Dead-time compensation for ABR traffic control over ATM networks

DEAD-TIME COMPENSATION FOR ABR TRAFFIC CONTROL OVER ATM NETWORKS F. G´omez-Stern, J.M. Forn´es, and F.R. Rubio Dept. Ingenier´ıa de Sistemas y Autom´atica. Escuela Superior de Ingenieros. Universidad de Sevilla. Camino de los Descubrimientos s/n. 41092-Sevilla. SPAIN e-mail: {fgs,fornes,rubio}@cartuja.us.es Abstract This paper presents the design of a rate-based controller for throttling Available Bit Rate (ABR) input rates in high speed Asynchronous Transfer Mode (ATM) networks with significant propagation delays. First, a classical control scheme based on the Smith predictor is analyzed in order to point out its drawbacks in terms of performance and stability. Saturation issues are handled with anti-windup techniques, widely used in industrial PID controllers. Moreover, performance is notably improved by means of the feedback of an estimation of the ABR disturbance, which remains unknown to the switch. This reduces the average queue level drastically, thus guaranteeing the shortest delays possible while keeping the channel fully occupied. Finally, sensitivity to delay estimation errors is analysed, and the limitations of the proposed controller are discussed with respect to ABR traffic parameters. List of Acronyms ABR Available Bit Rate ACR Allowed Cell Rate ATM Asynchronous Transfer Mode CCR Current Cell Rate CDV Cell Delay Variation CLR Cell Loss Rate CTD Cell Transfer Delay ER Explicit Rate FIFO First In First Out queue policy ICR Initial Cell Rate MCR Minimum Cell Rate NRM Network Resource Management PCR Peak Cell Rate PID Proportional-Integral-Derivative linear controller QoS Quality of Service RM Resource Management VBR Variable Bit Rate VC Virtual Channel 1 Introduction In ATM Networks, ABR service is provided to make use of the available bandwidth left unused by other co-existing types of traffic. Traffic sources expect fair bandwidth assignment among all ABR connections sharing the link. ABR is thus non-deterministic, and end-users are notified of the available capacity by tagging Resource Management (RM) cells at rate 1/NRM cells per second. ABR bandwidth can be modeled as a disturbance to the system, and delays appear due to the time deployed by RM cells traversing the links. In high speed communication networks, long propagation delays are critical for the stability of closed-loop congestion control algorithms. Smith’s principle is a key tool to design a feedback control law for congestion avoidance and high speed ATM networks. Many algorithms dealing with congestion control using Smith’s predictor have been proposed (see [1], [2], [3] and [4] for arguments for using the Smith predictor). Due to large delays inside the feedback loop, queue level dynamics might exhibit oscillations. Since the model of the communicaction system is known without parameter uncertainty, a controller can be designed following Smith’s principle. It is worth noting that, in wide area networks, roundtrip delays are mostly determined by propagation delay. To include in the analysis the jitter of roundtrip time due to queueing time, a model containing different delays could be considered. A complete fluid-flow model considering transport delays is proposed in the literature [1], where input-output stability is guaranteed when using a proportional Smith predictor based controller. The controller performance is improved by adding an integral part to it, thus becoming a linear PI that can better reject disturbances [2]. This model is not complete as it lacks saturations in the control action. Regarding the control strategy, a fundamental aspect must be revised: the queue, modeled as an integrator, is an unstable system in the disturbance-output transfer function and, therefore, it will not be eliminated by a Smith predictor [10]. This implies a direct dependence between the steady-state queue level and the real ABR bandwidth. As a consequence, the higher the occupancy level of the queue, the greater the delays. This paper is organized as follows: First, a state-of-the art in ATM traffic management is included and ABR service on ATM is defined. Section 3 illustrates the system model and settles the control objective. Section 4 begins with a basic proportional controller inside a Smith predictor designed to handle transmission delays. A discussion on the sensitivity of the output under different ABR conditions leads, through various improvements, to a final PI controller with feedforward and anti-windup mechanisms which appears to be the best choice for this type of systems. Further simulation studies illustrate the efficiency of the proposed controller. The results section analyses the advantages and drawbacks of these structures and points out the most significant parameters to evaluate the output. A final conclusive analysis and further suggestions are included in section 6. 