A Self-adaptive Predictive Congestion Control Model for Extreme Networks

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1 A Self-adative Predictive Congestion Control Model for Extree etworks Yaqin Li, Min Song, and W. Steven Gray ECE Deartent, Old Doinion University 3 Kafan Hall, orfolk, VA 359 {yli, song, sgray}@od.ed ABSTRACT To cobine the design strategies of both reventive control and reactive control, a self-adative redictive congestion control odel for extree networks is roosed. First, a odel is eloyed to redict the data traffic. Then the reference trajectory of the traffic is dated, and thereafter transission flow is adjsted according to the rediction reslts by otiization of a erforance index. The odeling of the syste can be erfored on-the-fly to accoodate the variation of network traffic and to adat to the ncertainties of the environent. Silations are rovided to evalate the syste. Keywords - Predictive control, self-adative control, congestion control, extree networks, and orthogonal fnctional series.. ITRODUCTIO Conication networks, sch as the Internet, are rotinely sbject to extree traffic conditions. One of the reasons is the lack of efficient congestion control. Extree networking is based on the idea that networks shold oerate reliably and offer excellent erforance to sers nder all ossible oerating conditions []. In extree networks, congestion controllers are careflly designed so that networks still oerate efficiently nder the worst-case condition. Varios congestion control echaniss roosed for conication networks can be classified into two categories: oen-loo reventive control and closed-loo reactive control. As the nae indicates, oen-loo reventive control techniqes attet to revent congestion by taking aroriate action before congestion actally haens. However, this techniqe is sscetible to network traffic ncertainties and other stochastic factors. Therefore, oen-loo reventive control does not rovide sfficient in networking congestion control in extree networks, which shold oerate robstly and offer excellent erforance to sers [3]. Conseqently, closed-loo reactive congestion control algoriths for network control have been roosed, sch as credit-based control and rate-based control [,4,]. The credit-based control schee oerates on a ho-by-ho basis, while the rate-based schee is an end-to-end flow control ethod [5]. Both aroaches have advantages and disadvantages. The credit-based schee is ch ore effective in reglating bandwidth iediately, bt it reqires ore overhead. The rate-based schee is cheaer to ileent, bt the latency of acting on forward and backward congestion notification can reslt in soe oscillatory behavior in the network. A odified rate-based schee is designed in a way that the Congestion otification (C) is directly sent fro the node at which congestion occrred to the involved sorces, rather than to the destination. This is based on the concet of virtal sorce/virtal destination [][7]. Congestion control incororating feedback ths involves the following featres: ) Recognizing the onset of congestion; ) Invoking an aroriate control; and 3) Sending a signal back to the sers casing congestion. Control ethodology, esecially the Model Predictive Control (MPC) aroach is widely sed in the stdy of congestion control in high-seed conication networks. MPC has been fond to be robst for systes with tie-delays, even ncertain ones. This characteristic akes MPC an effective tool in the control of network traffic to revent and resolve congestion. Most MPC-based congestion control schees roosed in the literatre are based on the ARMA (Ato- Regressive Moving Average) [9,] or CARIMA (Control Ato-Regressive Integrated Moving Average) odel [8]. The odels are eloyed to redict the bffer level, and the best-effort traffic rates are adjsted according to the rediction reslts. Tie delays are exlicitly inclded in those odels by an assignent of strctral araeters for syste identification beforehand. Incororating tie delay in the syste odel hels to coe with the resence of roagation delay in real-tie networks. Bt as the roagation delay in networks is always tie varying, resetting a tie delay in the odel ight indce robles. In order to irove the odel robstness in the face of large variations in tie delay, syste odeling based on orthogonal series exansions is introdced in this aer. The orthogonality of the basis brings robstness into the odeling and redces the cotational deands when a higher order odel st be constrcted sing an existing lower order odel. There are any choices for a colete orthogonal fnctional series in a Hilbert sace,

