The effect of per-input shapers on the delay bound in networks with aggregate scheduling

Transcription

1 The effect of per-input shapers on the delay bound in networks with aggregate scheduling Evgueni Ossipov and Gunnar Karlsson Department of Microelectronics and Information Technology KTH, Royal Institute of Technology, Sweden Abstract. In order to provide modern multimedia applications with firm guarantees on quality of service (QoS) we have proposed a simplified guaranteed service. In this paper we introduce a router model with per-input shapers for the aggregate flows at the output ports. We calculate the delay bound for the guaranteed-service traffic. The existing QoS architecture for differentiated services does not give a computable delay bound, which is essential for interactive real-time communications. We show that at the expense of some modifications to the structure of the output port of the routers it is possible to compute a finite delay bound in the case of aggregate scheduling. 1. Introduction The problem of computation of a finite delay bound in a network with aggregate scheduling is known since three years ago. The RF 2598 [3] for the expedited forwarding PHB states that the finite end-to-end delay cannot be computed unless serious restrictions on the EF utilization and network topology are imposed (the ustification of this claim is extensively given in [4,5 and 6]). This is due to the specific properties of the strict priority first-in-first-out (SP FIFO) scheduling where the creation of a burst of several packets cannot be controlled in the network. The work in [7] elaborates on the reasons for the instability of the FIFO scheduling algorithm. Nevertheless the need for computable delay bounds for real-time application remains. An architecture for a simplified guaranteed service (GS) has been proposed in [7, 10] in response to the growing demand on quality of service for real-time applications. The architecture combines the strengths of the two dominant QoS architectures in today s Internet: The integrated services (intserv) [1] and the differentiated services (diffserv) [2]. Our definition of the guaranteed service is similar to the one of the intserv: The service should provide absence of packet loss in routers and tightly bounded delay. The capacity for a GS connection should be explicitly reserved in every router on a path of a connection. In the case of our architecture an application can reserve the capacity specifying only the desired rate, which is an upper bound on source s bit rate. The specification of the proposed signaling protocol is presented in [11]. In comparison to the intserv, where scheduling

2 is done per flow, in our architecture we schedule all the flows of the GS class together in the diffserv like manner. In our architecture we assume the reservation state to be purely additive: The reserved rate of an outgoing link of a router equals the sum of the incoming rates for the link. In order to satisfy the properties of our service model, a router needs a special scheduling algorithm to enforce additivity of the reservation state and to ensure absence of packet loss for GS traffic in the network. The designed scheduling has the following properties: It works with variable length packets up to some MTU. The algorithm prevents starvation of best effort traffic. The calculated buffer space for the GS traffic in the routers is enough to avoid packet loss, taking into account the worst arrival pattern. The scheduling algorithm that we will analyze in this paper was originally proposed in [9], we will refer to this algorithm as SGS, which is an acronym for scheduling for a guaranteed service. We will concentrate on a router model with two stages of such schedulers which allow the computation of a finite delay bound in the case of aggregate scheduling. Our contribution is essentially the development of the twostage scheduling architecture and the formal and experimental analyses of the delay properties of this approach. The remainder of the paper is organized as follows. In Section 2 we describe our scheduler. A formal calculus of the end-to-end delay bound is presented in Section 3. The comparison of the delay bound to experimentally obtained values is given in Section 4. We summarize our work in Section Scheduling for a Simplified Guaranteed Service The router model that we are considering for the analysis defines a cascade of schedulers at the output port, as shown in Figure 1. In the first stage of the cascade we have a set of schedulers that are responsible for smoothing out the incoming flow aggregate from a particular input port directed to the output port. A scheduler in the second stage interleaves packets from different input ports so that additivity of the outgoing data rate is preserved and the traffic of other service classes is not blocked. Output scheduler First stage of of the second The scheduling rule for the schedulers stage output scheduler in the second stage is straightforward. The scheduler 1,n will serve one or more packets from q_gs 2,n n-1 the GS queue (q_gs in Figure 1), input ports n and it will schedule an idle period n-1,n that is long enough to preserve the q_be outgoing reserved rate of the GS traffic. During the idle period, it output port n will serve packets from other Fig. 1. Router model for guaranteed service flows. service classes (for simplicity of discussion we assume that there are only two traffic classes: the guaranteed service and the best effort service). The number of GS packets served SWITH

