+ j To account for the FEC overhead, the actual average servce capacty observed at the output of the buffer s C n, where C s the maxmum capacty for the wreless channel. Fgure V-3. Flud Verson of Fnte-State Marov Model of a Wreless Channel Although the statstcal characterstcs of a wreless channel can sgnfcantly vary wth tme, the basc system parameters reman constant over short tme ntervals. Therefore, we can model the channel to be a quas-statonary channel. Ths type of channel can be modeled wth fnte-state Marov chans [50]. We use a flud verson of a fnte-state Marov-Modulated model wth L states ( 0,,, L ) as shown n Fgure V-3 [53]. The bt error rates (BER) durng State are gven by p, where we assume 0 p0 < p < < pl. The duratons n State before beng transtoned to State

84 7 + and are exponentally dstrbuted wth means and λ µ assume that the transtons only happen between adjacent states., respectvely. We It s generally dffcult to get analytcally tractable results that accurately represent the behavor of ARQ and FEC and map the channel model nto the respectve ln model. To solve ths, the authors n [53] assume that the pacet departure s descrbed by a flud process wth an average constant servce capacty that s modulated by the channel state (Fgure V-4). Fgure V-4. Approxmaton Model of a Wreless Ln Each state then gves rse to a statonary ln-layer servce capacty C, whch taes pacet re-transmssons nto account. The total tme needed to successfully delver a pacet, condtoned on the channel state, follows a geometrc dstrbuton. Let N tr denote the number of retransmssons (ncludng the frst transmsson) untl a pacet s successfully receved. For the gven pacet error probablty p of the channel n State, the expected value for N tr s E[ N ] = 5. Thus, C can be wrtten as [53] tr p 5 If we predefne a lmt N on number of retransmssons, l N p l E[ N tr ] = p [53].

85 72 C = C ( Pnc ( p )). (V-2) n As the state transton rates of the channel are not affected by ARQ or FEC, the result s a Marov-modulated model wth L state ( 0,,, L ) wth ln capacty C assocated wth State. 2.b. Stochastc Servce Curve of a Wreless Ln In order to determne the performance guarantees that can be gven by a wreless ln, we must descrbe the amount of servce that the ln can provde. For ths, we mae use of so-called servce curves. In the followng we show how we derve the servce curve from a gven ln model. The stochastc servce curve t S( t) = C( τ ) dτ s defned as the traffc amount that 0 can be served durng tme nterval [0, t] by the wreless channel, where C( τ ) s the capacty at tme τ. Correspondngly, we defne S ( t ) as the traffc amount that can be served durng tme nterval [0, t] wth the system n State at tme t, F ( t, x) and F ( t, x) as the cumulatve probablty dstrbuton of S ( t ) and S( t ), respectvely. We S denote π as the probablty that the ln s n State at any tme when the system s steady, and we then have L F ( t, x) = π F ( t, x). (V-3) S l= 0

86 73 We need to compute F ( t, x) : followng a standard flud approach [79], we proceed by settng up a generatng equaton for F ( t, x) at an ncremental tme t later n terms of the probabltes at tme t. F ( t + t, x) = ( λ t) F ( t, x C t) + ( ( µ + λ ) t) F ( t, x C t) + ( µ t) F ( t, x C t), (V-4) as =,, L 2, and F ( t + t, x) = (( λ ) t) F ( t, x C t) + ( µ t) F ( t, x C t), (V-5) F ( t + t, x) = ( λ t) F ( t, x C t) L L 2 L 2 L 2 + (( µ ) t) F ( t, x C t). L L L (V-6) Both sdes are dvded by t n the above equatons. As t 0, we have F ( t, x) F ( t, x) + C t x = λ F ( t, x) ( λ + µ ) F ( t, x) + µ F ( t, x), + + (V-7) as =, 2,, L 2, and F ( ) ( ) ( ) ( ) 0 t, x F t, x λ F t, x + µ + F + t, x, = + C = t x λ F ( t, x) µ F ( t, x), = L (V-8) The ntal condtons are 0, x 0 F (0, x) =, x > 0 for = 0,,, L. The partal dfferental equatons can be rewrtten n matrx form as follows: F F + C = QF, (V-9) t x where F = ( F0 ( t, x), F ( t, x ),, FL ( t x)),, C = dag( C0, C,, CL ) and

87 74 λ µ 0 λ ( λ + µ ) L L Q = µ µ (V-0) The above lnear frst-order hyperbolc PDEs can be solved numercally, and the F ( t, x) s can be computed. Furthermore, f we defne π = ( π 0, π,, π L ), the π s n (V-3) are gven by π = πq, and π =. (V-) Fgure V-5. The Stochastc Servce Curve for a Wreless Ln

88 75 Fgure V-5 shows smulated data for the dstrbuton of S( t ) for a two-state 6 Marov model, where we specfy C = 2 Mbps, λ = 0, λ = 30, p = 0. We vary the 0 0 BER p and the code parameters ( n,, r). The data llustrates that BER and codng substantally affect the servce dstrbuton. In Secton 3, we wll llustrate how the servce dstrbuton F ( t, x) can be used to perform statstcal delay analyss. S 3. Statstcal Delay Analyss n a Wreless Networ 3.a. Statstcal Delay Analyss In ths subsecton, we wll perform the delay analyss needed n order to provde end-to-end guarantees. Our analyss wll be based on the servce descrpton (servce curves) ntroduced n Subsecton 2.b and the worload descrpton (traffc arrval) dscussed n the begnnng of Secton 2. A statstcal delay guarantee can be defned as a bound on the probablty of exceedng a deadlne,.e., Pr{ d > D} ε, where the delay d suffered by a pacet s a random varable, D s the gven deadlne, and ε s the gven volaton probablty, whch s generally small. We consder networs that use statc-prorty schedulers at the networ nodes, as opposed to prevous wor consderng FIFO buffers [53]. For wred networs wth statc prorty schedulng, we addressed the ssue of how to provde statstcal real-tme guarantees n Chapter IV, based on Knghtly s earler wor n [44]. Defne C as the

