UNIVERSITY OF CALIFORNIA, SAN DIEGO. A Simulation of the Service Curve-based Earliest Deadline First Scheduling Discipline

Transcription

1 UNIVERSITY OF CALIFORNIA, SAN DIEGO A Simulation of the Service Curve-based Earliest Deadline First Scheduling Discipline A thesis submitted in partial satisfaction of the requirements for the degree Master of Science in Computer Science by Jesse Shoresh Hose Committee in charge: Professor George C. Polyzos, Chair Professor Rene L. Cruz Professor P. Venkat Rangan 1995

2 Copyright Jesse Shoresh Hose, 1995 All rights reserved.

3 The thesis of Jesse Shoresh Hose is approved: Chair University of California, San Diego 1995 iii

4 DEDICATION To my wife Michelle and my son Nathan whose presence brought a measure of balance to the process. iv

5 TABLE OF CONTENTS Signature Page iii Dedication iv Table of Contents v List of Figures vii List of Tables viii Acknowledgments ix Abstract x I Introduction II Scheduling with Service Curves The SC-EDF Scheduling Policy Generation of Service Curves Call Admission III Single Node Model Network Topology Traffic Source Model Simulation Results Delay Distributions FCFS Delays Service Curve Delays Firewall Properties of Service Curve Scheduling Advantages of SC-EDF Over VirtualClock v

6 TABLE OF CONTENTS (cont.) IV Network Model Network Topology Network Service Curves Simulation Results VI Conclusion Appendix References vi

7 LIST OF FIGURES 2.1. A Service Curve Generation of a Service Curve Network Topology: Single Node Model FCFS Probability Density Function of Queue Delays Service Curve representation of VirtualClock QOS Network Topology A.1. State transition Diagram for SC-EDF process vii

8 LIST OF TABLES 1. FCFS Queue Delays Delays for SC-EDF Scheduling with non-conforming load source Delays experienced by conforming sources with large maximum allowable delays in the presence of a non-conforming source at switch utilization Comparison of delays for SC-EDF and VirtualClock Delays for voice source traversing multiple hops viii

9 ACKNOWLEDGEMENTS I would like to express my gratitude to Hanrijanto Sariowan for the time and patience he afforded me as I strove to understand and implement SC-EDF. I would also like to thank my advisor George C. Polyzos for his suggestions and encouragement during the difficult times. ix

10 ABSTRACT OF THE THESIS A Simulation of the Service Curve-based Earliest Deadline First Scheduling Discipline by Jesse Shoresh Hose Master of Science in Computer Science University of California, San Diego, 1995 Professor George C. Polyzos, Chair With the proliferation of multimedia applications, high speed packet switched networks are being called upon to provide a wide variety of services. A crucial problem is the ability to provide applications with quality of service (QOS) guarantees. In this study, through simulation using the network simulation program OPNET, we investigate the behavior of a scheduling discipline for performance guarantees via service curves called SC-EDF [5]. A comparison of delay distributions is made between SC- EDF, VirtualClock [7] and the first-come first-served (FCFS) discipline. A single node is considered with traditional voice (ON-OFF) source models along with variant models of ON-OFF based sources. A multiple node network, with similar source configurations as those used in the single node case, is used to investigate the end-to-end delays experienced by packets under the SC-EDF scheduling discipline. Simulation results show that SC-EDF is an effective scheduling discipline for providing sessions with QOS guarantees. It is shown that SC-EDF is able to provide QOS guarantees in situations that VirtualClock cannot, specifically when a low bandwidth, low latency is desired. Further results show that SC-EDF provides an effective firewall, the isolation of a session conforming to its agreed upon transmission rate from the ill effects of a x

11 session transmitting at a rate higher than agreed upon at admission time, which could potentially deny conforming sources of their guaranteed QOS. xi

12 Chapter I Introduction With the proliferation of multimedia applications, high speed packet switched networks are being called upon to provide a wide variety of services. A crucial problem is the ability to provide applications with quality of service (QOS) guarantees. Many applications, such as packetized voice and video, have stringent delay requirements. Other applications, such as distributed computing, may be able to tolerate large delays yet can still benefit from QOS guarantees since overall system performance can be severely impacted by large communication latencies. Thus, an interesting measure of QOS is the delay experienced by packets in the network. Some applications, such as those using real-time voice and video, are delay sensitive but can tolerate a certain amount of packet loss. Losses occur when a packet is excessively delayed or when finite buffers overflow, so that the delay distribution experienced by packets is an important measure of QOS. Computing the worst case delay bound is one way to provide QOS guarantees. The worst case delay bounds are computed upon call admission to determine whether a call can be admitted at its requested QOS. It is shown in [6] that worst case bounds tend to be greater than the actual worst case observed delays, often by an order of magnitude or more. This results in under utilization of the network. Having knowledge of the actual delay distribution experienced under a given scheduling discipline may give rise to techniques for statistical multiplexing that can be applied to the call admission policy, thus increasing network efficiency. The ability to provide QOS guarantees for virtual circuit packet switched networks has been an area of active research in recent years resulting in the introduction of several link scheduling policies, e.g. see [7][3][5]. These scheduling policies are designed to allow multiple connections to share network resources while providing QOS guarantees to the individual connections. At the same time, the scheduling policies aim to shield the connections from ill-behaved sources. 1