3 back to back at link speed is called a GS burst. The reservation ratio of the output port GS in a router is defined as. Idle GS We compute the smallest value of a GS burst so that is maintained and the idle period is long enough to transmit one BE packet of maximum size. Thus, the size of the burst of the guaranteed service traffic is at most MTU bytes for > 0.5 and 1 at most MTU for 0.5. The traffic patterns which are possible with our scheduling for different values of the reservation ratio are illustrated in Figure 2. GS MTU Idle Idle MTU GS GS BE BE GS BE BE GS BE GS GS BE GS GS BE a.) 0.5. b.) >0.5. Fig. 2. Output traffic patterns of our scheduling. The schedulers in the first stage are the same type as the output scheduler except that during the GS idle period they do not serve any traffic and the idle period can hence be of any length. In our architecture an application can reserve the capacity on an outgoing link specifying only desired rate. Therefore an individual flow i is constrained by a single leaky bucket with the rate parameter r i and the burst equals maximum transfer unit. Furthermore we define as the minimum allowed rate, or reservation quantum as defined in [10], for a GS connection measured in bits per second. We also require that sources reserve the desired rate as multiples of, therefore n. Denote the capacity of all network links as. Denote the share of r i the outgoing GS capacity for the shaper () as. We have the following properties of our scheduling scheme: The reserved peak rate of individual flows is preserved. An aggregated output flow is smooth. While certain subaggregates of the output flow can be bursty with respect to the output port of the next downstream router, the burst size is finite and easy to compute. The first property follows directly from the property of a shaper in network calculus: The shaper keeps the arrival constraints of a flow [6]. What a shaper does is that it delays the packets which would violate the constraint for the output traffic. The second property of our architecture follows from the use of a non-work-conserving output scheduler. It will multiplex and shape aggregates from different inputs so that the outgoing peak rate of GS traffic equals the sum of individual rates. Although all individual flows in an aggregate at a particular input are smooth because of shaping in the upstream router the aggregate directed to an output port can be bursty as described in Section 3.1.

4 3 Delay bound calculus In this section we present a calculus of the delay bound for our scheduling algorithm. The calculus of the end-to-end delay bound, D e2e, is based on the following property of shapers: The shaper does not increase the delay bound [6]. Therefore calculating the worst-case delay in one node, D node, will mean that all other nodes will introduce the same delay bound for the aggregate. Hence D hd, where h is the number e2 e node of routers traversed by the flows. Before proceeding further with the calculus we make an observation about the burst creation process when our scheduling architecture is used. 3.1 Quantification of a burst of a subaggregate under our scheduling onsider a network of four routers depicted in Figure 3. Assume all routers have the architecture depicted in Figure 1. Router one in the figure aggregates the traffic from a number of sources. The total rate of the aggregate on the link between router one and router 2 is ten packets per second (pps). The aggregate consists of ten individual connections, each with a rate of one pps. The individual connections in the aggregate are shaped by the sources according to their reservations. Let us pick input port one of router two at which traffic from router one arrives. Router 3 a) i h g f e d c b a i h g f e d c b a Router 1 1 Router Router 4 b) c) Time, future Time, future Time, future i 1 second g e c a i g e c 1 second e d c b a e d c b a 1 second a Fig. 3. A network topology for the definition of a burst. Fig. 4. The possibilities of arrival of the five pps aggregate. In Figure 4a we have an aggregate flow of ten packets per second (pps), observed at the shaper of the considered input of router 2 during two seconds. Now, consider the possibilities of the arrival of a part of the aggregate with a total rate of five pps to the output port two of this router. The best case for the corresponding queue will be when the aggregate of five pps is smooth. This will occur when connections a,c,e,g,i are destined to port two (Figure 4b), but it could also occur that the five pps aggregate will consist of flows a,b,c,d,e (Figure 4c). We can quantify the burst of a subaggregate directed from the input i to the output as follows. The worst case for a particular input shaper will be when the number of MTU-sized packets arriving back to back from the upstream router (with the rate of the whole aggregate) is equal to the number of GS connections with minimum allowed bit rate. In our service architecture the minimum allowed bit rate b/s is a constant specified for the guaranteed service. With knowledge of the number of i connections with this rate is equal to Num,.