89 76 capacty of a ln and G as a group of flows that are served by the ln at prorty. Assume F, j ( I) and B, j ( I) to be the determnstc traffc constrant functon and statstcal traffc envelope, respectvely, for the traffc arrval for the ndvdual flow j G. Then the deadlne volaton probablty Pr{ d D } for a random pacet wth prorty at the output ln can be bounded by Pr{ d D} maxpr{ B ( I + D ) C ( I + D )}, (V-2) t< I where B ( ) s the statstcal traffc envelope of aggregated traffc of same and hgher prortes: (V-3) B ( I + D ) = B ( I + D ) + B ( I), q, j, j q= j Gq j G and I s a bound on the busy nterval and s defned as follows: I = mn{ I > 0 : Fq, j ( I) C I}. (V-4) q= j Gq The above formula cannot be appled drectly for wreless lns however, as ther capactes vary over tme. Fortunately, as the followng observaton shows, t s not dffcult to ntegrate stochastc arrvals and a stochastc servce curve to compute deadlne volaton probabltes: Consder a wreless ln wth a statc-prorty scheduler and maxmum capacty C. Let C( t ) be the avalable capacty for traffc as a functon of tme. Thus C C( t) s the unavalable capacty of ln at tme t. We can equvalently model ths system f we defne a vrtual traffc arrval wth nstantaneous capacty

90 77 C C( t) to a ln wth constant capacty C, by requrng that ths vrtual traffc s gven strctly hghest prorty durng schedulng. Pacet delays for real traffc n the orgnal system are dentcal to delays n ths vrtual-traffc model. Snce the wreless ln servce capacty s modelled as a statonary process, S(t) can be drectly appled to S(I) n the tme nterval doman. In partcular, f the wreless ln has a stochastc servce curve S( I ) and the system s always steady, then the equvalent vrtual traffc on the wreless ln has the statstcal envelope B ( I) = C I S( I ). Ths gves rase to the followng theorem: Theorem V-. Consder a wreless ln wth a statc-prorty scheduler and stochastc servce curve S( I ). Assume B, j ( I) s the statstcal traffc envelope for the traffc arrval of the ndvdual flow j G. Then, the deadlne volaton probablty for a random pacet wth prorty can be bounded by Pr{ d D } maxpr{ B ( I + D ) + B ( I + D ) C ( I + D )}, (V-5) t> 0 where B ( I) = C I S( I ), and B ( t + d ) s defned n (V-3). Here the maxmum busy nterval s canceled out due to the possbly unconstraned stochastc servce curve. The vrtual traffc may produce an nfnte-length maxmum busy nterval. So the deadlne volaton probablty may appear to be loose. In our smulaton data, we fnd that the maxmum value wll be acheved for relatvely small values of t, therefore, the bound s tght.

91 78 We mae the followng observatons about Theorem V-: Frst, B ( I + D ) and B ( I + D ) are ndependent. Gven ther dstrbuton functons, the dstrbuton functon of the summaton B ( I + D ) + B ( I + D ) can be obtaned by ther drect convoluton. Second, the dstrbuton of B ( I + D ) can be drectly obtaned from S( I ), whch we n turn derved n Subsecton 2.b. Note that (V-5) holds for any S( I ), no matter what specfc wreless ln model s chosen. The man challenge for statstcal delay analyss s how to obtan the dstrbuton functon of B ( I + D ),.e., how to clearly descrbe the traffc arrval envelope. It s nherently very dffcult for the networ to enforce or polce the stochastc propertes of traffc streams. Consequently, f a partcular applcaton does not conform to the chosen stochastc model, no guarantees can be made. Moreover, f admtted to the networ, such a non-conformng stream could adversely affect the performance of other applcatons f t s statstcally multplexed wth them. Therefore, we must fnd a means to descrbe the non-conformng traffc so that we can perform delay analyss. We wll use the approach prevously developed n Chapter IV for the statstcal delay analyss. We start by representng the nput traffc flows as a set of random processes. Traffc polcng ensures that these processes are ndependent. If we now the mean value and the varance of each ndvdual traffc random varable, and the number of flows s large enough, then by the Central Lmt Theorem we can approxmate the random process of the set of all flows combned. The Central Lmt Theorem states that

92 79 the summaton of a set of ndependent random varables converges n dstrbuton to a random varable that has a Normal Dstrbuton. We assume that a flow of prorty s controlled by a leay bucet wth burst sze σ and average rate ρ at each router. Assume that Flow j n the group of flows G has mean rate φ, j and rate-varance envelope RV, j ( I). Wth applcaton of a Gaussan approxmaton over ntervals, B ( I + D ) n (V-3) can be approxmated by a normal dstrbuton N( φ ( I ), RV ( I)) [44], where (V-6) φ ( I ) = ( I + D ) φ + I φ, q, j, j q= j Gq j G 2 2 q, j, j q= j Gq j G (V-7) RV ( I ) = ( I + D ) RV ( I + D ) + I RV ( I). n Gven the determnstc traffc arrval envelope F, j ( I ) = σ + ρi, for any flow j G, we can easly obtan mean rate φ, j for each ndvdual flow, and an adversaral mode s chosen for obtanng the rate-varance envelope RV, j ( I) [44]. 6 We obtan the mean rate and the rate-varance envelope as follows: φ ρ, j =, (V-8) ρσ RV, j ( I). (V-9) I In summary, ths leads to the followng lemma: 6 In adversaral mode, the traffc arrval process conforms to a bnomal dstrbuton, where the ratevarance envelope s upper bounded.

