CONTROL SYSTEM SOLUTION TO NETWORK CONGESTION: A MODIFIED PID METHOD

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1 Control 4, Unverty of Ba, UK, September 4 ID-89 COTROL SYSTEM SOLUTIO TO ETWORK COGESTIO: A MODIFIED PID METHOD K. H. Wong, L Tan and S.H.Yang Computer Scence Department, Loughborough Unverty, UK Computer Scence Department, Central Chna ormal Unverty, Chna Snce TCP e prmary protocol for controllng e ABSTRACT Th paper analye e current Internet congeton control mechanm and preent two control eoretcal approache baed on e extng Proportonal-Integral-plu-Dervatve (PID) controller. The parameter were elected to enure e tablty of e control loop. It hown at a modfed PID controller offer a quck repone, good utlaton and far hare of avalable bandwd and table buffer occupancy. The bac control eoretcal approach preented n e frt part of e paper. Then e qualte of performance of e two PID controller are compared rough mulaton. An adaptve PID controller llutrate great potental to e congeton control for dynamc network envronment. KEYWORDS: Computer etwork Congeton Control, PID controller, ABR ervce. etwork tablty.. ITRODUCTIO The Internet a computer network whch cont of mllon of computer worldwde. A technologe advanced e Internet readly avalable to more and more uer. For e pat decade e number of Internet ervce provder and e avalable bandwd have contnued to ncreae. But a e level of ntegraton between e Internet and our daly lfe ncreae, e demand for e Internet growng even fater and e avalable bandwd per peron ha proven to be far le an etmated 4. The level of conumer enuam ha preented many challenge to centt and engneer; one of e challenge to provde an effectve oluton to congeton control. Congeton e tate of utaned network overloaded, n whch e network reache a tuaton where e demand for network reource approxmate to or even exceed t capacty. Congeton n a ngle lnk could ecalate nto e break down of e whole network. Th epecally true at ome bottleneck wtch node. One of e eaet oluton to reduce congeton to provde more bandwd va upgradng e hardware, uch a a cable w a larger bandwd and a buffer w an enormou capacty. However oluton ha proven to be bo technologcally and economcally mpractcal; due to e prce of e hardware and e ntallaton cot and e fnte lfetme of e data packet. traffc of e Internet. The focu of paper on e congeton control meod for TCP. The predomnant congeton control are called Tahoe and Reno 3. The bac concept of ee two protocol for e ource to lnear ncreae t endng rate untl congeton occur and en exponentally decreae e endng rate. The ource tart w a mall wndow e ze of one packet. TCP provde confrmaton of delvery. When e packet arrve afely at t detnaton, an acknowledgement ent to e ource, en e ource ncreae e wndow ze by one, called e Addtve Increae. Upon e detecton of packet lot, e ource node wll et e wndow to half prevou ze (multplcatve decreae) and retranmt e lot packet. Then e ource wll tart to ncrement e wndow ze by one agan untl congeton occur. Alough TCP Reno ha performed better an expected and wdely deployed, recent tude ha hown at TCP Reno and t varant are prone to ntablte; due to e fact e algorm ued wa tuned to react too quckly to e change and produce dramatc ocllaton whch n turn caue ntablte. Tradtonally, network congeton control mechanm were degned by Computer Scentt w experence outde e realm of control eory. Snce e Internet n eence a large feedback ytem, t can be modeled by maematcal equaton ung Control Engneerng Theory. But due to e hghly decentralzed nature and dverty of e Internet, mot of e work done by Control Engneer contrbuted toward etwork uch a ATM where nformaton centralzed. However on a node to node ba raer en an end to end ba, control eory hould alo have a gnfcant contrbuton to bo localzed network and e Internet. The man objectve of paper to analye e performance of e Proportonal-Integral-plu-dervatve congeton (PID) controller propoed by Tan at el under varou network condton and load and compare t w e tradtonal PID controller. The crtera are ytem tablty, rate of convergence and far harng.. ETWORK MODEL A typcal network cont of a number of ource and detnaton node. The ource node end out packet of