5 3.2 alculus of the delay bound for SGS scheduling Let us now calculate the delay bound at a node. Recall the structure of the output port of a router shown in Figure 1 and consider a cascade of two routers as shown in Figure 5. In each router we have two SWITH 1,n 2,n n-1,n Router k n output port n SWITH Router k+1 1, 2, n-1, stages which introduce delay for the aggregate. In the first stage we have per-input shapers. Let us denote the delay after this stage as D 1. In the second stage packets from all shapers are interleaved at the output scheduler, denote the delay in this stage as D 2. Finally the delay experienced by an aggregate at a particular router is simply D node =D 1 +D 2. Let us now derive expressions for the arrival and service curves in our scheduling scheme. For the calculus we assume that all links in the network have the same reservation ratio and the capacity of each link is. 3.3 The service and arrival curves The traffic pattern generated by our scheduling algorithm is a sequence of GS bursts followed by idle periods. Graphically it can be represented as shown in Figure 6 for 1, where is the minimum possible reservation ratio. Depending on the value of the reservation ratio, the service curve of the output scheduler for the aggregate can be stated as: t min t, t GS(1 ) out (1) As is stated in Section 2, the length of the GS burst depends on the value of and is MTU, 0.5 GS MTU, output port Fig. 5. Output ports of two directly connected routers umulative service GS GS(1-) Slope= t (t)=min(t, t+gs(1-)) Fig. 6. Service curve for the aggregate 1, (t) is a bound on service curve of the aggregate, GS is the length of the GS burst. t (2)

6 Recall the cascade of two routers and consider the shaper () in router k+1. The shaper smoothes out an aggregate from input port i directed to output port. Since in our architecture the shaper () is the same kind of scheduler as in the output case a service curve for the subaggregate in the shaper () is t t MTU 1 ) (3) ( where is the reservation ratio of shaper (); note that GS burst is one MTU in this stage for all reservation ratios. In Section 3.1 we quantified the worst case burst which can arrive to the shaper as i the number of connections with minimum allowed rates Num,. The arrival process of the subaggregate entering the shaper () is bounded by a curve which is the minimum between the arrival curve of the whole aggregate arriving at input i and the arrival curve that describes the subaggregate. Since the output scheduler is a shaper, then according to the definition of a shaper [6]: The arrival curve of the whole aggregate equals the service curve out of the output scheduler in router k. a t min t t b (4) i, out, The burst parameter b in (4) depends on, the share of the outgoing capacity reserved from a particular input port. Namely, if the number of connections with minimum rate is smaller than the number of packets in the GS burst of the aggregate as shown in Figure 7a, then MTU Num bits may arrive at link speed. Otherwise, if the number of connections is larger than the number of packets in the GS burst, MTU Num bits will arrive with the rate of the aggregate as shown in Figure 7b. umulative arrivals t umulative arrivals MTU Num t GS MTU 1 MTU Num b MTU a (t) out(t)=min(t, t+mtu) t GS MTU 1 b MTU a.) MTU Num GS b.) MTU Num GS a (t) out(t)=min(t, t+mtu) Fig. 7. Arrival curve of the subaggregate 0.5 1, out (t) is a bound on arrival curve of the aggregate and a is a bound on arrival curve of the subaggregate. onsidering the service curves of the output of router k for all possible values of and accounting for all possible values of in router k+1, b is calculated as t