93 80 Lemma V-. Defne nq = Gq, q =, 2,,. Wth applcaton of a Gaussan approxmaton over ntervals, B ( I + D ) can be bounded by a normal dstrbuton N( φ ( I ), RV ( I)),.e., where x φ ( I) Pr{ B ( I + D ) < x} Φ ( ), (V-20) RV ( I ) φ ( I) = ( I + D ) n ρ + In ρ, (V-2) q q q= RV ( I ) ( I + D ) n ρ σ + In ρ σ, (V-22) q q q q= and 2 a x Φ ( a) = exp( ) dx 2π., (V-23) 2 The dstrbuton functon of the summaton B ( I + D ) + B ( I + D ) can be obtaned by convoluton. Defne ths dstrbuton functon as F ( I + D, x). Then, the deadlne volaton probablty can be upper-bounded wth utlzaton as shown n the followng theorem: Theorem V-2. Consder a wreless ln wth a statc-prorty scheduler and stochastc servce curve S( t ). Assume the same traffc envelope as n Theorem V-. The deadlne volaton probablty for a random pacet wth prorty s bounded by B Pr{ d D } mn F ( I + D, C ( I + D )). (V-24) B t> 0

94 8 We have now derved the statstcal delay formula for a sngle wreless ln. Based on ths result, we obtan the end-to-end deadlne volaton probablty along each flow route as follows: Gven the deadlne volaton probablty ε and the end-to-end deadlne D along route R, we can partton when [45] D nto { D : R}, and the delay guarantee s met (V-25) e2e Pr{ } ( Pr{ }) R R d > D d > D ε. Ths bound on the end-to-end real-tme guarantee reles on the nformaton of flow dstrbuton. In next subsecton, we wll develop utlzaton-based statstcal delay analyss approach, whch s ndependent of such run-tme nformaton. 3.b. Utlzaton-Based Statstcal Delay Analyss As opposed to run-tme calculatons per flow, utlzaton-based admsson control requres off-lne delay computatons per traffc prorty to obtan what we call a safe utlzaton bound. Snce flow dstrbuton nformaton s unavalable for off-lne calculatons, we must obtan a utlzaton-based statstcal delay formula, whch can be used to compute the safe utlzaton bound. Durng run-tme, utlzaton-based admsson control checs whether the ln utlzaton allocated to each traffc prorty (ths allocated utlzaton should not exceed the safe utlzaton bound) s not exceeded. The total number n of flows of Class on a ln s therefore subject to the followng constrant: n α C, (V-26) ρ

95 82 where α s the rato of the ln capacty allocated to traffc of prorty, and ρ s the average rate of prorty traffc. Wth ths constrant, the mean rate and the rate-varance can be upper-bounded as follows: φ ( I) = ( I + D ) α C + Iα C, (V-27) q q= RV ( I ) = ( I + D ) α σ C + Iα σ C. (V-28) q q q= Correspondngly, Lemma V-, Theorem V- and Equaton (V-25) can be reformulated usng the utlzaton-based defnton for the new φ ( I) and RV ( t ) gven above. 4. Performance Evaluaton In ths secton, we evaluate the performance of the utlzaton-based delay guarantee technque. The smulated wreless networ could be representatve of a ground-space-ground wreless communcaton system (Fgure V-). We allow any par of nodes n the networ to establsh a real-tme prorty connecton (voce n ths case). All traffc s routed along the shortest-path route. In our wreless ln model, we assume that all lns n the networ have a maxmum capacty of 2 Mbps. Lns follow a twostate Marov model as prevously defned. In the smulaton, we specfy the ln parameters as follows: λ 6 0 = 0, λ = 30, p0 = 0, and we vary the bt error rate (BER) p for State (BAD state). We also adopt fve dfferent Bose-Chaudhur-Hocquenghem (BCH) [80] codng schemes for FEC. We assume that requests for real-tme flow

96 83 establshment form a Posson process, and that flow lfetmes are exponentally dstrbuted wth an average of 80 seconds. 7 In obtanng our results, we are nterested n two metrcs: ) MUU The maxmum usable utlzaton s the maxmum ln utlzaton that can be safely allocated to real-tme traffc; ) Admsson Probablty Ths s the probablty that a flow can be admtted wthout volatng delay guarantees. Both metrcs reflect on the effcent use of networ resources. We fnd that the conclusons we draw based on the cases descrbed here generally hold for other cases we have evaluated. 4.a. MUU Comparson The underlyng networ topology n the MUU experment s the networ shown n Fgure V-, where nodes communcate through a space-based reach-bac networ. We vary the ln characterstcs by varyng the bt error rate (BER) p for State (BAD state). We also consder fve dfferent BCH codng schemes wth ncreasng level of correctablty (.e., dfferent ( n,, r) [53]. In our traffc model, we assume that all traffc belongs to a sngle real-tme prorty. We smulate voce traffc, wth bursts σ = 640 bts, and average rate ρ = bps. We assume that the end-to-end deadlne s 5 ms. The end-to-end deadlne volaton probablty s ether or 0. 7 A real system would support best-effort traffc as well. Snce ths traffc would not affect the results of ths evaluaton, we omt t from our experments.

97 84 6 (a) ε = 0 (b) ε = 0 Fgure V-6. MUU Comparson 3 The MUU can be computed by Equaton (V-25) that we obtaned n the prevous secton usng smple bnary search. The results of our MUU experments are shown n Fgure V-6. The followng observatons can be made from these results: ). Senstvty of MUU to channel codng: Our results show the performance tradeoff of usng varous channel codes. Codes that provde greater error correcton decrease the amount of actual traffc ncluded n pacets. For low error rates, ths capablty s not worthwhle, as shown n Fgure V-6, snce error correcton s rarely useful, and n fact decreases the overall achevable utlzaton. 2). Senstvty of MUU to BER: As the BAD-state BER p ncreases from to 0. 0, the MUU decreases for all cases. These results support the ntuton that, as the error probablty of the networ ncreases, the amount of

98 85 capacty that can be supported for real-tme traffc should decrease. 3). Senstvty of MUU to deadlne volaton probablty: As expected, the MUU ncreases when the deadlne volaton probablty s decreased. In other words, allowng hgher loss probabltes creates addtonal avalable utlzaton for real-tme traffc. 4.b. Admsson Probablty Comparson In addton to the topology (Fgure V-) used n the last secton (called Net n ths context), we use a random networ topology (generated wth GT-ITM [8] usng the Waxman 2 method) wth the same number of total nodes, whch we refer to as Net 2. We use ths randomly generated topology n order to support the fact that our results are not dependent upon a partcular topology. We fx bt error rate (BER) p for State (BAD state) p = and choose BCH codng scheme wth parameters 6 ( n = 442, = 424, r = 2). The end-to-end deadlne volaton probablty s 0. We smulate the case when there s only a sngle real-tme prorty n the networ wth same parameters σ, ρ, D as the frst smulaton. We also smulate the case when there are two real-tme prortes n the networ to see how multple prortes affect the admsson probablty. In ths case, we choose addtonal hgher-prorty traffc as follows: σ = 280 bts, ρ = bps, D = s. The capacty s allocaton wth rato α : α = : 3. hgh low