2 Control 4, Unverty of Ba, UK, September 4 ID-89 data to e detnaton node va a ere of ntermedate node. To analye a network, t eental to dentfy e number of ource and detnaton node and e rate of traffc between em. Fgure dplayed below repreent a mple congeton control model for an ATM wtchng network. Fgure A congeton control model for an ATM wtchng network For e ake of mplcty only one ngle wtchng node condered. The ource node and e wtchng node are connected by Vrtual Connecton. The total number of Vrtual Connecton at controlled by e controller equal to e number of connecton made between e ource node and e wtchng node whch denoted a, and e number of actvated connecton are denoted a M whch may vary w tme t. The wtchng node ha a fnte buffer of ze K to tore at ncomng data before endng em out at a rate v. For each Vrtual Connecton ere are two type of delay. Frt e pa delay from e node to e wtchng node, denoted a. Second type e feedback delay ( ) from e wtchng node back to e node. There are two type of traffc n e network model; uncontrolled traffc w(t) and controlled traffc q(t). Uncontrolled traffc (e.g., guaranteed ervce traffc uch a CBR, VBR and UBR traffc) wll not be congeted at e ource node. It ha e prorty on e bandwd over e econd type of traffc; e controlled traffc whch can only be tranmtted w e remanng bandwd after e tranmon of uncontrolled traffc and when ere no congeton appearng n e network. The rate of controlled traffc q (t) of e node dependent on e buffer occupancy x (t). The buffer occupancy meaured at every T econd and e occupancy level wll be ent back to e controller and e controlled traffc rate q (t) adjuted to mantan a dere level of buffer occupancy. W e above notaton and aumpton, e tate of a wtchng node n a network can be decrbed by e followng non-lnear tme -varant and tme-delayng equaton 6,7. / x& ( t) = Sat K{ e q ( t ) + w( t) υ} () = Where x(t) e buffer occupancy at tme t, and K, x > K; Sat K { x} = x, x K;, x <, e, e ourcenode =, oerwe. actve; For e above ytem when a feedback control cheme appled e nput to e cloed loop ytem wll have a round-trp delay of = +, =,, L,. Th round-trp delay cont of propagaton, queung, and tranmon and proceng tme. For e ake of mplcty, ee are aumed to be contant. The tate of e buffer wll be ampled at every T econd. and e exact ntegral of T. and are nteger. Let d ( = Tw ( nt) be e uncontrolled traffc and λ ( Tq ( nt) be e controlled traffc flowng out of = node durng e n nterval of T, and let η = Tν denote e number of cell emtted from e wtchng node durng e n nterval. Subttutng oe varable nto Equaton () and tranfer to a dcrete form: x( n+ ) = Sat { x( + K = e λ ( n ) + d( η}. () Saturaton of non-lnearty mpoed on e Equaton () wll not be actvated for mall devaton around e operatng pont Hence e aturaton non-lnearty can be removed and e Equaton () under aumpton can be decrbed a e followng equaton: x( n + ) = x( + e λ ( n ) + d ( n η (3) = ) 3. COGESTIO COTROL METHOD There are two type of control meod under conderaton. The frt meod e tradtonal PID controller and can be decrbe by e followng equaton. λ ( = µ + α ( x( n ) x ) + β ( x( n j) x + γ ( x( n ) x( n j = )) The econd controller a varaton of e tradtonal PID controller propoed by Tan et al. Th wll now be referred to a e modfed PID controller and can be decrbe by e followng equaton. λ ( n ) = µ + α ( x ( n ) x ) + β λ + γ + γ ( x ( n ( x ( n ) x ( n ) x ( n λ (, e explct rate of e )) j = ) )) ( n j ) (4) (5) ource node

3 Control 4, Unverty of Ba, UK, September 4 ID-89 calculated by e wtchng node at dcrete tme n. µ e dered nput(5.5 Mbp) for e tradtonal PID controller and e maxmum number of packet allowed to tranmt nto e network n one nterval T from e ource node for e modfed PID controller, value to be determned baed on e teady tate analye on e latter part of paper. x e dered buffer occupancy and x ( e buffer occupancy level at tme n. e feedback delay from e wtchng node to e ource node and e total delay (Round trp tme delay) n one nterval. The coeffcent α, β, γ and γ are proportonal, ntegral, e frt and econd dervatve gan repectvely, whch are to be determned on e ba of e tablty crtera and ued to locate all e pole of e cloed loop ytem. The detal maematcal analye are preented n []. The only major dfference between e two controller e Integral gan component. In e tradtonal PID controller e Integral component meaure e value of pervou buffer occupancy. Wherea e modfed PID controller meaure e value of prevou rate of controlled ncomng traffc. 