Modelling BLUE Active Queue Management using Discrete-time Queue

Transcription

1 roceedngs of e World Congress on Engneerng 7 Vol WCE 7, July - 4, 7, London, U.. Modellng BLUE Actve Queue Management usng Dscrete-tme Queue H. Abdel-jaber Deartment of Comutng, Unversty of Bradford, U habdelja@brad.ac.uk M. Woodward Deartment of Comutng, Unversty of Bradford, U m.woodward@br ad.ac.uk F. Thabtah MS, Deartment, hladelha Unversty, Amman, Jordan ffayez@hladel ha.edu.jo M. Al-dabat hladelha Unversty, MS Deartment, Amman, Jordan maldabat@hlad elha.edu.jo Abstract Ths aer rooses a new dscrete-tme queue analytcal model based on BLUE algorm n order to determne e network congeston n relmnary stages. We comare e orgnal BLUE, whch has been mlemented n Java, w our roosed analytcal model w regards to dfferent erformance measures (average queue leng, roughut, average queueng delay and acket robablty). The comarson results show at e roosed dscrete-tme queue analytcal model outerforms BLUE algorm n terms of roughut and acket robablty. Moreover, e roosed model mantans e roughut erformance regardless wheer e amount of e traffc load s lght or heavy. Furermore, we calculate e acket drong robablty functon for our analytcal model and e BLUE algorm n order to decde whch algorm dros fewer ackets. ndex Terms Dscrete-tme Queue, Congeston Control, erformance Measures, Analytcal Model. NTRODUCTON A network becomes congested when e ncomng ackets exceed e avalable network resources (bandwd allocaton and buffer saces) []. Congeston lays a man role n e deteroraton of network erformance and can cause low roughut, hgh delay for ackets and hgh acket rate. n order to manage congeston n comuter networks, one must utlse a control meod such as dro-tal (DT) [, ], whch dros ackets from e buffers tals solely after e router buffer becomes overflow. The DT algorm gves oor erformance wn Transort Control rotocol (TC) networks [4, 5, 6, 7] snce e TC sources adjust er sendng rates only after e DT router buffer becomes overflow. Several researchers [8, 9,,, 7, 8] have develoed Actve Queue Management (AQM) congeston control technques such as Random Early Detecton (RED) [8], Adatve RED [9], Gentle RED [], Stablze Random Early Dro (SRED) [], Dynamc Random Early Dro (DRED) [], Random Exonental Markng (REM)[, 4, 5, 6], BLUE [7, 8] and oers. The goals for most of e above AQM algorms are: to acheve hgh roughut erformance, low acket rate, low queueng delay for ackets, and mantan an average queue sze as small as ossble. n s aer, we roose a new dscrete-tme queue analytcal model based on BLUE algorm [7, 8] n order to control congestons n nternet and cellular networks. Moreover, we conduct a comuter smulaton usng e BLUE algorm n order to obtan ts erformance measures. aql, Secfcally, we record e average queue leng ( ) roughut (T), average queueng delay ( D ), acket and acket drong robablty ( D ) results for e BLUE and comare em w ose of our roosed analytcal model. The man reason of e comarson s to decde whch of e two algorms offers better Qualty of Servce (QoS). The aer s organsed as follows: The classc BLUE algorm s resented n Secton, and our roosed dscrete-tme queue analytcal model s ntroduced n Secton. The comarson results of e BLUE and our roosed BLUE-based analytcal model are gven n Secton 4, and fnally Secton 5 gves e conclusons and future works. rate ( ). THE CLASSC BLUE ALGORTHM BLUE s one of e known AQM algorms, whch was On losng of e ackets or ( < B leng ) (( current _ tme last _ adjustment) freeze) f > { D D nc ; last _ adjustment current _ tme ;} When e buffer s emty (or B leng ) f ( current _ tme last _ adjustment) > freeze { D D dec ; last _ adjustment current _ tme ; } ( ) Fg. BLUE seudocode. SBN: WCE 7

