Informaton Management n Modern Organzatons: Trends & Challenges 89 Traffc Management for the Gentle Random Early Detecton usng Dscrete- Tme Queueng. Introducton Abstract Hussen Abdel-aber Deartment of Comutng Unversty of Bradford BD7 DP U habdela@ Bradford.ac.uk Fad Thabtah Deartment of MIS Phladelha Unversty Amman Jordan ffayez@hladelha.edu.o Mke Woodward Deartment of Comutng Unversty of Bradford BD7 DP U m.e.woodward@ Bradford.ac.uk artcular router buffer when the connectons demand Snce some network connectons transmt ackets on network resources.e. buffer rooms and larger than others there could be unbalanced share n the avalable bandwdth and buffer rooms among the exstng connectons. Further connectons that send ackets more than others buld more buffer saces whch therefore cause the network to become congested. Ths aer rooses a dscrete-tme queueng analytcal model based on Gentle Random bandwdth exceed the avalable bandwdth caacty at the router [6 8 9] whch consequently deterorates the nternet erformance. The congeston can also lead to drong large number of ackets obtanng long average queueng delay for arrval ackets unstable average queue length and unfar share of network resources among network hosts [8]. Early Detecton (GRED method whch controls the Several actve queue management (AQM congeston ncdent by decreasng the connectons transmttng rates lnearly at certan levels. We comare our analytcal model wth the classc GRED n terms of several dfferent erformance metrcs ncludng average queue length throughut average queueng delay and acket rate n order to dentfy the one that offers better Qualty of Servce (QoS. Furthermore we comare both models accordng to the acket drong robablty to determne the one that dros smaller number of ackets. Lastly n ths aer we nvestgate the mnmum otmal oston at both the GRED and our analytcal model router buffers that gves a satsfed erformance. methods.e. [5 7 9 3 5 6 7 8 ] have been develoed n the comuter networks lterature n order to control the congeston. These methods were rmarly roosed to ( manage and control the congested routers buffers n the nternet ( deloy farness among network connectons (3 otmse the network erformance by drong fewer number of ackets (4 acheve low average watng tme for ackets n the routers buffers and (5 guarantee hgh throughut [9 ]. In order to desgn a new AQM method one has to answer three man questons accordng to [5]:. What s the congeston metrc that wll hel n controllng the congeston?. How the congested router buffer wll nform the eywords: Gentle Random Early Detecton (GRED nalytcal connectons to modfy ther transmsson rates. Model Queueng System Dscrete-tme Queue. Snce the massve develoments n the nternet technology n several alcatons such as audo and vdeo data traffc the nternet becomes one of the fastest develoment technologes n recent years [6 8]. These nternet alcatons necesstate hgh seed router buffers to delver data to ther rosectve recevers. One key ssue related to nternet alcatons erformance n comuter networks s congeston. The congeston occurs n the nternet at a 3. What s the acket drong robablty functon and what s the olcy used for drong the ackets.e. lnearly [6] exonentally [4 5] etc. One of the early and oular AQM methods s Random Early Detecton (RED [6] a number of successful AQM methods were roosed after RED such as Gentle RED (GRED [8] Random Exonental Markng (REM [4 5] Dynamc Random Early Dro (DRED [7] Stablzed RED (SRED [] BLUE [3 5] Adatve RED (ARED [7] and Generalzed Random Early Evason Network (GREEN [4]. However In accordance wth modellng queueng networks usng dscrete-tme