13 2 In this study we investigate the behavior of a scheduling discipline for performance guarantees via service curves called SC-EDF [5] using simulation. A comparison of delay distributions is made between SC-EDF, VirtualClock [7], and the firstcome first-served (FCFS) discipline. A single node is considered with traditional voice (ON-OFF) source models along with variant models of ON-OFF based sources. A multiple node network, with similar source configurations as those used in the single node case, is used to investigate the end-to-end delays experienced by packets under the SC-EDF scheduling discipline. Further study is made into the SC-EDF s ability to protect a stream from being denied its contract service guarantees by the traffic characteristics of other streams concurrently being serviced by the node. This property, known as a firewall, is especially important in the presence of streams transmitting at a rate greater than agreed upon at admission time, thus potentially denying conforming sources of their guaranteed service rate. In this study we look at queueing delay only, propagation and packet processing delays are not considered.

14 Chapter II Scheduling with Service Curves 2.1 The SC-EDF Scheduling Policy The Service Curve-based Earliest Deadline First (SC-EDF)[5] scheduling policy is motivated by the notion of a service curve, introduced by Cruz[1] as a general framework for characterizing the service provided to a connection by the network. The purpose of SC-EDF is to provide real-time QOS guarantees for sessions with burstiness constraints. Throughout this work we will assume that time is divided into slots, numbered 1, 2, 3. To understand what is meant for a session to be burstiness constrained we let R [ t] denote the number of packets flowing through a link during slot t. R [ s, t] is defined to be the number of packets flowing through the link in the time interval [ s, t]. A session is defined to be burstiness constrained, or b-smooth, if, given a nondecreasing function b, called an arrival curve, R [ s + 1, t] b ( t s) for all s and t satisfying s t. A service curve S, is a non-negative non-decreasing function. Let Rin i and Rout i describe the traffic flowing in and out of a network element respectively for a session i. We assume that the network element is empty at the end of slot 0 so that the number of packets from a session stored in the element at the end of slot t, called the backlog, is given by B i [ t] = R in i [ 1, t] Rout i [ 1, t] 0. A network element is said to guarantee session i a service curve of S i if, for any t, there exists s t such that B i [ s] = 0 and Rout i [ s + 1, t] S i ( t s) (1) Figure 2.1 shows a sample service curve. Note that if a session is guaranteed the service curve S in the figure, then at least three packets will receive service in time slot 8, assuming B i [ s] > 0 for all s such that 1 s 8. Earliest Deadline First (EDF) disciplines assign each packet a deadline, a time by which the packet must receive service by the network element. The packets are 3

15 4 queued and the queued packet with the earliest deadline is the next packet to receive service. SC-EDF uses a session s contracted service curve S i to determine a packet s deadline. Essentially, each packet that arrives at the network element from session i, at time t, is assigned a sequence number, seq i = 1, 2, 3. The sequence number assigned to a packet is unique within each session, arbitrarily selected from [ R in i [ 1, t 1] + 1, R in i [ 1, t] ]. The deadline d, is assigned to be the smallest d t such that S i ( d) seq i. We assume that the network element serves packets in a cutthrough manner so that a packet arriving in one slot may immediately depart in that same time slot if service is available. pkts. S(t) t Figure 2.1: A Service Curve A problem with this scheme arises when a session is idle and then transmits at a high rate. Consider a network element that has the capacity to service 3 packets per time slot and a session with service curve S as in Figure 2.1. If the session transmits only 3 packets in the time interval [0,7] and then transmits 4 packets in slot 8, then all 4 packets received by the network element in slot eight would be assigned a deadline of 8. Since the network element can only service 3 packets in any time slot, one of

16 5 the packets with deadline 8 would miss its deadline. Thus, a session must not be able to accumulate unused credits by becoming idle. This is accomplished by dynamically adjusting the service curve whenever a session has a backlog of 0 at the end of a given time slot t. The resulting curve is called a realized service curve Z. For a non-negative integer t, define τ( t) to be the last slot no later than t at the end of which the network element is idle. We say that a network element guarantees the realized service curve Z i if for every t, Rout i [ ( τ( t) + 1), s] Z i ( t), where Z i ( t) = min { Rout i [ τ( t) + 1, s] + S i ( t s) s: τ( t) s t and B [ s] = 0 i (2) It is shown in [5] that if a connection is guaranteed a realized service curve of Z, then it is also guaranteed the service curve S. The deadline for a packet is now determined by the smallest d t such that Z i ( d) seq i. 2.2 Generation of Service Curves One of the attractive aspects of using service curves is the flexibility inherent in the ability to specify any function as a service curve when requesting QOS guarantees from the network. The only restriction is that the function be non-negative and non-decreasing. The matter of how to specify a service curve function when requesting admission to the network is still an open question but some possibilities include specifying the coefficients of a polynomial or having a set of standard functions, each representative of a particular source model. The user would specify the desired function and supply the necessary parameters, such as burstiness and average rate, to achieve a customized service curve [4]. In this study a session requests a service curve by specifying the capacity C, of the link over which the traffic is being generated, the leaky bucket filter parameters ρ and σ, and the maximum allowable delay. A service curve is generated from these parameters as described in Figure 2.2. The curve S consists of two sections, the burst section which has a slope of C and a duration of b = σ/(c-ρ), and an average rate section that starts at the end of the burst section and continues out to infinity with a slope of ρ. The starting point of the burst portion of the curve is offset from the origin (time 0)

