Adaptive Congestion Control in ATM Networks

Transcription

1 Aaptive Congestion Control in ATM Networks Farza Habibipour, Mehi Galily, Masou Faris, Ali Yazian Iran Telecounication Research Center, Ministry of ICT, Tehran, IRAN Abstract. In this paper an aaptive iniu variance controller is propose to iniize the rate of stochastic inputs fro uncontrollable high priority sources. This etho avois the coputations neee for pole placeent esign of the iniu variance controller, an utilizes an online recursive least squares algorith in irect tuning of the controller paraeters. Introuction Congestion control of ATM (Asynchronous Transfer Moe) network with its wie use in high banwith counication systes is the source of attention an subject of active research []. There are ifferent types of counication services which are categorize in high priority sources incluing Constant Bit Rate (CBR) an Variable Bit Rate (VBR), an best effort sources often consiere as Available Bit Rate (ABR) sources. On the basis of QoS (Quality of Service) requireents, congestion control is possible by regulating the queue length at bottleneck noes via active controlling of Available Bit Rate (ABR) []. Another iportant factor is the unavoiable elay of close loop systes in high spee links such as satellite ATM networks or IP ATM. The Roun Trip Tie (RTT) elay is the tie fro the oent control inforation is sent to the source until an appropriate action takes place, an is the source of instability in siple control systes [3]. In this paper, a irect iniu variance self tuning regulator is propose to be use with an online recursive least squares algorith to estiate the appropriate control paraeters an to aaptively regulate the queue length to the noinal value. The siulation results show the efficiency of the etho in coparison to a proportional-integral rate atching controller. Queue Length Dynaics Each bottleneck noe of an ATM network has an output buffer to prevent cell loss, but the queue length of cells in the liite size buffer shoul be controlle to avoi overflow. Denoting the queue length at tie n by q, the queue length ynaics is written by a siple linear equation ( n ) = q + r q + µ ()

2 r is the total nuber of cells receiving in the tie interval [ n, n+ ), µ is the nuber of cells that epart fro this noe at the sae tie. The rate r, consists of inputs fro M controllable ABR sources an a rate of cells fro uncontrollable high priority sources (CBRs an VBRs) r u n. Clearly: where an of input cells to the buffer, enote by ( ) r M c u = r + r = () A high perforance tracking control etho, actually results in optial use of q n is referre to as the controlle variable an buffer an network capacity. ( ) r c u s are the M control signals. The available banwith for ABR, r µ, is a stochastic value since the rate of VBR traffic is tie varying. Therefore the uncontrolle traffic, r u, can be siply oele by a filtere rano isturbance sequence to the syste. There are noticeable roun trip tie elays in a congestion controlle feeback loop: r c u ( n ) = (3) where u is the available bit rate to the th source calculate at tie n, but is consiere by the source tie units later. We suppose iniu an axiu liits for these tie elays: in L (4) M By efining a noinal queue length value (Q), an the error variable siple proportional integral control law can be use u a [ u ( n ) + kq + k q( n ) ( k + k ) Q] ax q Q, a = (5) where a is the rate allocation coefficient for source, an k an k are control paraeters which are constant for all of the sources. Typically M a = = (6) The control signals of the ifferent sources are copute by iviing a unifie control signal proportional to the rate allocation coefficients: r ( n ) = u a u + (7) c =

3 To esign the pole placeent controller, the queue length ynaics are reforulate in frequency oain (Z-oain). A colore noise process is first assue for the rate of uncontrolle sources: C e r u = (8) Where e enotes a Gaussian rano sequence. By efinition of = q Q, the tracking proble is siplifie to the regulation proble, an y the ynaical oel is escribe by y B u C e A = + (9) in which A + ax = z + z A eg( ) = ax ; + ax () an B = az + a z + + a ; eg( B ) = = ax in K () 3 Miniu Variance Controller The iniu variance control law is esigne to iniize the cost function efine as the expectation of the controlle signal in equation 9: Equation (9) is then reconfigure as where in { y } J = E () e ( ) ( n ) z B C y ( n+ ) = u( n+ ) + + (3) A A = is the iniu tie elay for a control action to appear in output, an hence is the preiction horizon of the iniu variance controller. Equation (3) can be further oifie to yiel B zg y ( n+ ) = u( n+ ) + F e( n+ ) + e (4) A A