9 Informaton Management n Modern Organzatons: Trends & Challenges queues few research works have been mlemented.e. [ 3 9]. [9] has constructed an analytcal model based on RED to omt the bas aganst bursty flows and to manage the average queueng delay of ackets. Recently [ 3] roosed a number of new analytcal models for managng the congeston ncdent n wreless and fxed networks. Partcularly [3] resented a dscrete-tme queue analytcal model based on DRED [7] method and comared ther model wth DRED wth reference to dfferent erformance metrcs such as average queue length throughut etc. They showed exermentally that ther roosed analytcal model dros less number of ackets than DRED and t mantans the throughut better than DRED. [ ] develoed dscrete-tme queue analytcal models based on BLUE algorthm [3] and comared ther models wth BLUE. Ther exermental results demonstrated that ther roosed analytcal models outerformed BLUE wth resect to acket rate and throughut. In ths aer we resent a dscrete-tme queue analytcal model that uses GRED method [8] to control the congested routers buffers n relmnary stages. The roosed model s called GRED Lnear Decreasng (GREDLD. We comare between the roosed analytcal model and GRED wth reference to dfferent erformance metrcs n order to determne the one that rovdes better QoS. Moreover ths aer nvestgates the otmal oston for the mnmum at the router buffer for both the GRED and the GREDLD whch should guarantee a satsfed erformance. The rest of ths aer s organsed as follows: the GRED method s ntroduced n Secton. Secton 3 dscusses the roosed dscrete-tme queue analytcal model. The comarson results are resented n Secton 4 and Secton 5 concludes the aer.. The Gentle Random Early Detecton (GRED Random Early Dro (RED [6] s one of the known AQM methods whch has been used to detect and manage congestons. One of RED man lmtatons occurs when the average queue length ( aql becomes larger than the maxmum ( max oston at ts router buffer [6] whch forces RED to dro every arrval acket to allevate the congeston. Moreover snce the aql s larger than the max the queue length ( ql of RED becomes unstable. To overcome the above lmtaton [8] roosed the Gentle Random Early Dro (GRED algorthm. GRED manly uses the followng arameters: aql max mnmum oston at the router buffer ( mn and twce the maxmum oston at the router buffer ( double max. GRED does not dro ackets when the aql s less than the mn oston rather when the aql s between the mn and the max GRED dros the arrval ackets arbtrary and the D value ncreases from to D max. However f aql s between the max and the double max GRED dros ackets arbtrary and the from Dmax D vares to. Fnally f the aql exceeds the double max acket ( D. GRED dros each arrval 3. Dscrete-tme Queueng Analytcal Model Based on Lnear Decreasng In ths secton we roose a new dscrete-tme queueng analytcal model based on GRED for the queung system dslayed n Fgure and we call t GREDLD. The roosed model s aled to the queung network router buffer shown below to manage the congeston ncdent as early as ossble. The queueng system shown n Fgure has a fnte caacty ( ackets ncludng ackets n servce. It s connectons begn transmttng ackets at rate ql at the GRED router buffer s smaller when the ( than the mn ackets have been droed ( D therefore there mght be no. In cases where the queue length s between mn and max the sources decrease ther transmttng rates lnearly from to n order to allevate the congeston ( mn * ( ( double max mn f mn < max and the D value ncreases lnearly from to.
Informaton Management n Modern Organzatons: Trends & Challenges 9 Moreover when the queue length s between max and double max the sources decrease ther transmttng rates lnearly from to amng to reduce the mact of the congeston on GRED router buffer where ( ( mn ( double max mn f max < max double and the D ncreases lnearly from to. However n cases when the queue double max length exceeds the the sources decrease ther transmttng rates from to n order to control the congeston and thereby GRED dros ackets at DP rate. and reresent the average arrval rates for the sources n the queung system before reachng the mn ndex between mn and max ndexes between max and ndexes and after reachng double max double max ndex resectvely. β corresonds to the average servce rate at the GRED router the queung dsclne n the queung system shown n Fgure s frst come frst serve (FCFS and we assume that > > > andβ > therefore β > β > and β >. The state transton dagram for GREDLD s llustrated n Fgure 3.