2 sch as Lagerre series, Legendre series, etc. For ost stable systes, the ott always lies in L or l sace, so it can always be reresented by soe fnctional series. In this aer, Lagerre fnctional series are eloyed for the syste odeling.. SELF-ADAPTIVE PREDICTIVE COGESTIO COTROL Two distinct classes of traffic are first defined: controllable (e.g., delay tolerant traffic, sch as available bit rate traffic) and ncontrollable (e.g., delay intolerant traffic, sch as real tie constant bit rate and variable bit rate video). Both coete for finite bffer and link resorces. This allows one to introdce the concet of network controllability. Controllability is achieved by sily bonding the ncontrollable traffic. The controller anilates the flow of controllable traffic into the network to reglate qality of service (QoS) based on a erforance onitor. Controllability garantees that the network can be oerated efficiently (theoretically at % tilization) and still rovide the ser with tightly reglated QoS. In other words, the delay tolerance of a certain class of traffic (controllable traffic) is exloited in order to garantee delay and loss for another class of traffic (the ncontrollable traffic). ote that loss (within the network) for the controllable traffic is also garanteed. A er-flow bffering schee is assed at the interediate switching nodes. First, a odel is eloyed to redict the data traffic. Then the reference trajectory of the traffic is dated, and thereafter transission flow is adjsted according to the rediction reslts by otiizing a erforance index. The odeling of the syste can be erfored in real- tie to react to variations of the network syste and to adat to ncertainties in the environent. The dynaics of the network qee are odeled by the difference eqation. qk ( + ) = qk ( ) + k ( ) dk ( ), qk ( ) is the bffer level at tie k ; k ( ) is the bffer int, which is the desired transission rate effective tie slots later on the bffer. Here, the delay is assed to be the roagation delay fro the sorce to the bottleneck bffer. Usally, the delay is ncertain and tie-varying. dk ( ) odels the best effort bandwidth that is available for the flow at the bottleneck link. In [8], the available service rate is odeled and estiated by a th order AR (Ato-Regressive) rocess: j= dk () d= α() j dk ( j) d+ φ( k ), d is the ean vale of the available caacity and φ is a zero-ean i.i.d. seqence with finite variance. Let ξ () k = d() k d, the th order AR rocess driven by φ is then j= ξ = α( j) ξ( k j) + φ( k ). The objective of this aer is to control the bffer occancy below the congestion threshold, and therefore redce the acket cell ratio. This stateent can be interreted as follows. First, a contract is assed between the ser/flow and the network. The flow is garanteed to receive a certain QoS rovided it confors to the contract. Therefore, the congestion controller ainly throttles the sers that violate the contract. Second, to irove the network tilization, the network will try to accoodate as ch traffic as ossible. Ths, a flow will be acceted as long as the exected bffer occancy is below the congestion threshold. In this aer, we address the congestion control in extree networks, i.e., we asse that heavy traffic is always resent at the bffer. So the ain objective of the controller is to kee the bffer occancy jst below the threshold. On the other hand, if there is not enogh traffic and the bffer occancy is far less than the congestion threshold, the controller jst behaves as a traffic observer. To redce overhead, the saling rate can be lowered in this sitation. The control objective is to iniize the erforance index { J = E δ() i q( i+ k) Q + [ + + ]} λ() i ( i k ) d( i k ) nder the constraints: q and, when congestion is abot to occr, and to onitor the bffer occancy when the occancy is far less than the congestion threshold. By changing variables xq = q Q = d, q the dynaic of the bffer occancy can be written as x ( k+ ) = x + ( k ) ξ () q q q