2 roceedngs of e World Congress on Engneerng 7 Vol WCE 7, July - 4, 7, London, U.. rmarly develoed to enhance e erformance of e wellknown RED algorm [7, 8]. BLUE deends uon a sngle D and a certan acket drong robablty arameter ( ). f e buffer leng of e BLUE router becomes larger an oston, BLUE ncreases D value to allevate e congeston. Whereas, f e buffer s emty or e lnk s dle, e D value wll be decreased. BLUE also reles on oer arameters as congeston metrcs, ncludng, acket, lnk utlsaton and buffer leng. The seudocode of e BLUE algorm s shown n Fgure. Accordng to Fgure, BLUE uses several arameters n order to adjust e D value lke e freeze arameter, whch s utlsed to determne e least tme erod between two successve adjustments. freeze s often set to a fx value accordng to [7, 8], however, t can also be gven an arbtrary value n order to avod global synchronsaton [9]. Oer arameters assocated w D are nc and dec at are usually used to determne e ncreasng or decreasng amount of D. Generally, nc arameter s gven a larger value an dec n order to revent underutlsaton [7, 8]. t should be noted at BLUE algorm dros ackets at e router buffer arbtrarly. reshold ( ). THE ROOSED DSCRETE-TME QUEUE ANALYTCAL MODEL n s secton, we ntroduce our dscrete-tme queue analytcal model, whch s based on BLUE algorm. Ths system deends on a artcular tme unt named slot [], where each slot could occur n sngle or multle events. An examle of a sngle event s ackets arrval or dearture n a slot, whereas ackets arrval and dearture n e same slot s an examle of multle events. The roosed dscrete-tme queue system model has a fnte ( ackets) caacty ncludng ackets currently n servce. Moreover, e arrval rocess utlsed s e dentcal ndeendent Dstrbuton (..D) Bernoull rocess, a {,}, n,,,..., where a n n denotes e acket arrval at slot n. The roosed queung system model uses e classc BLUE algorm as a congeston control meod, and us, t reles on a BLUE sngle reshold ( ) [8]. Our queung system model s shown n Fgure where, e queung system sources (or connectons) start sendng er ackets at α rate, and at occurs only when e queue leng at e BLUE router buffer s equal or smaller an, and us, no ackets are droed ( D ). However, when e queue leng at e router buffer becomes above, en α α ( D ) value ncreases from to. α and α α denote e average sendng rates for e sources n e queung system before and after reachng, resectvely. denotes e average dearture rate at e BLUE router buffer, e queung dsclne whch we use here s frst come frst serve (FCFS). We assume at e robablty for ackets arrval n a slot s α solely f e current queue leng s equal or less an, and α when e queue leng exceeds.we also assume at e queung system model s equlbrum, and e queue leng rocess s a Markov chan w fnte state saces. These state saces are:{,,,,,,,,-,}. Fnally, we assume at α > α and > α, and erefore > α. The state transton dagram for e BLUEdscrete tme queung model s gven n Fgure. From Fgure, we can obtan e balance equatons for e resented dscrete-tme queue analytcal model, e balance equatons are defned n e eleven equatons below, ( α ) [ ( α )]..... () [ α ( α)( ] [ ( α )] α () [ α( ] [ α ( α)( ] [ ( α) ]... () [ α( ] [ α ( α)( ] [ ( α) ]... (4) n general we obtan, SBN: WCE 7

3 roceedngs of e World Congress on Engneerng 7 Vol WCE 7, July - 4, 7, London, U.. [ α ( ] [ α ( α)( ] [ ( α) ] where,,4,...,..... (5) [ α ( ] [ α ( α)( ] [ ( α ) ].. (6) α [ ( )] [ α ( α )( ] [ ( α ) ].. (7) [ α ( ] [ α ( α )( ] [ ( α ) ].. (8) α ( [ ( α ) ].. (9) [ ] [ α ( α )( ], ( γ ( α) ( α,,,...,... (8) α ( ( α) ( α ) γ ( α) ( α )( α α ( ( α) ( α ) γ γ ( α) ( α )( α α ( ( α) ( α ) γ γ ( α) ( α )(. (9)...().. (),where n general we obtan, α ( α α [ ( α ) ]. () Where,, 4,..., [ ] [ ( )( ], Fnally, [ α ( ] [ α ( ], Where... () ( ( α) ( ( α ) α Letγ... () α andγ... () After solvng e balance equatons ( - ) and by substtutng equatons ( and ) we obtan, α γ... (4) ( α) ( α ( γ... (5) α ( ) ( ) ( γ ( α) ( ( γ ( α) ( α. (6) α... (7) n general we obtan, n general we obtan, α α ( ( α) ( α ).. () γ γ ( α) ( α )( Where,,,...,. After e robabltes of e queung system states are comuted, we need to calculate e robablty where ere s no ackets n e queue (also called e robablty when e queung system s dle ( ) ), where s calculated by alyng e normalzed equaton exressed as n equaton (), () Then by substtutng equatons (4-) n equaton (), we get, γ ( γ) ( ( γ)... (4) γ ( α)( γ ) ( ( α )( γ ) After s estmated, we utlse t to calculate e queung system erformance metrcs ( aql, T, D, ). Frstly, we calculate aql by alyng e generatng functon ( z) exressed n equaton (5), SBN: WCE 7