9 Informaton Management n Modern Organzatons: Trends & Challenges Based on Fgure 3 the balance equatons for the GREDLD are roduced and gven n equatons - below: ( [ β ( ] ( [ β ( ( ] [ β ( ]... ( In general we obtan Fnally [ ( ] [ β ( ( ] [ β ( ] [ ( ] [ β ( ] where 34...mn..... (3 mn [ ( ] mn [ β ( ( ] mn [ β ( mn ] mn [ ( ] mn mn β mn mn ( mn ( [ β ( mn ] mn In general we obtan... (4. (5 [ ( ] [ β ( ( ] [ β ( ].. (6 β γ where where mn mn mn β ( ( 3... double max 3...mn... (3 double max double max double max [ ( ] double max double max β ( double max ( [ β ( ] double max... (7 double max [ double max ( ] double max [ β ( ( ] [ β ( ] double max... (8 In general we obtan double max [ ( ] [ β ( ( ] [ β ( ] where double max double max....... (9..... ( Where double max X double max max J and max mn I therefore also can be defned as below: mn I J X.. ( ( ( Letγ β mn < double max where..... ( After comutng the balance equatons we aly equaton ( on them to evaluate the robabltes of the queueng system states whch are defned as follows: γ β mn ( mn ( mn ( ( ( γ mn mn mn ( (............ (4 Where mn mn mn... double max and < mn
Informaton Management n Modern Organzatons: Trends & Challenges 93 doublemax mn doublemax ( mn max β β double doublemax γ Where mn γ... X β ( ( ( double max γ mn... (5 After the states robabltes are comuted we calculate the robablty of no ackets n the system queue node ( where can be obtaned usng the normalsed equaton (6b. Then T Packets/slot ( doublemax mn threshol ( ( ( (6a.. (6b....(7 P aql P γ ( ( γ mn γ ( z z mn β ( γ ( ( γ double max ( ( mn (.(8 mn ( Next we evaluate the erformance metrcs (average mn queue length ( aql throughut fracton (T average queung delay ( D ackets robablty P ( for the roosed analytcal model. Frstly we estmate the aql utlsng the generatng functon ( z P shown n equaton (7. The aql equals the frst dervatve of the generatng functon z and ths s defned n equaton (9. ( z X ( ( γ ( ( ( γ mn γ γ double max mn mn double max double max ( γ l l mn P at Secondly we comute the T usng equaton (. Thrdly D s calculated based on aql and T results usng equaton (. Fnally we comute utlsng equaton (. double mn max l mn [ γ mn ( γ ] ( γ ( γ * ( ( ( aql P D slots T T ( γ ( ( γ l slots ( T slots P X X ( γ ( γ γ γ X ( γ ( ( γ γ mn [ ] ( *
94 Informaton Management n Modern Organzatons: Trends & Challenges aql P ( ( mn γ γ double max β mn mn double max ( (9 [ γ mn ( γ ] ( γ ( γ * ( ( [ ] X X ( γ ( γ γ γ X( γ ( ( γ γ mn double max ( γ l l mn 4. The Probablty of Arrval ( Versus Performance Metrcs Results P mn... ( 4. Exermental Results Ths secton res(6bents numercal results for the GREDLD and the GRED methods wth resect to dfferent erformance metrcs ncludng ( aql ( T ( D and ( P to dentfy the model that rovdes better erformance. In addton we roduce the acket drong robablty ( D values for both models to decde the model that dros fewer numbers of ackets. Ths secton s organsed as follows: The erformance metrcs aganst the robablty of arrval ( results of both the GRED and the GREDLD are demonstrated n Subsecton 4.. Subsecton 4. examnes the otmal oston for the mn n both models and the D results are gven n Subsecton 4.3. The goal of ths secton s to determne whch of GRED and GREDLD offers better QoS wth resect to the erformance metrcs dscussed n Secton 4. The arameters of both models were set as follows: β mn max qw and the number of slots D System Caacty ( max were set to.8.9 3 9.. and resectvely. was set to varable values rangng between [.3.7]. Fgures 4 5 6 and 7 show the numercal results of versus aql versus T versus D and versus P resectvely for the models we consder. Fgures 4 and 6 dect that GRED generates better aql and D results than the roosed analytcal model. Secfcally Fgure 4 demonstrates that GRED stablses the aql better than that of GREDLD and ts D results are smaller than that of GREDLD. Whereas Fgures 5 and 7 exhbt that our analytcal model outerforms GRED wth reference to T and P results. To be more secfc Fgure 5 llustrates that GREDLD roduces a hghert results than that of GRED and thus t serves larger number of ackets. Further Fgure 7 dects P robablty of Arrval (Alha Vs. Average Queue Length Probablty of Arrval (Alha Vs. Throughut.8.7.6.5.4.3....4.6.8 P robablty of Arrval (Alha.8.6.4...4.6.8 Probablty of Arrval (Alha Lnear Decreasng Analytcal Model Fgure 4: Vs. aql results. The Orgnal GRED Lnear Decreasng Analytcal Model The Orgnal GRED Fgure 5: Vs. T results.