99 86 (a) Sngle prorty (b) two prortes Fgure V-7. Admsson Probablty Comparson We measure the admsson probablty n the system under Delay-Based Admsson Control (DBAC) 8 and n our system under Utlzaton-Based Admsson Control (UBAC). As expected, n both sngle-prorty and two-prorty cases, the admsson probablty decreases wth ncreasng flow arrval rate. The substantal concluson we draw from these results s wth regard to the relatonshp between UBAC and DBAC: It s clear from Fgure V-7(a) that n the sngle-prorty case, UBAC s n fact able to provde the same effectveness wth regard to networ resource allocaton as DBAC. Ths result s sgnfcant because t means that the effectveness of DBAC can be 8 The delay computaton under DBAC wll rely on the delay analyss n Secton 3, not the one n Subsecton 3.b.

100 87 provded wth low run-tme overhead by usng UBAC. Thus, costly run-tme delay computatons can be removed wthout sacrfcng performance. From Fgure V-7(b), we fnd that DBAC obtans more gans n terms of admsson probablty than UBAC when there are multple prortes. Ths can be attrbuted to the fact that the pre-allocaton of capacty n UBAC dsables the capacty sharng between the traffc wth dfferent prortes, so that the overall achevable utlzaton s decreased. Therefore, DBAC acheves much hgher admsson probabltes than UBAC n the multple-prorty case.

101 88 CHAPTER VI DELAY GUARANTEES IN COMPONENT-BASED SYSTEMS In ths chapter, we focus our study on provdng delay-guaranteed servces n component-based systems, whch now serve as an mportant platform for developng a new generaton of computer software. We develop a utlzaton-based delay guarantee technque to provde effcent and effectve delay-guaranteed servces whle mantanng the mportant feature of components reusablty.. Overvew Reusablty n component technology s a ey factor that contrbutes to ts great success [68]. Wth component technology, software systems are bult by assemblng components that have already been developed earler, wth ntegraton n mnd. Wth the software component framewor, the non-functonal codes, such as securty and consstency parts, are automatcally generated, and system developers can focus on core busness logc parts, wthout wastng tme on common non-functonal parts. The reuse of components and developers' focusng on core parts lead to a shortenng of software development cycles and savngs n software development costs. Although component-based models deal successfully wth functonal attrbutes, they provde lttle support for delay-guaranteed servces. Most real-tme extensons use tradtonal approaches to provde delay-guaranteed servces and lac of consderaton for reusablty of components n terms of both functonal and delay-guaranteed servces.

102 89 In the followng, we wll develop a utlzaton-based delay guarantee technque to enable the true reusablty of components n terms of both functonal and delayguaranteed servces. 2. Component-Based Resource Overlays In component software, a component has three basc characterstc propertes [68]: () Isolaton A component should be deployable ndependently. The component s an atomc unt of deployment, as t wll never be deployed partally. () Composablty A component should be composable wth other components. It needs to be a self-contaned functon unt wth well-specfed nterfaces. A thrd party can access the component through ts contractually specfed nterfaces. () Opaqueness Nether the envronment, other components, nor a thrd party have access to ts mplementaton or other nternal detals. Fgure VI- llustrates a component archtecture. Fgure VI-. A Component Archtecture We extend the component archtecture descrbed above to buld a real-tme component archtecture. For ths, we augment the largely functonal nterfaces and context dependences wth contractually specfed temporal nterfaces and explct tme-

103 90 related context dependences. Any such augmentaton of the component nterface archtecture should contnue to satsfy the three basc component propertes descrbed earler: () The real-tme nterface archtecture should not nterfere wth the solaton property. Each component should be separated from other components n provdng realtme servce guarantees. For example, uncontrolled resource conflcts among dfferent components should be avoded. () Composablty should be mantaned. The real-tme servce nterface should represent the real-tme servce provded by the component. Applcatons can access the servce through the real-tme servce nterface. () The realtme nterface archtecture should mantan opaqueness. Applcatons do not need to now how real-tme servces are provded by each component. The nterfaces should not nclude nformaton relatng to the underlyng component mplementaton, such as methods worst-case executon tme, or any schedulng algorthm used n method executon n components, for example. We use a very smple contractual nterface, whch formulates the real-tme servce provded n terms of the servce guarantee (descrbed n the form of a deadlne) gven a worst-case arrval (descrbed n the form of an arrval constrant functon). We frst ntroduce the arrval constrant functon. Defnton VI-. If the maxmum number of method nvocatons durng any tme nterval of length I s bounded by A( I ), we defne A as an arrval constrant functon of ths sequence of method nvocatons.

104 9 For example, a bursty arrval can be descrbed usng a burst sze σ and average arrval rate ρ as 9 A( I ) = σ + ρ I. The arrval constrant functon A and the deadlne D gve a contractual defnton of the real-tme servce provded by the component: If the sequence of nvocatons of methods n Component e has an arrval constrant functon below A, t s guaranteed that any nvocaton n ths sequence wll meet ts deadlne D at Component e. Ths nterface specfcaton clearly meets the solaton, composablty, and opaqueness requrements for real-tme components. However, ths specfcaton has two shortcomngs n practce: Frst, a component wll only provde a sngle real-tme servce to applcatons. Often, dfferent applcatons may requre dfferent levels of tmng requrement. Second, each component usually exposes a number of methods and dfferent methods could be nvoed at dfferent tmes, whch have dfferent resource consumptons. In order to allow components to provde more flexble servce and better utlze the underlyng resource usage, we extend the above specfcaton by ntroducng dfferent servce levels and tang nto consderaton dfferent methods exposed by components. We defne class of servce as the servce level for each component. Assumng there are M classes of servce, we defne class- real-tme servce for Component e as Θ e,, Ae,, De,, where Θ e, s a group of methods exposed by Component e, A e, s an arrval constrant functon of nvocatons of methods n Θ e,, and D e, s a deadlne for any nvocaton of methods n Θ e,. In other words, If the sequence of nvocatons of methods n Θ e, has an arrval constrant 9 Here we use a bound nstead of usng operator