7 MTU b MTU (5) 1, and, 1 1 GS 1, otherwise. 3.4 Delay calculus of the first stage onsidering the arrival curve a and the service curve of the shaper for all possible values of we calculate the delay after the first stage as the maximum horizontal deviation between a and. The resulting formula is MTU D1 MTU MTU 1 1, GS 1 MTU 1 1, and otherwise. 1 Assume the following choice of parameters: =100Mb/s, MTU=576B, =100kb/s. The plots in figures 8a and 8b show the dependence of D 1 on the value of the reservation level in shaper () for different values of the total reservation level on the links., (6) Delay, s ={0.8,1.0} MTU/ Delay, s MTU/ =0.2 =1 =0.8 =0.2 a.) 1,. i b.) Small. Fig. 8. Delay of the first stage vs. reservation ratio at the shaper Figure 8a shows that for the values of equal to and 1 the shapers of the first stage do not introduce the delay. In both cases the system is transparent for the aggregate flows. The case where corresponds to one GS flow with the minimum rate traversing the shaper (). The arrival curve of the flow in this case equals the service curve of the shaper, therefore D 1 =0 in this case. In the case where 1 the whole aggregate from the upstream router traverses the shaper, in this case the arrival curve for the aggregate equals the service curve of the upstream

8 output scheduler. Again the arrival curve for the aggregate and the service curve of the shaper () are equal and D 1 =0. We can observe from the figures that for the MTU values of in the range (0.01, 0.03) the maximum delay tends to which is The implications of this observation are described in the next section. 3.5 Delay calculus of the second stage and buffer requirements Recall our architecture of a router with shapers. In the first stage incoming aggregates pass through the shapers. In the second stage, smooth aggregates from n-1 inputs arrive to the queue of the output scheduler. The service curve of the output scheduler is given as t min t, t GS(1 ) out (7) An arrival process of the whole aggregate is bounded by the following arrival curve. t t n MTU a 1 (8) 2 In (8) n 1MTU is the number of packets which may arrive simultaneously from n-1 input ports. Now computing the maximum horizontal deviation between a 2 and out we obtain the bound on the delay in the output scheduler. D 2 n 1 MTU GS 1 At the final step we compute the delay bound at any node: D max 2 (9) D 1 D (10) node In (10) max is the value of the reservation ratio in shaper () that maximizes D 1. In Section 3.4 we found that the dominating term which contributes to the maximum MTU delay was. Therefore the smaller the value of the minimum allowed GS rate, the higher the delay bound. As an example let us calculate the delay bound for a network with the following parameters. The maximum number of routers between any two edges of the network is h=10. All routers in the network have 10 ports. The capacity of all links is 100 Mb/s, in the attached links 20 Mb/s is available for the guaranteed service traffic (=20Mb/s), and the MTU is 576 bytes. Assume we designed the network to support individual calls from a computer to a GSM phone; therefore, we set the minimum allowed GS rate equal to 13 kb/s. The maximum end-to-end queuing delay with 10 routers is 3.4 seconds. This is of course unacceptable for real time voice communication. However if under the same conditions the minimum allowed GS rate is 390 kb/s which corresponds to 30 GSM calls, the end-to-end queuing delay with 10 routers is 106 milliseconds which is more acceptable for this type of service. In fact in order to provide a guaranteed service for low bit rate applications a network operator can establish channels of larger bit rates to gateways for a particular service. In the example of calls to GSM phones, the

9 network provider can reserve a channel to the gateway for 30 users and offer this channel to its customers (the task of channel establishment for a particular type of application is out of scope for this paper and will be considered in future work). 4. Experimental study In this section we present the description of simulations which we conducted to evaluate the delay properties of our scheduling. We will show that the delay values obtained from simulations are bounded by the theoretically computed values and the effect of having per-input shapers at the output ports of routers. We have implemented our scheduling algorithm in routers for the network simulator ns-2 [13]. The aim of the experiments was to compare the maximum endto-end delay and the delay itter which we achieve with our scheduling architecture to the same conditions when using the expedited forwarding per hop behaviour of the differentiated service architecture. According to the specification of the EF PHB [3] one way to provide necessary QoS for the delay-sensitive applications is to treat EF flows as the highest priority flows. One can use a class-based output scheduling in routers (e.g. per-class weighted fair queuing) or a strict priority FIFO scheduling. A series of simulations were performed in order to compare the performance of our scheduling algorithm to WFQ scheduler. The extended results of our simulations including the comparison of the delay properties of SGS to SP FIFO are given in [12]. In order to study QoS characteristics of the above mentioned scheduling algorithms we modeled the case where arriving traffic contains bursts. Recall that in our architecture we use additional schedulers at the output port of a router as was shown in Figure 1. The purpose of these schedulers is to smooth out the bursty input traffic. The main difference of an EF router from our approach is that it does not have such shapers for the incoming aggregates at the output. Therefore, under WFQ a burst of packets from individually smooth flows can be created at the output of an upstream router as shown in Figure 9a. Once created it will appear at the output of the next router. In our architecture this burst will be smoothed out and will appear at the output port of the downstream router as shown in Figure 9b. a) e d c b a e d c b a BE(1) GS(2) GS(2) SINK1 Time, future 1 second GS(1) GS(n) GS(n) b) Time, future e d c b a e d c b 1 second a GS(2) GS(n) R1 R2 Rn-1 Rn BE(2) SINK SINK2 Fig. 9. Burst of a subaggregate. Fig. 10. The experimental topology. 4.1 Simulation description We used the topology in Figure 10 to study the delay properties of WFQ and SGS scheduling. In Figure 10 we consider a part of a network. The following setup was