Informaton Management n Modern Organzatons: Trends & Challenges 95.5.5.5 P robablty of Arrval (Alha Vs. Average Queueng Delay..4.6.8 P robablty of Arrval (Alha Lnear Decreasng Analytcal Model Fgure 6: Vs. D results. The Orgnal GRED.5..5..5 P ro bablty o f A rrval (A lha Vs. P acket Lo ss R ate..4.6.8 P robablty of Arrval (Alha Lnear Decreasng Analytcal Model Fgure 7: Vs. P results. The Orgnal GRED M nthresho ld Vs. A verage Queue Length M nthresho ld V s. T hro ughut.8.7.6.5.4.3.. 3 4 5 6 7 8 9 Fgure 8: M nthresho ld Lnear Decreasng Analytcal Model mn The Orgnal GRED Vs. aql results..8.6.4. 3 4 5 6 7 8 9 Fgure 9: M nthresho ld Lnear Decreasng Analytcal M odel mn Vs. T results. The Orgnal GRED that the GREDLD derves smaller P results than that of GRED and as a result of that our analytcal model dros less number of ackets than GRED. 4. The mn Versus Performance Metrcs Results Ths secton ams to determne the otmal locaton (ndex of the mn at the router buffer whch gves a satsfed QoS n both models. Ths can be acheved by generatng numercal results wth resect to the erformance metrcs and settng the mn arameter to dfferent values n both the GRED and the GREDLD. The arameter values for the roosed analytcal model and GRED were set to the same values gven n Subsecton 4. wth two excetons. These are and mn whch were set to.7 and any value n the range between [3-8] resectvely. Fgures 8 9 and dslay the results of the mn versus aql the mn versus T the mn versus D and the P resectvely for mn versus GRED and GREDLD. We observe n Fgures 8 and that GRED offers better aql and D results than that of GREDLD wth reference to the mn oston at the router buffer. Whereas Fgures 9 and llustrate that the roosed analytcal model derves bettert and P results than that of GRED. The results of Fgures 8 and dect that the best mn oston at GRED s the furthest value from the max.e. 3. Whereas the otmal mn oston at GREDLD router s 8 whch s the largest ossble value. Ths means that the otmal oston for the mn of GREDLD that gves a satsfed erformance s to set t to the largest ossble value.e. the max.
96 Informaton Management n Modern Organzatons: Trends & Challenges.5.5.5 M nthresho ld Vs. A verage Queueng D elay 3 4 5 6 7 8 9 M nthresho ld Lnear Decreasng Analytcal Model Fgure : mn The Orgnal GRED Vs. D results. 4.3 The Packet Drong Probablty ( D Functon Results Ths secton comares the roosed analytcal model and GRED wth reference to the D n order to determne the one that dros less number of ackets. The arameters used to roduce the results n ths secton for both models are smlar to those gven n Secton 4. wth three excetons. These are and number of slots whch have been set to.85.85 and resectvely. Fgures and 3 show the D results for the GRED and GREDLD resectvely. In artcular Fgure llustrates the slots versus the D where a slot reresents a basc tme unt and contans the acket arrval and/or dearture tme. The current queue length versus the D s dslayed n Fgure 3. After analysng Fgures and 3 we found out that GREDLD router buffer dros fewer numbers of ackets than GRED. In addton we notced n Fgure.5..5..5 M nthre s ho ld V s. P a c k et Lo s s R a te 3 4 5 6 7 8 9 Fgure: M nthresho ld Lnear Decreasng A nalytcal M o del The Orgnal GRED mn Vs. P results. that GRED starts drong ackets at t s router buffer when the number of slots reaches 883. Ths means that GRED ncreases t s D lnearly from to D.( max as long as the number of slots s between 883 and 9 and when the number of slots becomes 9 the aql reaches the max also ncreases ts oston. Furthermore the GRED D value lnearly as long as the number of slots s between 9 and 44. Ths means that the aql value s also between max and doublemax and when number of slots becomes 44 the aql becomes double max and D consequently GRED dros every arrval acket (. Fgure 3 shows the D results of GREDLD at each queue length. After analysng ths fgure we observed that when the queue length reaches 3 GREDLD router buffer begns ( mn Slots Vs. Packet Drong Probablty The Current Queue Length Vs. Packet Drong Probablty Packet Drong Probablty.9.8.7.6.5.4.3.. 45 89 3 67 45 89 333 3637 Slots Packet Drong Probablty.35.3.5..5..5 3 4 5 6 7 8 9 3 4 5 6 7 8 9 The Current Queue Length The Orgnal GRED Lnear Decreasng Analytcal Model Fgure : The D results for the GRED. Fgure 3: The D results for the GREDLD drong ackets because of the congeston ncdent.