105 92 functon below A e,, Component e guarantees a worst-case delay bounded by any method nvocaton n ths sequence. D e, for Table VI-. A Real-Tme Servce Interface Specfcaton Class Θ A ( I) e, e, D e, θ, θ2 + 2 I sec 2 θ, θ I sec 3 θ, θ2, θ3, θ I sec 4 θ3, θ4 + 4 I sec For example, assume that Component e exposes four methods θ,, θ4 and defnes four classes, an real-tme servce nterface specfcaton s llustrated n Table VI-. In ths example, θ and θ 2 may represent man methods exposed by the component, whle θ 3 and θ 4 are used for management and audtng of the component. Clents that use Class- 2 servce can access the component at a hgher rate than ones that use Class- servce, but receve less strngent tmng guarantees ( sec nstead of sec). Clents that use Class-3 servce have a dfferent vew of the component than those that use Class- or Class- 2 servce (they may need to access all methods of the component) and have dfferent real-tme requrements. In ths example, test sutes may need to access all methods exposed by a component, and may need to do ths n a tmely fashon. Audtng and management applcatons, on the other hand, may need to access only a small subset of methods, and have only loose tme requrements. Note that Class-

106 93 and Class- 2 servces expose the same set of methods; that s, Θ e, and Θ e, 2 are dentcal. The functonal aspect of the servce nterfaces s therefore dentcal, whle ther dfference les entrely n the real-tme specfcaton, more specfcally n the expected arrval and tmng guarantees. Ths separaton of functonal from tmng specfcaton allows for a confguraton of real-tme components nto resource overlays, whch n turn allow for the solaton of applcatons from the detals of the low-level specfcaton and management of the underlyng computatonal resources. Fgure VI-2. A Component-Based Resource Overlay. Fgure VI-2 shows an example of a component-based resource overlay. Ths fgure llustrates how resource overlays separate component development from applcaton development and releve the applcaton desgner of the underlyng resource management. In fact, applcaton desgners mplement and deploy ther systems on the resource overlay, whch provdes well-defned functonal abstractons and tmng behavors. The real-tme servce nterface specfcaton n real-tme components does not

107 94 provde access to ther underlyng mplementaton. Any change n the mplementaton of components wll therefore not affect the applcaton desgn or behavor. It s up to the component provders to map the nodes of the component-based resource overlay to the underlyng avalable resources. Ths s typcally done ndependently of the partcular applcaton. In the followng, we descrbe n Secton 3 how applcaton desgners mae use of resource overlays to buld real-tme applcatons. Gven a set of real-tme component servces, t s the component provders responsblty to mplement the component functonalty defned by ts set of nterfaces. Component provders must ensure that both functonal and tmng propertes are satsfed for each mplemented real-tme component. We wll address ths ssue n Sesson Buldng Real-Tme Applcatons Applcaton desgners develop and deploy applcatons on the resource overlay provded by the set of avalable real-tme components, whch n turn expose ther realtme servce nterfaces Θ e,, Ae,, De, s to applcatons and applcaton desgners. To buld real-tme applcatons, we frst ntroduce the applcaton model. 3.a. Applcaton Model We consder hybrd open/closed systems, where applcatons nclude clents and applcaton servers each of whch hosts one or more components. Each nvocaton from a clent trggers executon of one or more methods, ether on a sngle component, or on several components. These components, n turn, can be located on one or across several

108 95 applcaton servers. A sequence of clent nvocatons resultng n such a sequence of method executons s called a tas. In a component-based system, an nvocaton from a clent can pass through several components and we assume all nvocatons n the same tas to execute on the same components n the same order. Tass n applcatons can be modeled as a drected acyclc graph whch we call tas graph. Each node s a component and each tas forms a tas route. There could be multple tass along each tas route. 3.b. Servce Guarantees wth Admsson Control Any tas s assocated wth an arrval descrptor (n form of the source arrval constrant functon) and a tmng requrement (n form of the end-to-end deadlne). To provde real-tme servce guarantees, applcaton desgners have to ensure that every nvocaton n a tas meets the end-to-end deadlne requrement. Moreover, the applcaton desgner must ensure that the real-tme servce specfed n each real-tme component wll not be volated. Snce the maxmum arrval s part of the real-tme servce of the component, and the clent populaton s not under the control of the applcaton servers, an admsson control mechansm has to be n place. For a new Tas T, admsson control has to address the two parts of the real-tme specfcaton of the components (tmng guarantee and arrval descrptor) to provde realtme guarantees. Frst, what s the worst-case end-to-end delay experenced by any nvocaton n Tas T? In Tas T, all of ts nvocatons have an end-to-end deadlne requrement components T D. Assume each nvocaton n Tas T wll go through a sequence of e h of Class, h 2 H h =,,,, and any method that Tas T wll call n

109 96 Component e s n Θ e,. Recall that the worst-case delay provded by Component e of Class s D e,. To guarantee the end-to-end deadlne for any nvocaton n Tas T, admsson control has to ensure that the end-to-end delay T d suffered by any clent nvocaton n Tas T should be bounded as: T T d De, D eh, D H = + +. (VI-) Second, what s the consumed resource by Tas T? Provded that a tas has an n arrval constrant functon A ( I ) before arrvng at a component, the arrval constrant functon wll become out n A ( I) = A ( I + d) just after a worst-case delay d at ths component. We defne T A as the source arrval constrant functon of Tas T (before callng the frst component). Then the arrval constrant functon of T at Component e h of Class h, h =, 2,, H, s T T Ae ( ) ( ) h, I = A I + D h e, + + D eh, h. (VI-2) If T A s defned wth a burst sze T σ and an average arrval rate T ρ as A T ( I) = σ T + ρ T I, then the consumed resource by Tas T at Component e of Class s A ( I) = ( σ + ρ D + + ρ D ) + ρ I. (VI-3) T T T T T eh, h e, eh, h Admsson control has to ensure that the real-tme servce specfed at each real-tme component along the tas route of Tas T wll not be volated,.e., T Ae ( ) ( ) h, I A h eh, I, (VI-4) h T Se h, h