17 6 by the maximum delay value. The number of bits in the burst is given by Cb, the capacity of the source multiplied by the duration of the burst. bits Cb slope = ρ S slope = C b = σ / (C - ρ) max delay b time Figure 2.2: Generation of a service curve S from parameters C - the input link capacity, ρ - the average rate of the session, σ the burst size, and max delay. 2.3 Call Admission It is proven in [5] that a sufficient condition on which a set of service curves can be simultaneously guaranteed by a network element is, given a set of M connections served by a network element of capacity c, for all non-negative integers t M i = 1 S i ( t) ct (3) This formula can be used by the network element to determine whether a call request can be accepted and the guarantees met. If this condition holds when including the newly requested service curve then the call can be admitted to the network, otherwise the call is rejected. When a session is accepted with a service curve S, the network allocates sufficient resources to guarantee the service curve S. The session being admitted agrees not to generate packets at a rate greater than that which can be served by the curve S. This rate is referred to in this work as the session s contracted rate. If a session generates packets at a rate greater than its contracted rate then no service guarantees can be assumed.

18 7 In this study all sessions were statically allocated, with the aggregate service curves of the sessions being verified using this formula so that over-allocation of network element resources did not occur.

19 3.1 Network Topology Chapter III The Single Node Model In this model the network consists of a single switch, fed by five traffic sources. Figure 3.1 shows the network topology. Sources 0-2 are standard voice model sources producing packets at a maximum rate of 32Kbps. Source 3 is an ON-OFF source producing short bursts of traffic in intervals of approximately 1 second over a 32Kbps link. This source is intended to simulate traffic that might be produced by a control channel needing a very low latency QOS. This source will be referred to as the control packet source from here on. Source 4 is an ON-OFF source whose parameters are varied per simulation, with a maximum transmission rate of 128Kbps. During certain simulations, source 4 is deactivated. The switch transmits at a rate of 128Kbps. Fractional T1 lines are currently available from commercial carriers in increments of 64Kbps. A switch output rate of 128Kbps was chosen because it was the smallest fractional T1 rate that could accommodate the combined maximum needs of the three voice model sources (96Kbps). A basic assumption of SC-EDF as presented in [5] is that the system is slotted and time takes on only integer values. The network simulation application, OPNET, used for this study uses continuous time and thus it was necessary to model a slotted time network within this framework. An interval of seconds was used for each slotted clock tick. The study used fixed size packets of 53 bytes each, the size of an ATM cell, and the interval chosen was the time needed to transmit eight packets over a 128Kbps link. Each voice source, generating at maximum rate, would require two packets to be serviced in this interval, leaving potential service of two packets to be split between the remaining sources 3 & 4. 8

20 9 Src 0 Sources 0-3: 32Kbps Src 1 128Kbps Src 2 Switch Sink Src 3 Src 4 Variable 0-128Kbps Figure 3.1: Network Topology: Single Node Model 3.2 Traffic Source Model Each source was modelled as a Markov process. The process consists of two states, ON and OFF. During the ON state, packets are produced at a rate of one every T seconds, where T sources 0-3 operating at 32Kbps, is the time needed to transmit a packet over the given link. For T = as a parameter of the given simulation, ms. For source 4, whose link speed varies T = packet_size / link_speed, where packet_size is in bits and link_speed is in bits/second. The duration of the ON and OFF states is exponentially distributed with mean duration of α 1 for the ON state and a mean duration of β 1 for the OFF state. For the standard voice model, α 1 = 352 ms and β 1 = 650 ms[6]. For a source generating at 32Kbps, α 1 = 352 ms gives us an average burst length of packets. The control packet source (source 3) was given an average burst length of 5 packets or approximately 2Kb worth of data occurring an average of once each second. This resulted in α 1 = ms and β 1 = ms.