3 () ξ = α( j) ξ( k j) + φ( k ), j = and the objective fnction can be rewritten as { J = E δ () i xq ( i+ k) + λ() i q ( i+ k ) ξ( i+ k ) }. To aly the redictive control, the syste is reresented by a state-sace realization as follows. First, the state sace odel of the syste x ( k+ ) = x + ( k ) is reresented as an q q q extended Lagerre fnction odel [6]: L( k + ) = ALL + BL y = C L, q L Lk ( ) = l l l ( ) ( ) T k yq k is the extended state vector of the Lagerre fnction odel, CL = [ c c c ] is coefficient vector which can be identified and a η a AL = 3 ( a) η ( a) η η a c c c Al = Cl BL = η ( a) η,, ( a ) η η = a, a < is the constant araeter in discrete Lagerre kernel fnction. If one chooses a =, it will be exactly an integral syste with tie delay eqal to. By adative identification of the coefficients c, this odel can be sed to reresent any integral syste whose tie delay is bonded by soe finite. To incororate the odeling ncertainty, in this aer, we choose a to be in a neighborhood of. The th order syste reresenting the AR rocess is xar ( k+ ) = AARxAR + BARφ y = C x, AR AR AR A AR B AR = α α α = C =. AR The overall agented syste odel is x( k + ) = Ax + B + Gφ y ( ) ( ), k = Cx k xk ( ) = ( ) ( ) ( ) T xl k xq k xar k A l A = Cl C AR A AR T B = B l T G = B AR C = C C. l AR Select the redictive horizon as horizon as the syste will be, and the control, the estiated redictive state vector of xk ( + ) = Axk ( ) + Bk ( ) + Gφ x( k + ) = A x + AB + B( k + ) + AGφ + Gφ( k + ) xk ( + ) = A xk ( ) + A Bk ( + i) + A Gφ

4 x( k + ) = A x + A B + A Gφ The ftre odel ott can be estiated by y( k + ) = CAx + Cb + CGφ y( k + ) = CA x + CAB + CB( k + ) + CAGφ + CGφ( k + ) y ( k+ ) = CA x + CA B( k+ i) + CA Gφ y ( k+ ) = CA x + CA B( k+ i) + CA Gφ If the exected vale of φ is zero, the ott eqation can be written in a coact for Y( k + ) = HlX + HU + H ( ) φφ k = HX + HU, l CA CA Hl = P CA CB CAB CB H = CA B CB CA B CA B The state estiator can be constrcted fro the Lagerre odel as. xk ˆ( + ) = Axk ˆ( ) + Bk ( ) + Fyk [ ( ) Cxk ˆ( )]. The rediction fro the state estiator is Yˆ ( k+ ) = H xˆ P l = yˆ ( ) ˆ k y( k ) + +. Here y Cx = is the ott of the odel at tie k, and F is the state feedback gain. Generally, one can F = f, < f <. select P The P ftre horizon ott of the odel obtained fro the estiator is Yˆ ( k + ) = Yˆ ( k+ ) + H U. The reference trajectory vector of the syste Yr( k+ ) = yr( k+ ) yr( k+ ) can be constrcted and dated each ste by i i y ( k+ i) = α y + ( α ) w,,, r <α <, and w is the target bffer occancy. When congestion is abot to occr, the controlled int is obtained by iniizing the objective fnction J = Y ( ) ˆ r k+ Y( k+ ) + U, Λ = diag { δ δ }, Λ= diag { λ } λ are weights for erforance otiization. The otial soltion is ( ) T ˆ U () k = H ( ) ( ) QH+ R HQ Yr k+ YP k+ k ( ) = U. Least-sqare identification can be alied for the online cotation of the Lagerre coefficientsc. The forla for recrsive least-sqare identification is: Pk ( ) xk ( ) Ck () = Ck ( ) + [() yk Ckxk ()( )] T λ+ x ()( k Pk )() xk Pk ( ) xkx ( ) ( kpk ) ( ) Pk () = Pk ( ) λ λ+ x () k P( k )() x k. Here < λ < is the factor that deterines how fast the identification ethod forgets recent history. The redictive controller is activated when the bffer occancy is aroaching soe level (a little below the

5 threshold) and the bffer occancy is increasing. The traffic for otiized threshold tracking is calclated by the adative redictive rocedre described above. Once the bffer occancy is below the activation oint, the controller acts as a onitor for the syste. 3. SIMULATIO RESULTS The following silations deonstrate how the odel is sefl to control the bffer level nder the congestion threshold in an extree networking environent. The silations were erfored on a single congested node. The AR rocess is assed to be 3 rd order with α =.3, α =., and α =.. The target bffer occancy is set at.7. The araeters for the Lagerre odel are =, a =.. The araeters for otiization are: the rediction horizon =, the control horizon = 4, the weights = I and Λ=.I 4. The initial bffer 4 occancy is set to. The controller is activated whenever the bffer occancy exceeds.5. In all silation rns, only the controllable traffic is considered. the rate inforation to the ser throgh the interediate nodes. Whenever the ser