110 97 where S, s the set of exstng tass that use class- h servce of Component e h. eh h In summary, admsson control ensures that suffcent overlay resources are avalable to meet the requrements of both the new and the exstng tass whenever a new tas has been admtted. In other words, both (VI-) and (VI-4) should reman satsfed for both new and exstng tass f a new tas s admtted. Ths admsson control mechansm s smple to mplement effcently. It s utlzaton-based admsson control even though the resource s the vrtual one real-tme components. 4. Buldng Real-Tme Components Gven a set of real-tme component servces, t s the component provders responsblty to mplement the component functonalty so as to satsfy the gven set of nterfaces Θ e, Ae, De s.,,, 4.a. Servce Implementaton Servce mplementaton ssues can be dvded nto two categores: () Intercomponent Recall that each real-tme component should be solated from others n terms of the underlyng resource usage to meet the solaton requrement. The underlyng resource could be CPU, memory, ln bandwdth, or others (here we focus on CPU). We use a guaranteed-rate scheduler to ensure temporal solaton of components on the same processor, and we allocate the requred amount of the processor utlzaton to each component. A total bandwdth server (TBS) [] can acheve ths; () Intra-component Each component wll provde multple classes of servce. To dfferentate among classes

111 98 of servce wthn the same component, we use a smple statc-prorty scheduler, and use the class-d as prorty level. The major remanng mplementaton ssue s how to determne the processor utlzaton that needs to be assgned to each component. We wll address ths n the followng. Snce the component mplementaton s bound to the underlyng hardware platform, the executon of the component s methods can be characterzed at componentmplementaton tme. In partcular, each exposed method can be assocated wth ts worst-case executon tme (WCET) on the specfc platform. We am to compute the worst-case delay suffered by executon of any method n the maxmum WCET of all methods n Θ e,. For ths, we denote C e, as Θ e,. In conjuncton wth the arrval constrant functon defned as part of the real-tme servce nterface specfcaton, the WCET gves rse to the worload characterzaton for the method set Θ e, on the underlyng mplementaton platform. Defnton VI-2. If the cumulatve executon tme of a sequence of method executons s bounded by F( I ) durng any tme nterval wth length I, we defne F as a worload constrant functon of ths sequence of method executons. It s smlar to the defnton of traffc constrant functon defned n Defnton III-. Gven the nvocaton arrval constrant functon A ( I) = σ + ρ I for e, e, e, Component e of Class and the assocated C e, of Θ e,, the worload constrant functon for Component e of Class can be expressed as F ( I) = C A ( I). If we e, e, e,

112 99 assume a constant processor utlzaton α e to be assgned to real-tme Component e, we can use a tme demand/supply argument to derve the worst-case delay any method nvocaton n Component e of Class as follows: d e, suffered by d max{ ( ( ) ( )) } e, F e, I + d F I I I I p e, + e,, < (VI-5) e, α e p< where I e, s the maxmum busy nterval, satsfyng Ie, = mn{ I : Fe p ( I) I} p,. (VI-6) α e If Ae, ( I) can be defned usng burst sze σ e, and average arrval rate ρ e,, we can explctly express d e, as the followng nequalty d C σ. p e, p e, p e, De, αe C p e, pρ < e, p (VI-7) Therefore, n order to satsfy all classes of servce, the allocated processor utlzaton for components has to be set at least to α = max{ C σ + C ρ }. (VI-8) e e, p e, p e p e p M p,, < De, p When allocatng processor utlzaton to components, component developers should ensure that the overall processor utlzaton does not exceed the safe utlzaton level allowed by the specfc platform.

113 00 4.b. Servce Optmzaton The functonal specfcatons Θ e, of a real-tme component can be defned only n the component desgn, and the tmng requrement D e, s typcally defned early on as well. The arrval descrptor A e,, on the other hand, depends on the expected arrval, and requres some understandng of the deployment envronment n order to allow effcent resource utlzatons. In the followng, we descrbe how component provders can optmally specfy arrval descrptor based on the applcaton arrval pattern. Assume that the tas arrval along Tas Route r s a Posson process wth average rate λ r, the runnng duraton of any tas along Tas Route r s exponentally dstrbuted wth average duraton, and any tas along Tas Route r s assocated wth real-tme µ r source servce specfcaton A ( I ), D. The average number of tass along Tas Route r r r s gven as λr ν r =. Defne rejecton probablty µ r r b as the probablty that a tas request for Tas Route r s rejected. Then the overall admsson probablty AP for applcatons n the system can be expressed as ν r ( br ) r R AP =. ν r R r (VI-9) The objectve s to fnd the optmal real-tme servce specfcaton to maxmze the overall admsson probablty. Then we have the optmzaton problem as shown n Fgure VI-3. It can be summarzed as follows:

114 0 Input: Tas graph G and the set of tas routes R ; Θ e, and D e, for Output: =,, M ; Ar ( I ), Dr, λ r and for r R. µ r A e, s. Objectve: Maxmze the overall tas admsson probablty AP. Constrants: The overall utlzaton does not exceed the safe utlzaton level for each applcaton server. Fgure VI-3. Servce Optmzaton maxmze AP (VI-0) subject to α α γ e γ e γ, Γ (VI-) where e s located n Processor γ belongng to processor set Γ and α γ s the safe utlzaton bound for Processor γ. How to solve ths optmzaton problem s addressed n Appendx F. 4.c. Servce Adaptaton Note that n a component-based system, components compete a lmted amount of underlyng resources, and the solaton property of components dsables the dynamc sharng of the underlyng resource among components, whch results n an overall resource underutlzaton. However, due to varatons n the applcaton envronment, components may not receve constant rate servce request from the applcaton at each servce level. Based on these observatons, t s necessary to use servce adaptaton mechansms to acheve better resource utlzaton.