2 Available Bit Rate traffic ABR is an ATM layer service category defined by The ATM Forum [11] that may be used by applications which expect cell loss guarantees but can control their data dynamically as demanded by the network. In ABR there is a feedback mechanism to control the source rate in response to changing ATM layer transfer characteristics. An end-system that adapts its traffic in accordance with the feedback is expected to experience a low Cell Loss Ratio (CLR), although a quantitative value for CLR is network specific. This feedback is supported by specific control cells called Resource Management Cells, or RM-cells. The ABR source sends data at a rate less or equal than the Allowed Cell Rate (ACR), which in turn is smaller than a negotiated Peak Cell Rate (PCR) and greater than a negotiated Minimum Cell Rate (MCR). Immediately after establishing a connection and after an idle 2 time-out , ACR is set to an Initial Cell Rate (ICR), which is also negotiated with the network. The source sends an RM-cell after Nrm-1 cells, where Nrm is a parameter. Among the RM cell fields, the Current Cell Rate (CCR) field informs the network about the source’s ACR, and the Explicit Rate (ER) field is used by the network to give its rate feedback. The destination returns RM cells back to the source. The ABR framework is predominantly closed-loop, i.e., sources normally change their rates in response to network feedback. Open-loop control complements closed-loop control when the network delays are long compared to application traffic chunks, or when network feedback is temporarily disrupted. Although no numeric commitment is made regarding cell transfer delays (see section (2.3.1) of [11]), network providers are expected to advertise delay bounds for the class of ABR as a whole [6]. CTD (Cell Transfer Delay) and CDV (Cell Delay Variation) are agreed on for a VBR source whereas for an ABR source only MCR is agreed on. However, if the agreed CTD and CDV are not demanding, they can be easily satisfied and there may be a possibility to improve the quality of the ABR service by changing the class service priority. If a VBR source is sent, producing a deterministic CTD, the ABR source does not need to wait until the VBR source queue is empty, its CTD and CDV become smaller [7]. The introduction of VBR background traffic makes ABR capacity variable. ABR switch schemes usually use the current demand and capacity to calculate feedback to the sources. The variable demand and variable capacity introduces variance in measurements made by switch schemes, and as a result, in the feedback given. When the switch is overloaded the source takes feedback delay to respond to new feedback, and it is regarded to minimize its effect in following iterations between the source and the network. 3 System model The system model considered here for control is the same as used by [5], with a FIFO queue on each switch. We do not need a measure of ABR to design the control law and hence it will be regarded as a disturbance (d(t)). We consider a deterministic fluid flow model to obtain the cell rate. The control signal u(t) will be measured in cells/s and it is the ACR offered to ABR sources. The controller output is an indicator of the available capacity conceded to each source. This capacity is expressed as the bitrate allowed to be transmitted by the source.This information is transmitted within an ATM cell and is routed towards the origin of each source. Each virtual channel will receive the same u(t) and hence fairness is guaranteed because the controller fills the cells with the same information for all sources. Nevertheless, each source can receive the cells at different times due to the different paths followed by the cells on their way to the origin. As a consequence not all sources will adapt their traffic simultaneously. This effect is modeled by a different delay for each source. It is not necessary to consider this delay as being random because ATM is connection oriented and the path is fixed for each connection. Each Virtual Channel (VC) will receive the same u(t) and so fairness is assured. The level of the switch queue is represented by x(t) and is measured in cells. This will be the level of the bottleneck queue that constrains the input rate for the VC. The set point r(t)isan occupancy level of the queue and so x(t)≤ro, where rois the queue capacity, is the condition to prevent overflow in the queue. On the other hand, x(t)>0 prevents queue underflow and so full link utilization. The model presented serves as a starting point for the analysis, but it is insufficient for several important reasons. First, it ignores saturations in the control signal and the queue level. The control signal can never exceed the ATM limit of 155 Mbits per second. Moreover, it can never offer negative capacity values to the sources. This limitation becomes apparent 3 r(t) 1 s d(t) e-Tis e-Tns e-T s 1 . . . . . . - x(t) C(s) u(t) Figure 1: Control scheme for ABR very easily: whenever the controller tries to compensate for a very high occupancy level in the queue, it will try to lower it by giving negative ABR values to the sources. On the other hand there are queue saturations. As an upper limit there is the available memory of the switch. Over a certain level, cells that cannot be stored are discarded. This could play in favor of the controller, preventing the output from growing to infinity, but cell-loss rate is a QoS parameter that has to be respected. The lower limit is the zero occupancy level, which must be properly modeled for simulations. 