21 10 Source 4, which will be referred to as the load source, was used to increase switch utilization or as a non-conforming source (a source generating traffic at rates above its contracted level). When using the load source as a source of congestion, α 1 was held constant at ms which translates to an average burst length of 40 packets over a 128Kbps link while β 1 was varied from 8 ms to 310 ms to achieve the desired utilization levels. When using the voice model and control packet sources described above with the load source generating packets in conformance with its contracted rate, the maximum switch utilization achieved was 38%. In order to observe how SC-EDF performed at high switch utilizations rates with all sources conforming to their contracted service rates, it was necessary to modify the voice models sources to increase the rate at which packets were generated. This was accomplished by holding α -1 constant at 352ms and reducing β -1, the mean off period, to achieve the desired switch utilization rate. A sufficient condition for obtaining performance guarantees through SC-EDF is that the generated traffic must be burstiness constrained. Hence all packets generated by each source are run through a leaky bucket filter prior to being introduced into the network. A leaky bucket filter can be thought of as a bucket with a capacity of σ permits. The bucket is replenished at a rate of ρ permits per second. Replenishment takes place only when there are less than σ permits in the bucket. When a packet wants to enter the network, it requests L permits, where L is the size, in bits, of the packet. If there are less than L permits in the bucket, the packet must wait for the bucket to be replenished. The packet may enter the network only when it can acquire L permits. The permits requested by the packet are then removed from the bucket and the packet enters the network. Thus a session s traffic can be characterized by its burstiness σ, its average rate ρ, and the capacity C, of the link being used. For this study, except where otherwise indicated, we set σ = L and ρ = C. In determining the capacity, C load, of the link for the load source, we used equation (3) to determine the maximum requirement of the voice and control packet sources (sources 0-3). We then allocated the remaining bandwidth to the load source as shown in equation (4), where c is the capacity of the network element and t is a non-negative integer.

22 11 S C load c max i ( t) = i = t 3 (4) 3.3 Simulation Results Delay Distributions This section looks at the delays experienced in the FCFS, Service Curve and VirtualClock disciplines under varied switch utilization levels. The sources used in these simulations are as described in section 3.2. Five simulations of 96 simulated minutes each were run for both service disciplines. The queue delay was recorded for each packet. A 96 minute simulation yielded, for the mean delay of a voice model source, a confidence interval of 95% with a variance of 7.8%. Utilization rates were varied from 38% to 96%. A sixth 96 minute simulation was run for both disciplines with Source 4 deactivated, resulting in a utilization rate of 28% FCFS Delays Table 1 shows the average, minimum and maximum queue delays experienced by all the sources of the FCFS service discipline for different switch utilization rates The delay is given in discrete time units. Notice that at the 28% utilization level (simulation with deactivated source 4) a queue delay of 0 was experienced. This is possible due to the assumption of cut through service made throughout this investigation. Since the packets experience no delay when source 4 is deactivated we can infer that the traffic patterns generated by source 4 heavily influence the delays seen by all packets. This conclusion is further supported by Figure 3.2 which shows the probability density function for both source 4, the load source, and source 0, a voice model source, at 96% switch utilization. The probability density function for the voice model source 0 is representative of those seen for the other voice and control packet sources, and its similarity to the curve of the load source (source 4) shows the influence that the load source has on the delays experienced by all sources.

23 12 Switch utilization Average delay Minimum delay Maximum delay 96% % % % % % Table 1: FCFS Queue Delays (Delays are in slotted time units)

24 13 Figure 3.2: FCFS probability density of queue delays for load and voice model sources at 96% switch utilization.

25 Service Curve Delays In this simulation, the traffic sources are identical to those in section Scheduling for the voice model sources was via service curves generated as described in section 2.2 with the parameters C = 32000bps, σ = L = 424 bits, ρ = 32000bps and max delay = 4, which results in a real time maximum delay of 106 ms. The traffic generated by the control packet source was given a maximum delay of 0 seconds. The leaky bucket parameters for the control packet source were ρ = 9600bps and σ = 9600bits. The selection of these parameters was an ad hoc process based on packet generation patterns of the control packet source observed in shorter, preliminary simulations. The objective in choosing these parameters was to allocate as narrow a bandwidth as possible without causing the leaky bucket to run out of permits, which would result in packets experiencing delay while being forced to wait for the necessary permits to be generated. The aggregate bandwidth required to provide guaranteed service to the voice model and control packet sources as configured is 105,620bps, leaving a bandwidth of 22,380bps for the load source. Thus, the service curve parameters were set at C = σ = ρ = 22,380 with a max delay of 0. Except where otherwise indicated, the σ and ρ parameters of each source s leaky bucket filter were set equal to the σ and ρ parameters of the associated service curve. The results of this simulation showed that SC-EDF is able to provide guaranteed service when all the sources adhere to their contracted rate or less. All packets for the control packet source and the load source experienced 0 delay in accordance with their maximum guaranteed delay of 0. The voice sources, whose guaranteed maximum delay was 4 time slots, experienced a maximum delay of 2 time slots. While there were some voice model packets experiencing a 1 or 2 time slot delay, most of the packets experienced a 0 delay. The probability of a voice packet experiencing a delay greater than 0 was less than This is not surprising considering that the overall switch utilization for this simulation was only 38.8%. Since configuration of the previously described simulation achieved such a low switch utilization rate, the next question to be answered was how SC-EDF would perform at a high utilization rate with all the sources conforming to their contracted rate. To increase the utilization level of the switch the voice model sources were modified to