4 F an iviing z C to G are copute as the quotient an reainer polynoials of A fro the following Diophantine equation: = A F G z C + (5) By a few atheatical anipulations through the noise innovation oel, the following equation is obtaine [4]: F C zb zg y ( n+ ) = F e( n+ ) + u + y (6) C The secon part of which is consiere as the preiction oel F C zb zg y ˆ ( n+ n) = u + y (7) C An to iniize the preiction error, ( n ) y( n n) variance control law is obtaine y ˆ + G F +, the iniu u = y (8) B 4 Self Tuning Regulator The pole placeent esign of the iniu variance controller via equations (5) an (8) is just applicable if the polynoials of the oel in equation (9), i.e. A, B, an C, are efinite; but this is not the case in real situation. So there is a nee to utilize an estiation etho either for these paraeters or irectly for the control paraeters in equation (8). Using an ientification etho to estiate the paraeters of the oel in equation (9) is followe by the har coputation of the Diophantine equation an is not efficient. Another approach is the irect tuning of the controller paraeters. To start, equation (6) is paraeterize in backwar ifference for as follow ( n+ ) ( R u + S y ) + R e( n ) y = + C in which R = F propose to estiate the polynoials R an (9). Recursive Least Squares (RLS) algorith is S as the coefficients of

5 y ). The coefficient can be C consiere as a filter on regressors, an is coonly replace by a stable filter of the Q rational for : P z the regressors of input ( u ) an output ( u ( ) Q Q = u an yf = y () P P f Therefore the RLS algorith is forulate to estiate the coefficients of z S z in the following oel R ( ) an ( ) ( n+ ) = R u + S y + ( n ) y ε + () where R S k = r + rz + K+ rkz l = s + sz + K+ s z l () ε The recursive least squares estiation is perfore via T = y R u ( n ) S y ( n ) = y φ ( n ) ˆ θ T φ T θ = [ u K u( n k) y K y( n l) ] = [ r K r s K s ] k f l f (3) 5 Siulation Results Three ABR sources with ifferent roun trip tie elays are assue, one of which has an allocation rate coefficient of.5 an the others have equal coefficients of.5. The output service rate of the noe is cells per tie unit an the traffic of high priority sources is oele as a filtere rano process with a Gaussian input sequence ( =5, σ =5). Noinal tie elays of ABR sources are x x = 3, = 4, 3 = 5 ; M = 3, an the esire queue length is 3. The noinal queue length is 3 an the axiu buffer size is 5. Siulation results of the propose controller are copare to the siple control structure of equation (4). Fig. presents a coparison of the queue length values for the proportional integral control etho, an the aaptive iniu variance controller. Both ethos have regulate the queue length to 3, but their ean values an stanar eviations are ifferent. Obviously, the iniu variance controller has resulte in lower variance

6 of the queue length about the noinal value. Figs. an 3 epict the robustness of the syste when one of the ABR sources is faile. Fig.. Tracking control of queue length, Upper: Control feeback loop, Lower: The self tuning iniu variance regulator Fig.. Queue length when a failure is occurre to ABR source at t=6 Fig. 3. Bit rate available to ABR sources 6 Conclusions The self tuning iniu variance regulator propose in this article, is esigne to iniize the effect of stochastic isturbance inputs of the high priority sources to the syste. While the queue length ynaics at bottleneck noes is uneterine an the roun trip tie elays are uncertain an tie varying for controlle ABR sources, an online recursive least squares algorith can irectly tune the control paraeters to achieve the esire perforance. The propose controller is autoatic an just nees goo estiations of the iniu an axiu liits of the tie elays. This aaptive syste is also robust to the changes in network conitions, an the failure of ABR sources, to prevent buffer overflow an efficient use of network resources. Reference:. Ier O.C., Copance S., Basar T., Srikant R.: Available bit rate congestion control in ATM networks, IEEE Control Systes Magazine, Vol. 35, () Altan E., Basar T., Srikant R.: Congestion control as a stochastic control proble with action elays, Autoatica, Vol. 35, (999) Liansheng Tan, Yang S.H.: Rate-base congestion controllers for high spee coputer networks, IFAC 5 th Triennial Worl Congress, () Barcelona, Spain 4. Astro K.J., Wittenark B.: Aaptive Control, Aison-Wesley, n Eition, (995)