10 used: R(1) to R(n) are the routers on the path of an aggregate flow from GS(1). The source GS(1) is an access gateway to the network. We will refer to this source as the monitored GS source. Sources GS(2) up to GS(n) are core routers connected by one of their output ports to the sequence of routers R(1) to R(n). We will refer to these nodes as background GS sources. Sources BE(1) and BE(2) are two sources which transmit best effort traffic. All links in the network are loss free, the capacity of each link is 100Mb/s and the delays on the links are 10 ms. A flow from GS(1) traverses the path towards SINK1. The best effort flows from BE(1) and BE(2) follow the path towards SINK2. The background GS traffic follows the path towards a SINK connected to the next downstream router. In all experiments the number of hops between GS(1) and SINK1 was 3, 5, 10, and 15. We used 10 background GS sources in all experiments to feed each router. The aggregated rate of GS(1) is set to 4Mb/s; the rest of the capacity available for the guaranteed flows is equally distributed between sources GS(2) up to GS(N); the best effort flow from BE(1) is 10 Mb/s; the rest of the capacity available for the best effort flows is assigned to BE(2). In our experiments we set MTU=576B. Experiments were done with the BR traffic. We conducted two experiments for the two types of schedulers, firstly with a reservation of 80 percent on all links secondly with 20 percent. The goal was to measure the end-to-end delay of the monitored flow and to see whether SGS scheduling introduces smaller queuing delay than WFQ. Then we repeated the simulations for the VBR traffic. The duration of each simulation was 20 seconds. We measured the average delay from 15 independent runs of each experiment. In each invocation the random generator was randomly seeded based on the current system time. This is recommended when using ns-2 to obtain non-deterministic results for the same simulation setup. In the experiments 95% of the measured delay values fell within 50 microseconds from the mean value. In order to capture the steady state behavior we began the measurements five seconds after the simulation was initiated. 4.2 Theoretical vs. experimental delay bound Let us apply now the delay bound (10) to our experimental topology (see Figure 10) and compare the results with the delay values obtained from simulations. In our experiments the monitored flow enters every router through a designated input port and is multiplexed at the output with flows arriving from other inputs. In order to compute the bound for this particular case consider an input shaper where the monitored flow arrives. Thus, setting =4 Mb/s and MTU=576 B as in our simulations we obtain the delay bound as shown in Figure 11. As we can see for both values of utilization factor the theoretical curve indeed bounds the experimental one. The maximum queuing delay for the monitored flow after 15 routers is 23 milliseconds in simulations with =0.2 and the theoretically computed bound for the same conditions is 33 milliseconds. As for the case where =0.8 the maximum delay attained in the simulations is 5 milliseconds and the theoretically computed bound is 8 milliseconds. The difference in the delay values between those obtained experimentally and those obtained theoretically is in order of tens of milliseconds. This is because in our experiments we could not model the worst possible case where the arrival time of packets from different inputs is synchronized in all routers.