26 15 increase their packet generation rate. This was accomplished by fixing the on-off source parameter α -1 at 352 ms and reducing the mean off period β -1 to ms. These sources will be referred to as the reduced off-period sources. The resulting source characteristic was an almost steady stream of packets at a rate of 32Kbps. For this simulation sources 0-2 were reduced off-period sources with their service curve parameters set at C = ρ = 32,000, σ = 424 and a max delay of 4. Source 3 was a reduced off-period source with max delay of 0. Source 4 was disabled. This simulation yielded a switch utilization rate of None of the sources experienced a delay greater than 0, confirming SC-EDF s ability to provide guaranteed QOS at high switch utilization rates. An additional simulation was performed to determine what effect increasing the maximum allowable delay would have on the actual delays experienced. Sources 0-2 were reduced ON-OFF sources as previously described with service curve parameters set at C = ρ = 32,000, σ = 424 and max delays of 40, 30 and 20 respectively. A consequence of increasing the allowable delay was that the bandwidth needed to provide the QOS guarantees for sources 0-2 decreased due to the time averaged manner in which SC-EDF determines the bandwidth requirements (see section 2.3). We used source 3 to generate the additional traffic required to achieve a high switch utilization. Source 3 generated a steady stream of packets at a rate of 33,360 bps (the total bandwidth required by sources 0-2 was 94,640 bps) with service curve parameters C = 64,000, ρ = 33,360, σ = 424 and a max delay of 0. This simulation yielded a switch utilization rate of Sources 1-3 experienced maximum delays of 0 while source 0 experienced maximum delay of 1. Only a few packets from source 0 actually experienced a delay of 1, with the probability of a packet from source 0 experiencing a delay of 0 being The reason that little or no delay was seen in the simulation was due to the characteristics of the traffic sources. All sources were generating at a constant, albeit maximum rate, such that the load on the switch was steady throughout the simulation. Subsequent simulations, discussed in section 3.3.2, showed that increased delays were experienced at lower switch utilization rates due to the bursty nature of the sources in those simulations. Thus, the conclusion is that it is the cumu-

27 16 lative characteristics of the inputs to a switch, not the maximum allowable delays, that effect the delays seen Firewall Properties of Service Curve Scheduling An important property of any scheduling discipline attempting to provide service guarantees is the ability to provide firewalls. To provide a firewall is to isolate a given session from undue influence of other sessions, particularly those that are nonconforming. A non-conforming session is a session that is transmitting at a rate greater than its contracted service rate. Thus, a conforming session must receive its contracted service rate regardless of the behavior of other sessions. In order to observe the firewall capabilities of SC-EDF discipline a simulation was performed with Sources 0-2 (the standard voice model sources), with maximum allowable delays of 4 slots. The control packet source had a maximum allowable delay of 0. The load source contracted a service curve with parameters C = ρ = σ = bps with max allowable delay of 0, while actually transmitting at a link rate of 128 Kbps with leaky bucket parameter ρ = σ = 128 Kbps and ON-OFF generator parameters of α -1 = ms, with β -1 ranging from ms to vary the switch utilization. This simulation is equivalent to the simulation achieving a 38.8% utilization rate described in section with the exception that here the load source is generating packets at a rate higher than its contracted rate Table 2 shows the maximum delays experienced by each of the different types of sources at varying utilization rates. None of the sources that are conforming to their contracted packet generation rate (the voice model and the control packet sources) experience any delay greater than the maximum requested delay. The load source experienced significant delays (its requested maximum delay was 0), but since it was violating its contracted packet generation rate, any guarantees provided by SC-EDF are no longer valid. Figure 3.2 showed how, in the FCFS discipline, the load source effected the delay distribution seen by all sources. In the 96% utilization run with SC- EDF, the load source experienced a similar delay distribution as that in Figure 3.2. The voice model sources in the SC-EDF run experienced a distribution much different

28 17 than that experienced under FCFS, most of the packets experienced 0 delay. This serves to further emphasize SC-EDF s ability to provide effective firewalls. Switch utilization Voice model max delay Control packet max delay Load source max delay 96% % % % % % Table 2: Delays for SC-EDF scheduling with non-conforming load source. It is interesting to note that the voice model sources experienced a greater delay at the 58% and 68% switch utilization levels than they did at the higher utilization levels. Only a few packets actually experienced a delay of 3. For the 68% utilization level, the probability of a packet experiencing a delay of 3 was 4.36e-6, while the probability of a packet experiencing a 0 delay was The reason for the increased delays at lower utilization is in the way that SC-EDF updates the realized service curve. At the lower utilization levels, the mean OFF period of the load source s ON-OFF generator is much longer than it is at the higher utilization levels. This gives the switch a chance to fall idle. When the switch falls idle, all the realized service curves are reset to their initial service curve and every session gets a fresh start. The switch carries no memory that a particular session has been violating its contracted service rate. This means that a source that is transmitting over its contracted rate with heavy bursts and long OFF periods has more potential to cause conforming sources to experience increased delays than a non-conforming source transmitting a steady stream of packets at a high rate. The increased delays experienced by the conforming sources would not be greater than their contracted maximum delay although this would cause increased jitter.