4 Control design The aim of this section is to design a feedback controller that fulfills the following criteria: •The average occupancy level of the queue must follow the desired set point. •The set point should be low in order to reduce the size of the output buffer and, therefore, the response time. This parameter is critical in some applications as in voice communications or real-time video. A low set point will also permit oscillations without exceeding the queue capacity. •As a compromise with the last objective, it is desirable that the queue level does not stay at zero for long intervals, which would mean that the channel is not being fully used. This implies that the set point should be adjusted (raised) taking into account the expected standard deviation of the buffer size. •The bandwidth must be fairly assigned. This is achieved in the control scheme (1) by generating a unique control signal which is delivered to each traffic source. •The delays of bandwidth notifications must be treated with dead-time compensation techniques to prevent oscillations. •The minimum cell rate (MCR) should be considered in the cases where this ATM Forum specification parameter is required. •The effect of transients in ABR capacity must be studied to view the limitations of the proposed controller. The presence of time delays in the system can alter the behavior by introducing oscillations or even causing instability. A classic approach to this, which has proved to be robust is the Smith predictor structure [9]. In this type of controller, the delay is separated from the model so that the nominal plant is described as Pn(s)=Gn(s)e−sT ,Gn(s) being the model without delay. Thus, the controller is designed to compensate Gn(s), and the estimation error is also corrected by a feedforward block Pn(s) with the delay. This scheme can be best understood in Fig.(2). 4 - Gn(s)e-sT Controller - Gn(s) Plant Output - Set Point Figure 2: Smith predictor structure In this figure, Pn(s)=Gn(s)e−Tisis the nominal plant. The inner controller compensating Gn(s) has to be determined. Re-arranging the structure, we can group this controller into only one block, as seen in Fig.(3). - Gn(s)e-sT Controller - Gn(s) Plant Output - Set Point d(t) + - Simth's Predictor C(s) Figure 3: Equivalent Smith predictor structure with disturbance This structure has the advantage of designing the controller as if there were no delays at all. Once the nominal plant is compensated using classical control techniques, we must observe the closed loop transfer function in order to analyze the behavior of the controller. Assuming a perfect model of the plant: X(s) R(s)=C(s)Pn(s) 1+C(s)Gn(s) where X(s) is, again, the output and R(s) is the set point. Another point of interest when using a Smith predictor architecture is the ability of the system to compensate for a nonzero averaged disturbance in the plant. By looking at the disturbance-output transfer function: X(s) D(s)=Pn(s)1−C(s)Pn(s) 1+C(s)Gn(s)(1) The poles of P(s) cannot be eliminated from this relation, and therefore the classic Smith architecture is not suitable to control unstable plants. In the sequel, the different approaches used in order to choose the internal controller of the Smith Predictor will be discussed. 4.1 Smith predictor with proportional controller The first controller studied is a Smith predictor with a proportional controller inside. It can be easily proved that this controller is sufficient to ensure input-output stability. Here, the transfer function of the controller, including the feedback of the nominal plant is obtained: C(s)= k/n 1+k/n s(n−n i=1 e−Tis)(2) 5 where nis the number of sources, kis the constant of the internal proportional controller and Tiis the delay of each source i. Including the expression of the controller in the block diagram of figure 1 and the expression of the Laplace transform of the occupancy level of the queue X(s) yields: X(s)=k/nn 1e−Tis s+kR(s)−1+k/s −k/(s·n)n 1e−Tis s+kD(s)(3) As can be observed in equation 3 the closed loop system is stable for all k>0 and it behaves like a first order system with a time constant 1/k. In addition to this, oscillations will appear due to the delays. It is also important to have an expression to calculate the steady state queue level. We can see how it is related to the amplitude of the disturbance d(t): x∞=r∞−1+k/nn 1Ti kd∞(4) To view the limitations of the proportional controller the following simulation analysis has been made. The simulated system has six sources with time delays varying between 0.01 and 0.1 seconds and a controller gain of 60. It has been stated that when a proportional controller is used, the queue level highly depends on the set point and the available bit rate. Let us suppose that under some particular traffic conditions denoted by ABR0, the set point r1has been established at the minimum required to maintain the queue level always above zero, i.e. the channel being occupied 100% of time. In Fig.(4), R1is the actual queue level when the set point is r1. The ACR for each sequence is shown in Fig.(5); thus, 1 Mbit/s is conceded approximately. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 1 2 3 4 5 6 7 8 9 10 Time(s) ABR used, Mbits/s ABR used 0 1 2 3 4 5 6 7 8 9 1 0 0 0.1 0.2 0.3 0.4 0.5 0.6 Time(s) Queue level, Mbits P controller, low ABR Figure 4: (a) ABR0[2-10 Mbps], (b)Queue level, P controller Now suppose that due to external conditions, the ABR traffic level increases to a different situation, namely ABR1>ABR 0. If the set point is kept at r1the queue level will decrease according to (4) and it will be too low to remain above zero, wich means that in some cases, the channel will be underused. Fig.(6) shows the queue level when ABR is ABR1. By observing the level of the queue we conclude that the channel is left unused used most of the time. To recover the queue up to a level where the channel is occupied 100% of time it would be necessary to raise the set point. It will be adjusted to r2>r 1in order to have an optimal link utilization. Fig.