4 roceedngs of e World Congress on Engneerng 7 Vol WCE 7, July - 4, 7, London, U.. ( z) z... (5) We calculate aql by takng e frst dervatve of ( z) at z as aeared n equaton (6), () aql ().. (6) Then, γ γ [ ( γ) ] () ( ) () γ aql ( ) ( ) ( )( ) [ ( )] α γ γ γ γ γ ( ) ( ) α γ... (7) t should be noted at ere s anoer way to calculate aql usng equaton. After aql s comuted, we calculate ( T ), whch reresents e number of ackets at have been assed rough e queung system successfully. We use equaton (8) to generate T result. T ( ) ackets/slot (8) Then by alyng equaton (4) n equaton (8), we get e fnal form of T as shown below, γ ( γ) ( ( γ) T ackets / slot. γ ( α)( γ ) ( )( )( ) α γ (9) Based on aql and T results obtaned from equatons (7) and (9), resectvely, we can estmate D usng lttles law as shown n equaton (). D aql T slots () () T slots T slots () Then by substtutng equatons (7 and 9) n equaton () we get, D γ γ γ ( ) [ ( γ )] ( γ ) ( α ) γ ( α ) γ ( γ ) ( )( γ ) [ ] ( )( γ ) γ ( γ ) γ ( γ ) ( α )( γ ) ( )( α )( γ ) slot..... () Fnally, we calculate, whch corresonds to e roorton of ackets at lost e servce at e BLUE router buffer. The BLUE router buffer starts drong ackets solely when e queue leng exceeds oston. Equaton () s used to comute e. Average Queue Leng () Then by alyng equatons (9 ) n equaton () we obtan fnal form. γ Average Arrval Rate (Alha) Vs Average Queue Leng BLUE Algorm ( α)( γ )... () ( ( α )( γ ) V. SMULATON AND ERFORMANCE EVALUATON n s secton, we resent a comarson between e orgnal BLUE algorm [7, 8] and e roosed BLUE-based analytcal model w reference to dfferent erformance measures, ncludng, ( aql, T, D and ). Bo e orgnal BLUE and our roosed BLUE dscrete-tme queue analytcal model are mlemented n java on a.7 Mhz rocessor machne w 5 RAM. The arameters of e classc BLUE algorm ( α, α,,, reshold, freeze, nc, dec, D nt and Number of slots) are set to [.8.85],.8,.9,, 8,.,.5,.5,.5 and, resectvely. Moreover, e roosed analytcal model arameters, α,, and, are set to values smlar to e ose of e classc BLUE s arameters. Fgures 4, 5, 6 and 7 show e erformance measures results of e orgnal BLUE and our roosed BLUE analytcal model. Secfcally, ese fgures dslay α results aganst aql, T, D, and results, resectvely. Average Arrval Rate (Alha) The roosed BLUE Analytcal Model Fg. 4 α Vs aql SBN: WCE 7

5 roceedngs of e World Congress on Engneerng 7 Vol WCE 7, July - 4, 7, London, U.. numbers w regards to T. Fnally, Fgure 7 dslays e acket robablty results for bo algorms. The results ndcate at e roosed analytcal model dros fewer Throughut Average Arrval Rate (Alha) Vs. Throughut BLUE Algorm Average Arrval Rate (Alha) The roosed BLUE Analytcal Model Fgure 5: α Vs T. Average Queueng Delay Average Arrval Rate (Alha) Vs. Average Queueng Delay BLUE Algorm Average Arrval Rate (Alha) The roosed BLUE Analytcal Model Fg. 6 α Vs aql. acket Loss robablty Average Arrval rate (Alha) Vs. acket Loss robablty BLUE Algorm Average Arrval rate (Alha) Fg. 7: α Vs The roosed BLUE Analytcal Model. acket Drong robablty Queue Leng Vs. acket Drong robablty Queue Leng The roosed BLUE Analytcal Model Fg. 9: Queue leng versus D for e roosed Queue Leng Vs. acket Drong robablty acket drong robablty Queue Leng Blue Algorm Fg. 8: Queue leng aganst D for DRED smulaton software. We observe from Fgure 4 at e orgnal BLUE roduces results n terms of aql smaller an ose of our analytcal model, and erefore BLUE mantans aql better an e roosed analytcal model. Furermore, Fgure 6 ndcates at e orgnal BLUE gves smaller results of e average watng tme for e ackets ( D ) n e queueng system f comared w ose of e roosed analytcal model. However, accordng to e roughut erformance results n Fgure 5, our roosed analytcal model outerformed e orgnal BLUE snce t roduces hgher ackets an BLUE, and us, t controls e roughut erformance more an e orgnal BLUE. The D results roduced by e classc BLUE and e roosed BLUE-based analytcal model are shown n Fgures 8 and 9, resectvely. BLUE arameters were set n e exerments to e same values mentoned at e begnnng of s secton. Moreover, e roosed analytcal model arameters have been set to e same arameters values of BLUE. The only exceton s at e number of slots for BLUE algorm s set. Fgures 8 and 9 clearly show SBN: WCE 7