11 Delay, s Theoretical Simulations Delay, s Theoretical Simulations Hops, h a.) =0.8 b.) =0.2 Fig. 11. Theoretical vs. experimental delay bound. Hops, h We continued our experiments by looking at the delay itter of the monitored flow for the VBR case. For the experiments using VBR flows, we modeled all GS sources as exponential on-off sources. Their peak rates are the same as in the BR case. The mean duration of ON/OFF periods is the default value for ns-2 and is equal to 500 milliseconds. Simulations show that for both values of the reservation level our scheme introduces much smaller itter than WFQ scheduling, Figures 12 illustrates this. When making a comparison of SGS with WFQ scheduling we may observe the effect of having per-input shapers at the output ports. Although functionally WFQ is similar to our algorithm, in the sense that the outgoing traffic rate is not larger then the sum of individual rates it has to deal with bursty traffic from the inputs. The traffic destined to a particular output port arrives with the rate of the aggregate from all inputs while the output WFQ scheduler works at the rate much lower than the sum rates of these aggregates. This causes very large queuing delay, which results in high delay itter values when WFQ scheduling is used, figures 12a and 12b show this. Delay itter, milliseconds WFQ SGS Delay itter, milliseconds WFQ SGS Number of hops Number of hops a.) =0.2. b.) =0.8. Fig. 12. End-to-end itter of the monitored GS flow for the VBR case with WFQ and our scheduler. 5 Summary In this paper we described the effect of having per-input shapers in the output ports of routers on the end-to-end delay of aggregate flows. We studied the per-input shapers in the context of a simplified guaranteed service which we are developing. Although the presented analysis uses the primitives specific for our guaranteed service, i.e.

12 explicit reservation of capacity, the reservation quantum, and the property of additivity of the reservation state, the results are general. The finite delay bound in the case of aggregate scheduling can be computed at the expense of some modifications in the internal structure of routers. From the viewpoint of implementing such an architecture consider the following, the assignment of the reservation ratio as well as n will be done during the connection establishment phase of each session. The signaling protocol which we have developed can perform this fast, see [11] for details. Since the number of queues equals the number of input ports in a router, they are limited to tens of ports. Implementation of that number of queues is feasible in fast routers. The classification and placement of packets into appropriate queue requires some modifications in the internal routing procedure of the switching fabric. However in this paper we are not concerned with the scheduling for the switching fabric, and leave this issue for future work. References [1] R. Braden, D. lark, and S. Shenker, Integrated services in the Internet architecture: an overview, RF1633, IETF, June [2] S. Blake, D.Black, M.arlson, E.Davies, Z. Wang, and W. Weis, An architecture for differentiated services, RF 2475, IETF, December [3] V. Jacobson, K. Nichols, K. Podur An expedited forwarding PHB, RF 2598, IETF, June [4] J-Y Le Boudec, A proven delay bound for a network with aggregate scheduling, EPFL- DS Technical Report DS2000/002, [5] A. harny and J-Y Le Boudec, Delay bounds in a network with aggregate scheduling, In Proc. of first International Workshop on Quality of Future Internet Services (QoFIS 00), October [6] J.Y. Le Boudec, P.Thiran, Network alculus, Springer Verlag LNS 2050, June [7] M. Andrews, Instability of FIFO in session-oriented networks, In Proc. of eleventh annual AM-SIAM Symposium on Discrete Algorithms (SODA 2000), January [8] G. Karlsson, F. Orava, The DIY approach to QoS, In Proc. of Seventh International Workshop on Quality of Service (IWQoS 99), 1999, pp [9] M. Mowbray, G. Karlsson, and T. Köhler, apacity reservation for multimedia traffics, Distributed Systems Engineering, vol. 5, 1998, pp [10] E. Ossipov, G. Karlsson, A simplified guaranteed service for the Internet, In Proc. of Seventh International Workshop on Protocols for High-Speed Networks [11] E. Ossipov, G. Karlsson, SOS: Sender oriented signaling for simplified guaranteed service, In Proc. of third International Workshop on Quality of Future Internet Services (QoFIS 02), October [12] E. Ossipov, The design and application of a simplified guaranteed service for the Internet, Licentiate thesis, KTH, Sweden, [13] Network Simulator NS-2,