29 18 As in section , we were interested in seeing how SC-EDF would perform with sources transmitting at close to their maximum contracted rate with high maximum allowable delays, now in the presence of a non-conforming source. We ran a simulation with sources 0-2 reduced ON-OFF sources, as previously described with service curve parameters set at C = ρ = 32,000, σ = 424 and max delays of 40, 30, and 20, respectively. Source 3 was allocated a service curve with parameters C = 64,000, ρ = 33,360, σ = 424 and a max delay of 0 but was generating packets at a steady rate of 36,000 bps, in violation of its contracted rate. Source Maximum Allowable Delay Actual Maximum Delay Table 3: Delays experienced by conforming sources with large maximum allowable delays in the presence of a non-conforming source at switch utilization. Table 3 shows the maximum delays experienced by source 0-2. The switch utilization was Only a few packets actually experienced the maximum delays while the probability of a packet experiencing a 0 delay was for source 2, for source 1 and for source 0. While just over 40% of the packets experienced greater than 0 delay for source 0, the probability of a packet experiencing a delay of 5 slots or less was greater than Thus we see that SC-EDF is able to provide effective firewalls at high switch utilizations and that, for sources with large maximum allowable delays, the delays seen by the conforming sources tend to be well below the maximum allowable Advantages of SC-EDF Over VirtualClock In this section we will look at some of the advantages SC-EDF presents over VirtualClock. VirtualClock emulates a Time Division Multiplexing (TDM) system while allowing statistical sharing of the switch. In this simulation, we implemented

30 19 the VirtualClock scheduling discipline as described in [7], with the exception that we used a leaky bucket instead of the user-behavior envelope described by Zhang. It is shown in [2] that a leaky bucket constrained session is the most general type of session for which an upper bound on delay can be provided by servers with finite link capacity. The parameters for a session in VirtualClock are AR, the average rate of the session and AI, the average interval which is used in determining how often a session traffic should be checked for conformity to its requested average rate. In this study, we set AI = s. This is the value of the discrete clock tick interval in SC-EDF. The discrete clock tick interval is the interval used by SC-EDF to check the behavior of its sessions. We wanted to create as much conformity as possible in the simulations used for comparing VirtualClock and SC-EDF. Since the value of the interval used to check the behavior of a session can have a potentially significant impact on the QOS provided by the switch, we felt that the interval should be the same in both disciplines. The delay experienced by the packets was calculated in slotted time units as in the SC-EDF simulations. In VirtualClock, a session requests an average rate of service AR. The average rate is used to determine the size of the virtual clock tick which is, for a session with fixed size packets, Vtick = packet _size AR. Each session has an associated counter auxvc that is used to time stamp the arriving packet. The packet is then placed in a queue and the packets receive service in order of ascending time stamps. The value of auxvc is determined at the time of packet arrival as auxvc = Vtick + max( real time, auxvc). (5) Thus, the QOS received by the session is fixed according to its average rate. This means that a session with a low average rate will be subject to larger delays, while a session with a higher average rate will receive preferential treatment, whether it needs it or not. It is not possible to get low latency with a low average rate or any type of service that cannot be characterized by a single average rate. Consider the control packet source similar to that in previous simulations. Assume that now the average rate of the control packet source is 8000 bps. With Vir-

31 20 tualclock we cannot provide the low latency service required since Vtick = 0.053s. This is the duration of two time slots, so that each control packet that arrives is scheduled to receive service 2 time slots after it arrives at the switch. Recall that for the control packet source, we want a maximum delay of 0. In order to have the packets scheduled to meet the maximum allowable delay, we would have to request an average rate greater than 16K bps, or more than twice the actual rate. One can think of the QOS provided by VirtualClock as a subset of the QOS that can be provided by SC-EDF. We can provide the average rate QOS of VirtualClock by allocating a service curve with parameters, max delay = Vtick. Figure 3.3 shows a service curve representation of the service provided by Virtual- Clock. C = ρ = σ = AR bits slope = AR Vtick time Figure 3.3: Service Curve representation of VirtualClock QOS. To demonstrate SC-EDF s ability to provide a broader range of QOS, we ran two simulations with identical traffic sources. One simulation used SC-EDF scheduling, the other used VirtualClock scheduling. Sources 0, 1, 2, 4 were reduced ON-OFF sources with parameters α -1 at 352 ms and β -1 to ms. Source 3 was the control packet source described in section 3.2. The leaky bucket parameters for sources 0-2 were σ = 424 bits, ρ = 32K bps. The leaky bucket parameters for source 3 were σ = 8K bits, ρ = 8K bps. The leaky bucket parameters for source 4 were σ = 24K bits, ρ = 24K bps. Our intention is to provide source 3, a low bandwidth source, with a low latency, and to provide source 4, a higher bandwidth source, with a high latency. While a high bandwidth, high latency service might not be particularly desirable, it is used