6 roceedngs of e World Congress on Engneerng 7 Vol WCE 7, July - 4, 7, London, U.. at our analytcal model dros fewer ackets an e orgnal BLUE algorm, and erefore, t mantans better roughut erformance an BLUE (Fgure 5 gves furer detals). V. CONCLUSONS A new dscrete-tme queue analytcal model based on BLUE algorm s resented n s aer. The roosed analytcal model reduces e arrval rate from α to α when e congeston aeared at e BLUE router buffer. We erformed a comarson between our roosed analytcal model and e orgnal BLUE w reference to aql, T, D and erformance measures. The exermental results ndcated at BLUE algorm outerformed our dscrete-tme queue analytcal model n terms of aql and D. However, our analytcal model mantans better T erformance an BLUE snce t dros fewer ackets regardless of e traffc load. n near future, we wll aly e resented analytcal model n queueng network system w multle nodes. Furer, we lan to aly our analytcal model n e nternet and cellular networks as a congeston control meod. [6]Auralya, S., Lasley, D., and Low, S., An Enhanced Random Early Markng Algorm for nternet Flow Control, NFOCOM, Telavv, srael, [7]Feng, W., kandlur, D.,Saha, D., and Shn,.G., Blue: A new class of actve queue management algorms, Unv. Mchgan, Ann Arbor,M,Tech. Re.UM CSE-TR-87-99,Ar.999. [8]Feng, W., Shn,.G., and kandlur, D., The Blue Actve Queue Management Algorms, EEE/ACM Transactons on Networkng, Volume. ssue 4, August. [9]Floyd, S., and Jacobson V., On Traffc hase Effects n acket-swtched Gateways, nternetworkng: Research and Exerence, V. N., Setember 99, []Woodward, M., E., Communcaton and Comuter Networks: Modellng w dscrete-tme queues, entech ress, London, 99. REFERENCES []Welzl, M., Network Congeston Control: Managng nternet Traffc, 8 ages, July, 5. [] Braden, R., Clark, D., Crowcroft, J., Dave, B., Deerng, S., Estrn, D., Floyd, S., Jacobson, V., Mnshall, G., artrdge, C., eterson, L., Ramakrshnan,., Shenker, S., wroclawsk, J., and Zhang, L., Recommendatons on Queue Management and Congeston Avodance n e nternet, RFC 9, Arl 998. [ Brandauer, C., annaccone, G., Dot, C., Zegler, T., Fdda, S., and May, M., Comarson of Tal Dro and Actve Queue Management erformance for bulk-data and Web-lke nternet Traffc, n roceedng. SCC, EEE, July. [4]ostel, J., B., Transmsson Control rotocol. RFC, nformaton Scences nsttute, Marna del Rey, CA, Setember 98, RFC 79. [5]Stevens, W., R., TC/ llustrated, Volume,. Addson-Wesley, Readng, MA, November 994. [6]ostel, J., Transmsson Control rotocol DARA nternet rogram rotocol Secfcaton, DARA, Setember 98. RFC 79. [7]Wrght, G., R., and Stevens, W., R., "TC/ llustrated, Volume (The mlementaton), Addson Wesley, January 995. [8]Floyd, S., and Jacobson V., Random Early Detecton Gateways for Congeston Avodance. EEE/ACM Transactons on Networkng, (4):97-4, Aug 99. [9]Floyd, S., Ramakrshna, G., and Shenker, S., Adatve RED: An Algorm for ncreasng e Robustness of RED s Actve Queue Management, Techncal reort, CS, August,. []Floyd, S., Recommendatons on usng e gentle varant of RED, May. avalable at htt:// []Ott, T., Lakshman, T., and Wong, L., SRED: Stablzed RED, n roc. EEE NFOCOM, Mar. 999, []Aweya, J., Ouellette, M., and Montuno, D., Y., A Control Theoretc Aroach to Actve Queue Management, Com. Net., vol. 6, ssue -, July,. -5. []Auralya, S., L, V., H., Low, S., H., and Yn, Q., REM: Actve Queue Management, EEE Network, 5(), May,. [4]Lasley, D., and Low, S., Random Early Markng: An Otmsaton Aroach to nternet Congeston Control, n roceedngs of EEE CON '99. [5]Lasley, D., and Low, S., Random Early Markng for nternet Congeston Control, roceedng of GlobeCom 99, , 999. SBN: WCE 7