Informaton Management n Modern Organzatons: Trends & Challenges 97 Moreover GREDLD ncreases ts D value from to as long as the current queue length s between 3 and 8. Whereas when the queue length reaches 8 ( double max the router buffer wll dro every arrval acket ( D. 5. Conclusons We roose a new lnear decreasng dscrete-tme queue analytcal model based on GRED and we call t GREDLD. We comare the roosed analytcal model and GRED amng to determne the one that offers better QoS. Dfferent evaluaton metrcs ncludng average queue length average queung delay acket drong robablty throughut have been used as the base of our comarson. We summarse the exermental results as follow: GRED outerforms the roosed analytcal model n terms of average queue length and average queueng delay erformance measures. GREDLD roduces throughut and acket rate results better than that of GRED method. Accordng to acket drong robablty GREDLD dros less number of ackets than GRED. The deal mn oston n GRED router that roduces a satsfed average queue length and average queueng delay s to set t far from the max oston. In terms of the deal oston of the mn n GRED router that roduces good throughut and acket rates s to set t as close as ossble to the max. Whereas settng the mn near the max n the GREDLD router roduces a satsfed erformance metrcs results. In near future we ntend to aly the roosed analytcal model n the nternet and at the base statons n wreless networks. We also ntend to use our analytcal model n networks wth n queues (fxed or wreless rather than sngle queue node networks. References. Abdelaber H. Thabtah F. Woodward M. Had W. Lnear Analyss for a BLUE Congeston Control Algorthm usng A Dscrete-tme Queue. Proceedng n the 3 rd Internatonal Conference on Informaton Technology ICIT 7 99. 8-4. Amman Jordan May 7.. Abdelaber H. Woodward M. Thabtah F. Al-dabat M. Modellng BLUE Actve Queue Management usng Dscrete-tme Queue. Proceedng n the 7 Internatonal Conference of Informaton Securty and Internet Engneerng (ICISIE 7. 536-54. London U.. July 7. 3. Abdelaber H. Woodward M. Thabtah F. Etbega M. A Dscrete-tme Queue Analytcal Model based on Dynamc Random Early Dro. Proceedng n the Fourth IEEE Internatonal Conference on Informaton Technology: New Generatons (ITNG 7.. 7-76. Arl 7 Las Vegas USA. 4. Athuralya S. Lasley D. and Low S. An Enhanced Random Early Markng Algorthm for Internet Flow Control INFOCOM Telavv Israel. 45-434. 5. Athuralya S. L V. H. Low S. H. and Yn Q. REM: Actve Queue Management IEEE Network 5(3 48-53. May. 6. Atsum Y. ondoh E. Altntas O. and Yoshda T. A New Congeston Control Algorthm for Sack-TCP wth RED Routers Ultra-hgh seed Network and Comuter Technology Labs. (UNCL Jaan. 7. Aweya J. Ouellette M. and Montuno D. Y. A Control Theoretc Aroach to Actve Queue Management Com. Net. vol. 36 ssue -3 July. 3-35. 8. Jan R. Congeston Control n Comuter Networks: Issues and Trends IEEE Network Magazne 99. 9. Bartek Wydrowsk B. P. and Zukerman M. Hgh Performance DffServ Mechansm for Routers and Swtches: Packet Arrval Rate based Queue Management for Class Based Schedulng Proceedngs of the Second Internatonal IFIP-TC6 Networkng Conference on Networkng Technologes Servces and Protocols; Performance of Comuter and Communcaton Networks; and Moble and Wreless Communcatons Lecture Notes In Comuter Scence vol. 345. 6-73 ISBN:3-54-4379-6.. Braden R. Clark D. Crowcroft J. Dave B. Deerng S. Estrn D. Floyd S. Jacobson V. Mnshall G. Partrdge C. Peterson L. Ramakrshnan. Shenker S. wroclawsk J. and Zhang L. Recommendatons on Queue Management and Congeston Avodance n the Internet RFC 39 Arl 998.. Brandauer C. Iannaccone G. Dot C. Zegler T. Fdda S. and May M. Comarson of Tal Dro and Actve Queue Management Performance for bulk-data and Web-lke Internet Traffc In Proceedng. ISCC. --9. IEEE July.. Chrysostomou C. Ptslldes A. Hadollas G. Sekercoglu A. and Polycarou M. Fuzzy Exlct Markng for Congeston Control n Dfferentated Servces Networks Proceedngs of the Eght IEEE Internatonal Symosum on Comuters and Communcaton (ISCC 3 53-346 3. 3. Feng W. kandlur D.Saha D. and Shn.G. Blue: A new class of actve queue management algorthms Unv. Mchgan Ann ArborMITech. Re.UM CSE-TR-387-99Ar.999.
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