115 02 The proposed adaptaton scheme, therefore, allows for a load balancng across the component servces on the applcaton server. We defne the resource resdue A ɶ e,,.e., the amount of currently unused resource as Aɶ ( ) ( ) ˆ e, I = Ae, I Ae, ( I ), (VI-2) T where Aˆ ( I) = Ae, ( I) s the amount resource currently used by the exstng e, T Se, tass. For any admsson request by a tas T for component servce e,, we have to borrow resources from some other component servce whenever the resources requested T by T exceeds the amount of resources currently used,.e., Aɶ e, < A e,. We defne A e, as the optmal servce specfcaton obtaned by servce optmzaton algorthm and defne a threshold s no e, for any real-tme component servce e,. If ts current assgned resource e, less than ts orgnal optmal assgnment, t could be one of canddates whose resources can be borrowed. The detals of ths algorthm are shown n Algorthm VI- n Fgure VI-4. In Step 2, the algorthm dentfes the component servce wth the maxmum resource resdue, whch can be potentally borrowed by other components n the same applcaton server. Dynamcally adaptng real-tme servces of components can mprove the statstcal multplexng gan of the underlyng resources. We wll show ths wth our evaluaton data n Secton 7.

116 03 Algorthm VI- Servce Adaptaton() Admsson request phase for any Tas T : : f ɶ < A then T A e, e,.: fnd a component servce eˆ, ˆ = arg max{ A ɶ e, }, where S s the set of all e, S possble component servce satsfyng that Ae Ae ae and the overall,,, new utlzaton wll not volate the overall safe utlzaton bound after resource adaptaton;.2: update the servces of ê, ˆ and e, wth ther correspondng adapted resource. Tear-down phase for any Tas T : : undo Step 3 n the above. Fgure VI-4. Servce Adaptaton 5. A Real-Tme Component-Based System Archtecture Fgure VI-5 dsplays the system archtecture that results from the descrpton above. In ths archtecture, there s one module utlzaton allocaton and schedulng for component development, and two modules admsson control and polcng for applcaton development.

117 04 Fgure VI-5. System Archtecture Before a real-tme Component e s deployed, ts real-tme servce nterfaces Θ, A, D s must be specfed, and wll be loaded nto the resource table of the e, e, e, admsson control module once the component s deployed. The utlzaton allocaton and schedulng module wll preserve the processng utlzaton assgned to each component wth the resource reservaton mechansm and schedule the executon of methods at each component wth the schedulng algorthm. Admsson control s performed at tas level: When the clent wants to start a new tas, t frst sends an admsson request to the admsson control module. The admsson control module wll mae a decson for ths admsson request based on the polcy n admsson control mechansm and the profle ncludng n the admsson request. If the admsson request s admtted, an acnowledgement message wll be sent bac to the clent, whch ncludes a tas ID. At the same tme, shaper nstances at the correspondng components for ths tas wll be created. Durng the tear-down process of ths tas, the

118 05 tas wll be removed from the exstng-tas table. Informaton about the admtted tas wll be mantaned n the exstng-tas table n the admsson control module. The modules for Servce Optmzaton and Servce Adaptaton are mplemented as submodules n admsson control module. When a tas s successfully admtted, the system wll protect ts resources aganst sources of nvocatons that exceed ther share of nvocaton arrvals. Ths s done by approprately polcng the nvocatons by the polcng module. One of the most wellnown polcng mechansms n the lterature s nown as leay bucet, n whch the arrval constrant functon s defned by a burst sze and an average arrval rate. Once polced, the nvocatons are passed on to utlzaton allocaton and schedulng module for executon of ther correspondng method on the processor. 6. Implementaton of a Real-Tme Component-Based System We used Enterprse JavaBeans (EJB) [56] as the underlyng framewor of a resource overlay nfrastructure based on real-tme components. In the followng, we frst ntroduce the bacground nformaton, such as EJB and ts mplementaton JBoss, and then address the mplementaton of our system n detals. 6.a. EJB and JBoss Applcaton Server EJB technology s a server-sde component archtecture that smplfes the development and deployment of mult-ter, dstrbuted, scalable, Java enterprse applcatons. Enterprse beans (beans, to be concse) are server-sde components n EJB, whch represents a busness concept. There are three basc types of beans: () entty

119 06 beans, whch represent data n a database, () sesson beans, whch represent processes or act as agents performng tass, and () message-drven beans, whch are asynchronous message consumers. JBoss [85] applcaton server s a popular, open-source EJB applcaton server. It provdes the basc EJB contaners as well as EJB servces such as database access(jdbc), transactons (JTA/JTS), messagng (JMS), namng (JNDI) and management support (JMX). As the foundaton for the JBoss nfrastructure, JMX [86] provdes a common server spne that allows the user to ntegrate modules, contaners, and plug-ns. Servce components are declared as Managed Bean (MBean), whch are then loaded nto JBoss and may subsequently be admnstered usng JMX. MBeans are managed resources and Java objects that follow certan conventons to expose ther management nterfaces to remote management applcatons. Remote management applcatons can access MBeans through JMX agent servces. Each MBean s gven a unque object name and regstered to MBean Server at ntal tme. MBean Server provdes a regstry servce for MBeans. The JBoss EJB server and EJB contaner are completely mplemented usng componentbased plug-ns onto JMX. When an EJB s deployed nto JBoss, a contaner MBean s created to manage the EJB [87], [88]. In our real-tme component-based system, we wll buld the admsson control module as an MBean. In JBoss, the dynamc proxy approach s used for the server to generate contaner classes and for the generated contaner to generate home and remote nterfaces of the EJB at run tme. Whenever a method nvocaton s ssued on the clent-sde proxy, the