(7) shows the resulting queue level. It is obvious that an extremely low queue level can be restored by raising the set point. Nonetheless if the external conditions return to ABR0the average queue level may be too high and transport delays could exceed their maximum permitted. In Fig.(8)it is shown that keeping the set point at r2and changing the ABR to ABR1results in an excess of average queue level. This analysis leads to the conclusion that under bursting ABR conditions, the set point must be readjusted continuously to keep performance optimal (lowest delay and full channel 6 0 1 2 3 4 5 6 7 8 9 1 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Time(s) ACR conceded, Mbits/s ACR conceded Figure 5: ACR per VC, ABR0[2-10 Mbps] 0 1 2 3 4 5 6 7 8 9 1 0 −0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 Time (s) Queue level, Mbits P controller, high ABR. Empty queue. Figure 6: Queue level, P controller, ABR1[36-44 Mbps] 0 1 2 3 4 5 6 7 8 9 10 0 0.5 1 1.5 2 2.5 3 3.5 4 Time (s) Queue level, Mbits P controller, high ABR. Queue level restored with new set point Figure 7: Queue level restored, P controller, ABR1[36-44 Mbps] utilization). Some improvements in the controller may reduce overall sensitivity as will be explained in the following sections. 4.2 Smith predictor with PI controller The addition of an integral term into the inner controller of the Smith Predictor will reduce the undesired sensitivity to ABR conditions. A straightforward calculation leads to the steady7 0 1 2 3 4 5 6 7 8 9 10 0 0.5 1 1.5 2 2.5 3 3.5 4 Time (s) Queue level, Mbits P controller, low ABR. New set point is too high Figure 8: Queue level, P controller, ABR0[2-10 Mbps] state queue level when using a PI controller: xPI∞=r∞−Ti nd∞(5) The term affecting the disturbance d∞can be compared to the one obtained with a proportional controller in equation 4 to observe that the PI is more efficient in rejecting this value: Ti n<1+k/nn 1Ti k(6) where the term on the left is the expression of the PI case. The improved behavior will be illustrated via simulation. Now let us simulate the system with a PI controller and ABR=ABR1[3644 Mbps] as in the last section. The set point r3is adjusted in order to have an optimal link utilization, as shown in Fig.(9). Due to the PI action, this reference must not be set as high as before, i.e. r3<r 2. 0 1 2 3 4 5 6 7 8 9 10 0 0.5 1 1.5 2 2.5 3 Time (s) Queue level, Mbits PI controller, high ABR. Set point is adjusted for optimum Figure 9: Queue level, PI controller, ABR1[36-44 Mbps] Now if the ABR suddenly falls to ABR0, the same reference r3(optimal for ABR1)givesa reasonably low queue level for ABR0, as shown in Fig.(10). This level is lower than the one in Fig.(8), obtained with a P controller, under the same circumstances, i.e. a constant reference for different traffic loads. As a conclusion, bursts in the ABR conditions can be more efficiently compensated for when a PI controller is used, with respect to the P controller. It is not necessary to continuously readjust the set point to keep a good performance (lowest delay and full channel utilization). Nevertheless, the queue level for low ABR values are still relatively high, and sensitivity to ABR conditions remains high. The controller can be improved to further reduce this sensitivity. 8 0 1 2 3 4 5 6 7 8 9 10 0 0.5 1 1.5 2 2.5 3 Time (s) Queue level, Mbits PI controller, low ABR. Set point adjusted for high ABR remains valid Figure 10: Queue level, PI controller, ABR0[2-10 Mbps] 0 1 2 3 4 5 6 7 8 9 1 0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Time (s) Queue level, Mbits PI controller, step−wise ABR ABR 50 Mbps ABR 30 Mbps ABR 10 Mbps ABR 20 Mbps Figure 11: Queue variations with a step-wise ABR, PI controller 4.3 PI controller with feedforward In order to compensate for the control delay caused by the NRM cells, a Smith predictor has been proposed. A PI controller inside attempts to lower the average queue level but it will not fully compensate for it, as is shown by the disturbance-rejection transfer function in Smith predictors (see [9]). This has been stated in equation (1). The previous section illustrates the effect of ABR variations on the average queue level. As Fig.(11) shows, steps appear in the average queue level, as ABR conditions change in a step-wise manner. Nevertheless, the structure can be modified by injecting the disturbance signal (if available) into the inner control loop of the Smith predictor. The disturbance-rejection transfer function then becomes: X(s) D(s)=Pn(s)−1 1+C(s)Gn(s)(7) Here, the PI controller C(s) will compensate the unstable pole of P(s). Whereas this is true whenever the disturbance is known (see Fig.12). As a result, the steady-state queue level would not depend on the average ABR, and the set point can be reduced to the optimal level for any ABR conditions. This is illustrated in Fig.(13). However, the disturbance is often difficult to measure and a noisy estimation should be enough. In those cases, a properly adjusted feed-forward filter can be added in order to handle estimation errors. In the problem treated here, the real ABR capacity is unknown to the switch, but the switch can observe the movements of the queue level. Differentiating the queue level with respect to time and subtracting the control signal from it yields the estimation. Nevertheless, this will be a very noisy estimation because control signals are delayed and 9