32 21 here to illustrate the wide variety of services attainable under SC_EDF. Sources 0-2 will receive QOS close to their average rate, but with maximum allowable delay of 0. For SC-EDF we allocated service curves in the following manner: sources 0-2 had service curve parameters C = ρ = 32,000, σ = 424 and a max delay of 0, source 3 was allocated a service curve with parameters C = 32,000, ρ = σ = 8000 and a max delay of 0, while source 4 was allocated a service curve with parameters C = ρ = σ = 24,000 and a maximum delay of 14 slots. For VirtualClock, all sources were assigned an average rate such that AR = ρ, their corresponding leaky bucket parameter. In previous simulations we had used parameters ρ = σ = 9600 for the control packet source, chosen ad hoc. We later observed that this was an overallocation of resources and that ρ = σ = 8000 would suffice. Since a lower bandwidth for source 3 would only serve to emphasize the advantage of SC-EDF, we chose to modify source 3 s parameters for this simulation. Since source 4 was allocated the left over bandwidth after sources 0-3 were allocated their service curves, its value changed accordingly as well. The maximum delay of 14 slots for source 4 was chosen to be just larger than the duration of the burst of the control packet source, which was 13 slots. Table 4 shows the delays experienced by the sources under SC-EDF and VirtualClock. Note that under these circumstances, VirtualClock was unable to meet the maximum allowable delays for all but source 4. Still, VirtualClock did not provide the high latency we expected source 4 to receive. Clearly, in situations calling for low bandwidth, low latency QOS or high bandwidth, high latency QOS, SC-EDF is able to provide the desired QOS where VirtualClock cannot. Source SC-EDF maximum delay VirtualClk maximum delay maximum allowable delay Table 4: Comparison of delays for SC-EDF and VirtualClock.

33 4.1 Network Topology Chapter IV The Network Model The network model was used to investigate the end-to-end delays experienced by a packet under the SC-EDF scheduling discipline. Figure 4.1 shows the network topology. Src 0 Sources 0-3: 32Kbps Src 5 Src 6 Src 7 Src 1 Sources 5-6: 32Kbps Variable 0-128Kbps Src 2 Switch 1 Switch 2 Sink Src 3 Variable 0-128Kbps 128Kbps Src 4 Figure 4.1: Network Topology This model consists of two switches connected in tandem by a 128K bps simplex link. The first switch has five input sources and the second switch has four input sources, one of the inputs being the 128K bps link from the first switch. The input sources for switch 1 are configured as in section 3.2. For switch 2, sources 5 and 6 are standard voice model sources while source 7 is used as a load source to vary switch utilization rates. 22

34 23 A simple routing scheme was used. Switch 1 was assigned address 1, switch 2 was assigned address 2. If a packet was received at a switch with a destination address greater than the address of the switch, then the packet was assigned a deadline and placed in the queue to receive service. Therefore, if we wanted to route a packet from source 0 through both switches, we would assign its destination to be 3 since only packets with a destination greater than 2 would be scheduled for service in switch 2. Each packet contained a data field to store the cumulative time spent in the queues along its route. When a packet was removed from a queue the time it spent in the queue was added to the time it spent in previous queues and the new value was stored in the packet s data field. The packet was then transmitted to the next switch. If the packet had a destination address less than or equal to the switch s address, then the packet was sent directly to the sink. The sink was responsible for recording the total time each packet spent queued while waiting to be serviced. Finally, the sink discarded the packet, deallocating its associated memory. 4.2 Network Service Curves The concept of a network service curve, S net, is defined by Cruz [1] as follows. Consider a virtual circuit consisting of H switches. Let the traffic entering switch h, 1 h H, be denoted by R h 1 with traffic from switch h feeding into switch h + 1. Define R in = R 0 and R out = R H. The backlog at switch h at the end of time t is given by B h [ t] = R h 1 [ 1, t] R h [ 1, t]. A network guarantees a service curve of S net if for all t, there exists a slot s t such that B 1 [ t] = 0 and R out [ 1, t] R in [ 1, s] S net ( t s). (6) Furthermore, if a switch h guarantees a service curve of S h then the network guarantees a service curve S net, where H H S net ( x) = min S h ( x h ) :x h 0 and x h = x. (7) h = 1 h = 1

35 24 As a consequence of equation (7), if we wanted to allocate a network service curve with parameters ( C, ρ, σ, d), where d is the maximum allowable delay, we can do so by allocating a service curve ( C, ρ, σ, d h ) for each switch h such that H h = 1 d h = d. (8) 4.3 Simulation Results In this series of simulations, we attempted to create a situation whereby a packet traversing multiple hops in the network encountered cross-traffic at each hop. To accomplish this, two sessions were chosen to traverse multiple hops, a voice model source (source 0) and a control packet source (source 3), each being assigned destination address 3. The remaining input sources from switch 1 were given a destination address of 2 so that they traversed the link from switch 1 to switch 2 but were routed directly to the sink once they reached switch 2. The input sources to switch 2 (sources 5-7) were given destination address 3 so they would be placed in switch 2 s queue along with the packets from sources 0 and 3. Sources 1, 2, 5 and 6, the voice model sources that traversed only one link, were allocated service curves with the parameters C = ρ = 32,000, σ = 424 and a max delay of 4. In allocating a network service curve for source 0 we wanted a maximum delay of 4 slots. Using the results of the discussion in section 4.2, we chose C = ρ = 32,000, σ = 424 and d h = 2, h { 1, 2. For source 3, the control packet source, C = 32,000, ρ = σ = 9600 and d h = 0. The load sources (source 4 for switch 1 and source 7 for switch 2) were allocated identical service curves of C = ρ = σ = 19,556 and a max delay of 0. This was the amount of remaining bandwidth on each node after all the other service curves had been allocated. The load sources were used to vary the switch utilization by transmitting at several different rates, all of which were above their contracted service rate. This was accomplished by reducing the duration of the off period as described for source 4 in section 3.2.