receives this feedback inforation, it will redce the traffic according to the coand fro the controller. The controller is deactivated whenever the bffer occancy is going to be below.5, and then the ser can send traffic at the negotiated rate. Fig. also deonstrates the erforance that the ser attets to send traffic % faster than the negotiated rate when the controller is not in active. Fro the to art of Fig. one can see that the bffer occancy is ostly ket below the target.7 whenever congestion occrs, and the botto art of Fig. shows that the link tilization is close to %. In the case shown in Fig., the traffic is the sae as sed in Fig.. The roagation delay fro the ser to the congested node is assed to be a nifor distribtion on the interval (, 6). The controller shows robstness in the existence of delay variations. Still, the bffer occancy is ket below.7 ost of the tie, and the link tilization is near %. Fig. Perforance nder rando roagation delay (, 6) and exonential data rate increase Fig. Perforance nder a fixed roagation delay and exonential data rate increase In Fig., it is assed that the initial data rate is.3 of the negotiated bandwidth. This rate is dobled every 4 cycles before it receives the congestion control signal. At tie 84 (the roagation delay fro the ser to the congested node is fixed to 4), the bffer occancy is above the threshold and is increasing. Controller, therefore, cotes the accetable rate and sends back In the case shown in Fig. 3, it is assed the ser is sending traffic that increases linearly every cycles, beginning fro.3 of the negotiated bandwidth. The roagation delay of the syste is again fixed to 4. The ser is assed to send traffic that is % ore than the negotiated bandwidth whenever the controller is deactivated. In this case, the bffer occancy is ket at or below the target level. There are link nder tilizations and over-tilizations when congestion occrs, bt the overall link tilization is aroaching %.

6 4. COCLUSIOS This aer resents a self-adative redictive congestion control odel for extree networks that can tolerate fairly long roagation delays. It ses traffic rediction to forecast beyond the roagation delay. The orthogonal odel rovides robst control in the resence of varying roagation delay. Meanwhile, the sensitivity to traffic odeling is addressed by sing adative redictive control. REFERECES Fig. 3 Perforance nder a fixed roagation delay and linear data rate increase In Fig. 4, the roagation delay of the syste is assed to be a nifor distribtion on the interval (, 6). The traffic is the sae as sed in Fig 3. In this case, the bffer occancy is controlled below the target. The link tilization is % in the absent of congestion and is close to % whenever congestion occrs. Fig. 4 Perforance nder rando roagation delay (, 6) and linear data rate increase [] S. Kalyanaraan, et al., The ERICA Switch Algorith for ABR Traffic Manageent in ATM etworks, IEEE/ACM Transactions on etworking, Vol. 8, o., Feb., [] M. Song, Design and Perforance Analysis of Efficient Packet Schedling Algoriths for Internet Roting Switches, Ph.D. dissertation, The University of Toledo,. [3] htt:// [4]. Yin, M. G. Hlchyj, A Dynaic Rate Control Mechanis for Sorce Coded Traffic in a Fast Packet etwork, IEEE Jornal of Selected Areas in Conications, Set. 99. [5] R. Jain, Congestion Control and Traffic Manageent in ATM networks: Recent Advances and a Srvey, Coter etworks and ISD systes, Vol. 8, o. 3, , 996. [6] S. Li, Y. Li, Z. X, An Extension to Lagerre Model Adative Predictive Control Algorith, Jornal of USTC, Vol. 3, o.,. 9-98, Jan.. [7] D. McDysan, QoS and Traffic Manageent in IP and ATM etworks, McGraw-Hill,, [8] E. Melich and A. Barba, Congestion Control Algorith in ATM etworks, htt://casal.c.es/ieee/roceed/elich/elich.htl. [9] H. O. Wang, Y. G, and H. Fang, Robst Congestion Control in High Seed Conication etworks: a Model Predictive Control Aroach, htt:// nell/acc_gwhb.df [] J. W. Robert, Traffic Control in the B-ISD, Coter etworks and ISD Systes, Vol. 5, 99. [] A. Pitsillides, J. Labert, Adative Congestion Control in ATM Based etworks: QoS and High Utilization, Jornal of coter conications, , 997. [] J. Trner, Extree etworking Achieving onsto etwork Oeration nder Extree Oerating Conditions, DARPA PI Meeting, Janary 7-9, 3.