4. ETWORK PERFORMACE AD STABLITY AALYSES After etablhng e cloe loop ytem, t mportant to determne e charactertc polynomal (CP) of e cloed loop ytem gven by (3) and (5). If z-tranformaton appled to e equaton (3), one ealy arrve at (6) ( z ) X ( z ) = e z λ ( z ) + D ( z ) η R ( z ) = where e z-tranformaton of x (, λ (, and d( are decrbed by n X ( z) = x( z, n λ ( z) = λ ( z, ( z) = n= n= z R( z) =. z n= n D d( z and Applyng z-tranformaton to equaton (5) wll yeld: β ( z ) ( ) λ ( z ) = z ( z ) (7) (( α + γ ) z + ( γ γ ) z γ z ) X ( z ) + ( µ α x ) R ( z ) From equaton (6) and (7) we can determne e charactertc polynomal (CP): ( z) = z + 3 ( β + ) z + + ( β Mα Mγ ) z M ( γ γ ) z Mγ (8) We en apply e Schur-Cohn tablty tet to e charactertc polynomal and hence locate all e root of (z) wn e unt crcle to enure e tablty of e ytem. Anoer mportant apect for e degn of e congeton control mechanm e far rate allocaton polcy. In paper, we adopt e max /mn farne defnton n [8]. The modfed PID controller can acheve max/mn farne n a natural way wout addtonal computaton or nformaton about bottleneck rate of ndvdual connecton, and alo guarantee mnmum cell rate (MCR) > wout any addtonal computaton. Let x,λ, d be e teady tate value correpondng x(, λ (, d( n. Under e aumpton at e to ) nput traffc contant, en e orgnal tate equaton (3) and e controller equaton (5) take er teady tate form λ x = µ = x + = e λ + d η (9) ) + β λ + γ ( x x ) j= + α ( x x () From (), one ha d λ = η, () M Where e component M e total actve ABR ource node, e componentη e emttng rate of e wtch, and e component d e tranmttng rate of uncontrollable traffc. It noted at e componentη d e avalable bandwd for all ABR ource, whch dtrbuted equally amongt e actvate VC. Thu e requrement of Max/Mn farne acheved n approach. We furer fnd at e PID controller guarantee mnmum cell rate (MCR)> wout any addtonal computaton. Th expoton very mlar to at dcued n [9], t ha u been omtted. From (), we have λ = µ + α( x x ) + βλ,.e., ( β ) λ µ x x =. α It een at f e equaton ( β ) λ µ = () hold, en e teady tate value of e buffer occupancy equal to e pecfed rehold,.e., x x =. Conderng n () and (), we need to chooe e

4 Control 4, Unverty of Ba, UK, September 4 ID-89 admble parameter µ and β uch at η d µ = ( β ) (3) M 5. SIMULATIO PARAMETERS AD RESULTS To analye e performance of e two PID controller ree apect of er performance wll be under conderaton: Stablty of e ytem n term of e buffer occupancy. Tranent repone of e ource rate Utlaton of e lnk. Fgure 3: Source rate tranent repone for e tradtonal PID controller Fgure : Sngle-node network model 8. Fgure above e graphcal repreentaton of e network model ued n paper. There are a total of ABR ource node whch are plt nto two group of 5 node (Group A and Group B). The wtchng node SW e bottleneck lnk n mulaton. To better demontrate e adaptaton ablty of e controller. Group A wll be actvated frt at tme t=m and Group B wll be actvated at tme t=3m. The dtance between e ource node and e wtchng node km. All lnk have a capacty of µ = 55 Mbp n total. The ABR ource parameter choen at mulaton at: PCR = 365 cell/m (55 Mbp). In e model e pa delay and e feedback delay and are et a = m ec, ec, = m ( =,, L,) repectvely. It aumed e proceng tme and queung tme to be ngnfcant n comparon to propagaton delay. Hence e propagaton delay from e ource node to e wtchng node and en back equal to e Round Trp Tme delay mec. Baed on e maematcal analye from [], e PID controller parameter are choen a α, =-.95, β =-, γ =-.5 and γ =-.3 for e tradtonal PID controller and α, =-.95, β =-.5, γ =-.5 and γ =-.3 for e modfed PID controller. The optmum buffer occupancy x et at kb. The parameter µ et to 46.5Mbp from e teady tate condton (3). = Fgure 3 above how e ource rate tranent repone for e tradtonal PID controller. The tradtonal PID controller ha a good repone before all ource node are actvated but at 3m e rate of tranmon tart to ocllate and underable nce demontrate an unequal hare of e bandwd and could caue ytem beng ntable. Fgure 4: Buffer occupancy tranent repone for e tradtonal PID controller Fgure 4 how e buffer occupancy tranent repone for e tradtonal PID controller. Under control cheme e buffer occupancy never reache e pecfed rehold and never be table whch could lead to data lot.