120 07 nvocaton handler creates a specal Invocaton object, whch wll refy the method nvocaton. After traversng a chan of clent-sde nterceptors, the Invocaton object s sent by an nvoer proxy to an nvoer MBean at the server sde, where t s routed through the contaner MBean assocated wth the target EJB. Each Invocaton object ncludes nformaton about object name, method, and arguments for target EJB. Applcaton developers can place customzed nterceptors n the nterceptor stac traversed by the Invocaton object. Ths nterceptor stac mechansm allows developers to add addtonal servces to the called target [87]. We use ths nterceptor mechansm to buld the polcng module n our real-tme component-based system. 6.b. Real-tme Infrastructure The mplementaton of our real-tme component-based system s based on JBoss We use TmeSys Lnux RT 3. as the underlyng real-tme operatng system [90]. To complete the platform, we use the RTSJ Reference Implementaton (RTSJ-RI) from TmeSys [9] as Java VM. Snce TmeSys RTSJ-RI (just as other foreseeable RTSJ mplementatons) provdes only a lmted set of Java classes, and JBoss s ntended for buldng enterprse systems, we dsabled some advanced features n JBoss whle at the same tme addng RTSJ compatble Java class lbrares. In partcular, RTSJ-RI does not support real-tme capabltes for Java Remote Method Invocaton (RMI) [89] on whch remote nvocaton s based. As a result, we approprately extended RMI to mae t realtme capable. For ths, we elmnated sources for prorty nverson, such as for stuatons n whch the lstenng thread used to assgn ncorrect prortes to ncomng requests. As a result, ths combnaton of a real-tme OS, a real-tme capable Java, and Real-Tme

121 08 RMI n conjuncton wth an approprately trmmed JBoss framewor results n a powerful bass for a real-tme component-based system. 6.c. Implementaton of Real-Tme Component-Based System The core of the real-tme component-based system as descrbed n the prevous sectons s the Real-Tme Specfcaton, the admsson control, the polcer, and the thread scheduler. Real-Tme Servce Specfcaton: Each real-tme component wll expose ts realtme servce nterface. The real-tme servce s defned as a number of ClassOfServce objects. Class ClassOfServce s defned n Fgure VI-6, where Class ArrvalFuncton defnes the arrval constrant functon for the correspondng class of servce. class ClassOfServce { nt classid; Method[] groupofmethods; ArrvalFuncton arrval; long deadlne;... // methods not shown } Fgure VI-6. Real-Tme Servce Admsson Control Module: The admsson control module s mplemented as an MBean. Ths MBean realzes the admsson control mechansm and the decson mang

122 09 procedure. The resource table and the exstng-tas table requred by admsson control are mplemented as entty beans. Servce optmzaton and servce adaptaton are mplemented as sub-modules. Polcng Module: After a tas request s admtted, a tas ID s generated and forwarded to the clent. At the same tme, a shaper nstance (mplemented as entty beans) s created. Any nvocaton of ths tas wll add the tas ID to the Invocaton object at the AdmssonInterceptor on the clent sde. At the ShapngInterceptor on the server sde, the tas ID s retreved, and s used, together wth the name of the EJB, as a ey to match ts correspondng shaper nstance. Utlzaton Allocaton and Schedulng Module: As an example of a guaranteed-rate scheduler to provde temporal solaton, a Total Bandwdth Server (TBS) [] s mplemented to allocate the underlyng CPU utlzaton to each real-tme component. The nput parameters for TBS are WCETs of methods n the component and the allocated CPU utlzaton. Recall that when a tas s admtted, a correspondng shaper nstance s ntated. The shaper nstance also ncludes the prorty assgned to any runtme method executon n the tas. Once an nvocaton enters ShapngInterceptor, ts correspondng shaper nstance can be found n the same way as done n the polcng module. Then the prorty value can be retreved, and the prorty for the worer thread s set.

123 0 7. Performance Evaluaton Recall that one of the basc features n our desgned systems s the reusablty of real-tme components. Reusablty, however, s dffcult to evaluate quanttatvely. In the experments descrbed below, we focus on the performance of our system n terms of the admsson probablty for each tas request and the latency overhead ntroduced n our system. In our experments, we assume that the CPU on the EJB server s the bottlenec and that the other resources, such as memory, ds and networ bandwdth are never lmtng. 7.a. Admsson Probablty versus Tas Arrval Rate In ths experment, we choose two Pentum 4 machnes wth GHz CPU and GB memory as applcaton servers. These two machnes are n the same subnet together wth another machne chosen to host as the clents. The networ bandwdth for all connectons s 00 Mbps. The applcaton servers are nstalled wth real-tme component-based systems software. We deployed three real-tme components { e, e2, e3} real-tme sesson beans n the frst real-tme applcaton server and e 4 n the other real-tme applcaton server. Component e wll expose one method θ e and defne a sngle class of servce (therefore we can gnore the class ndex), and ts real-tme servce nterface s Θ, A, D, e e e where Θ = { θ }, and D =. 000 sec, for =,, 4. Methods are assocated wth e e e WCET C = sec, e C = sec, e2 C = sec, and e3 C = sec, e4

124 respectvely. The safe utlzaton for each processor at each applcaton server s 90%. The arrval constrant functon A ( I ) wll be optmally specfed and CPU utlzaton e α e wll be determned wth our servce optmzaton algorthm. The runtme method executon wll be assgned a sngle real-tme prorty. There are three tas routes as shown n Fgure VI-7. Fgure VI-7. The Experment Testbed In ths experment, we choose three dfferent system confguratons n the applcaton server: A system wth no component solaton and enabled admsson control (NCI), our system wth component solaton and enabled admsson control under servce optmzaton (CI-OPT), and our system wth component solaton and enabled admsson control under servce adaptaton (CI-SA). In CI-SA, we choose = A. 2 T e, e, Emulated applcatons consst of tas generators, and clent-server nteractons. Clents wll send a sequence of perodc tass. In each tas, the perod for nvocaton arrval s 2 sec and each nvocaton has a 2 sec deadlne requrement. Each tas has a exponentally-dstrbuted lfe tme and ncludes 6 nvocatons n a lfe tme n average. The tas arrval s a Posson process and each tas wll choose a tas route unformly randomly. We vary the overall tas arrval rate λ from 0. per sec to. 5 per sec.