36 25 The results of the series of simulations showed that the control packet source never experienced a delay greater than 0. All the voice model sources that traversed only one hop experienced maximum delays of 2, well within the maximum allowable delay. Table 5 shows the delays experienced by source 0, the voice model source traversing multiple hops. The network utilization rate was the average utilization of the two switches. Both switches experienced similar utilization rates, never differing by more than Practically all of the packets of source 0 experienced a delay of 0, with no packet experiencing a delay greater than 0 in both switches. As in the single node case, the delays experienced by the packets traversing multiple hops were well below the maximum allowable. Network utilization Maximum delay (slots) Probability delay = Table 5: Delays for voice source traversing multiple hops.

37 Chapter V Conclusion This work has studied, through simulation, the behavior of the Service Curvebased Earliest Deadline First scheduling discipline for virtual circuit packet switched networks. The SC-EDF discipline was implemented for a single node and a two node tandem network. SC-EDF s ability to provide QOS guarantees was observed using a voice model and other ON-OFF based sources at varying levels of switch utilization. Further simulations were performed to test SC-EDF s ability to provide firewalls against misbehaving traffic sources. A FCFS scheduling discipline was used to show the effect that rogue sources can have upon traffic in a switch, which was then used to emphasize SC-EDF s firewall ability. The VirtualClock scheduling discipline was implemented and it was shown that SC-EDF has an advantage in its ability to schedule diverse QOS requirements in situations that exceed VirtualClock s capabilities. The simulation results showed SC-EDF to be effective in providing QOS guarantees. Also evident was its ability to isolate sessions from misbehaving sources and to continue to provide QOS to the conforming sessions under highly stressed situations. Virtually none of the packets experienced a delay equal to the maximum allowable delay, with most packets experiencing delays well below the maximum allowable. The simulations ran at higher switch utilization rates (0.96 and 0.88) tended to suffer less delay than those simulations in mid utilization levels ( ). We believe this was due to the fact that in order to achieve the higher levels of utilization, the sources needed to generate packets at a steadier rate, thus smoothing out the overall traffic patterns seen by the switch. The traffic at the lower utilization levels tended to be burstier. Thus it may be possible for packets to experience delays closer to the maximum allowable in situations consisting of extremely bursty traffic. The advantage of SC-EDF is its ability to schedule diverse traffic sources while simultaneously providing each with its own QOS requirement. It was shown that SC- EDF was able to provide QOS to sessions requiring low bandwidth, low latency or high bandwidth, high latency service. Under the same circumstances VirtualClock was 26

38 27 unable to provide these sessions with their requested QOS. This is due to the fact that VirtualClock provides service based upon a session s average rate rather than taking into account a session s changing needs over time. In fact, the only limitation on the type of QOS that can be provided by SC-EDF is that the service curve describing the requested service be a non-negative, non-decreasing function. This gives SC-EDF the potential for providing QOS to future applications with novel traffic characteristics. The network case reinforced the conclusions drawn from the single node case. SC-EDF continued to provide QOS guarantees in adverse conditions, i.e. with nonconforming sources at high utilization levels. Of note was the ease in which we were able to adapt a single node service curve to the network model. All that was required was to change the maximum delay at each node so that the sum of the maximum delays allowed for the virtual circuit equalled the maximum allowable delay of the single node case. While SC-EDF proved to be quite capable in providing QOS guarantees in our simulation environment, the computational complexity involved in updating the realized service curve raised some concern over the ability of SC-EDF to perform adequately in a high speed switch. The realized service curve for session i, Z i, is updated by the switch each time the backlog of session i is 0 at the end of a time slot. Each update depends upon the previous values of Z i to minimize the value of the new Z i. When all sessions in the switch have a backlog of 0 at the end of a time slot, all the realized service curves are reset to their original value, that of their respective service curve S i. The information needed to generate the new Z i was the time, t, and Rout i [ t]. These values were stored in an update history list and the list was traversed once for every new value of Z i calculated. Once the switch fell idle and the realized service curves were reset to the original service curves, the update history list for each session was emptied and the process began anew. As an optimization, we used an array to hold the values of Z i. Knowing the most recent value of the realized service curve makes it easy to calculate the new value; so using an array yielded a significant gain in simulation performance at the lower switch utilization levels. This raised the question of how large to make the array. Too large an array would incur heavy overhead every time Z i was updated. Too small