5 Control 4, Unverty of Ba, UK, September 4 ID-89 controller. In e next ecton e focu on mprovng e modfed PID controller to gve a better repone before 3m. 3 Mbp 6. ADAPTIVE MODIFIED PID COTROLLER 5.5Mbp Fgure 5: Source rate tranent repone for e modfed PID controller Fgure 5 dplay e tranent repone for e modfed PID controller and how at before 3m e controlled tranmon rate for a ngle ource node reache e average of 3Mbp and after 3m when all ource node are actvated e rate at 5.5 Mbp. Th prove at under control cheme each lnk utle all e bandwd avalable. Fgure 5 alo how a good tranent repone and prove at control cheme provde a far harng bandwd for each lnk. There are ome ocllaton before 3m. It becaue e lnk under-utled. The ocllaton mght caue ome degradaton to e network performance. Lookng at Fgure 5 and 6 ere are tll ocllaton for e controlled nput rate and under-utlaton for e buffer occupancy before e equlbrum pont for e modfed PID controller. Th are due to e change occurred n e ytem and e controller beng not flexble enough to adapt to e change. To fully utle all e reource, we ue dfferent ntegral gan dfferent tuaton whch wll now be refer to a Adaptve Integral Gan. Th mean e value of Integral Gan wll change accordng to e tuaton. We chooe β =-.5 from tme t=m to t=3m, and β = - from 3m tll e end of e mulaton. The ret of e parameter wll reman unchanged. Fgure 7 and 8 demontrate e mulaton reult for e Adaptve modfed PID controller. kb Fgure 7: Buffer occupancy w e adaptve modfed PID controller Fgure 6: Buffer occupancy tranent repone for e modfed PID controller Fgure 6 how e tranent repone for e modfed PID controller. The repone ha a quck ettng tme and at approxmately 3m e buffer occupancy converge exactly to e pecfed rehold x = Kb. The buffer occupancy before 3m never approache e pecfed rehold.. In general, a le ettng tme mean e qucker acton of e network to congeton and to load change n e router. From mulaton reult t clear at e modfed PID controller better an e tradtonal PID Fgure 8 Source rate tranent repone for e adaptve modfed PID controller The mulaton reult how at e Adaptve modfed PID controller ha a very fat ettng tme and jut lke

6 Control 4, Unverty of Ba, UK, September 4 ID-89 e modfed PID controller acheve far harng and fully utl e all e avalable bandwd. The target rehold (kb) ha been acheved before and after e equlbrum pont. Thee reult how at under e Adaptve modfed PID controller e network can perform very effcently. 7. COCLUSIOS Th paper ha reved and analyed e performance of Internet congeton control mechanm baed on a control eoretc approach and ha produced trong evdence at bo e PID controller have performed better an e tradtonal Internet congeton control meod uch a Reno and Ve ga. Due to e nature of e controller ere are no harp ocllaton n comparon to e meod lke Reno. There le chance of data lo. Smulaton have been performed under varou condton, whch howed e PID controller can adjut e rate of controlled traffc and acheve a ma xmum roughput and farne n a natural way. The mulaton reult alo how e modfed PID controller perform better an e tradtonal PID controller. Our current reearch focung on how e adaptve control can be appled to a multcat network cenaro. A e lat part of e mulaton how e adaptve modfed PID controller mght have a great potental n Internet congeton control to adapt to e change of e network envronment. The ntegral gan can be automatcally tuned baed on a number of extng control technologe. In paper we only addre e fact at e adaptve control neceary n network congeton control to adapt to dfferent network envronment. Furer tude are needed and hould provde nteretng reult. 6. Benmohamed, L., and Meerkov, S.M., 993, IEEE/ACM Tranacton etworkng,, Flpak, J., 988, Modellng and Control of Dynamc Flow n Communcaton etwork, Sprnger-velag. 8. Kolarov, A and Ramamury, G., 999, IEEE/ACM Tranacton etworkng, 7, Correpondng auor: Dr. S.H. Yang, Senor Lecturer at Department of Computer Scence, Loughborough Unverty, Emal: S.H.Yang@lboro.ac.uk REFERECES. Tan, L., Lu, Q. and Yang, S.H.,3, Congeton Control of Hgh Speed Computer etwork: A PID Meod, European Control Conference, Cambrdge, UK.. Tan, L., Yang, S.H.,, Rate-baed Congeton Controller for hgh peed computer network, IFAC Congre, Barcelona, Span. 3. Low, S.H., Pagann, F., and Doyle, J.C.,, IEEE CSM,, Johar, R.,, Maematcal Modelng and Control of Internet Congeton, SIAM Onlne ew, 33, 5. Pagann, F., Doyle, J.C., and Low, S.H.,, A Control Theoretcal Look at Internet Congeton Control, Multdcplnary Reearch n Control: The Mohammed Dahleh Sympoum.