Traffic models and admission control for variable bit rate continuous media transmission with deterministic service

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Abstract

In this paper we address the problem of call admission based on general descriptions of stored continuous media (CM) flows. We show that such an approach to call admission can result in a very high resource utilization that can be significantly higher than that produced when using time-invariant flow descriptions. We present the admissibility conditions for flows, where packets are scheduled according to the earliest-deadline-first (EDF) scheduling policy. We further present an algorithm for testing for admissibility of a new flow whose computational complexity is linear in the number of flows and in the linear segments used for flow description. Last, we present an algorithm for producing a parsimonious flow description which produces most of the benefit of the best general description while requiring a small number of linear segments. Simulation shows that this improves the network resource utilization as much as 200–250% over the best possible utilization achieved using any time-invariant workload function. A significant improvement results even when the workload is smoothed.

Introduction

Future high-speed computer networks are projected to carry a large array of stored continuous media (CM) flows emanating from sources such as digital libraries and video servers. These flows are often variable bit rate in nature and are characterized by stringent delay requirements. In order to guarantee such delay requirements, the network must reserve resources at the links on the path of the given CM flow. The development of an efficient algorithm for determining whether a new flow can be supported while guaranteeing delay requirements for it and all existing flows is a challenging problem that has been the subject of considerable research [2], [3], [4], [9], [10], [11].

Much of the recent research has focused on resource reservation and call admission for the case when hard guarantees are required. In this case much of the attention has focused on the development of algorithms that take time-invariant descriptions of CM flows as inputs [3], [10], [11]. A CM flow description is said to be time-invariant if the flow’s description over an interval of time of arbitrary length does not depend on the starting point of the interval. The focus of much of this work has been on the development of parsimonious time-invariant flow descriptions that give rise to efficient call admission algorithms that provide high resource utilization. Unfortunately these algorithms are unable to generate high resource utilization when offered variable bit rate flows with stringent delay requirements (e.g., 100–500 ms).

In this paper we take a radically different approach towards call admission algorithms by using a more general description of stored CM flows, i.e., the workload descriptions need not be time-invariant. Using a result in [12], we decompose the end-to-end call admission problem into call admission problem for a single resource. We begin by demonstrating that the use of a complete description of a stored CM flow (e.g., frame sizes in the case of video) can result in a substantial increase in the number of supported flows over what is possible using time-invariant flow descriptions. Since the computational requirements of the algorithm are proportional to the length of the CM flow (e.g., the size of the video), we present an algorithm for producing a parsimonious flow description which still results in efficient call admission. We show that this simple algorithm supports a number of flows that is substantially larger than the number of flows that can be supported using the best possible time-invariant flow description.

In addition to the contributions described above, we present the admissibility conditions for flows with more general descriptions that need not be time-invariant, where packets are scheduled according to the earliest-deadline-first (EDF) scheduling policy. This generalizes earlier results in [4], allowing the approach to accommodate a larger set of descriptions and is of independent interest. Furthermore, we present an algorithm for admissibility checks whose computational complexity is linear in the number of flows.

The rest of the paper is organized as follows: Section 2 begins by explaining how the end-to-end call admission problem can be decomposed into call admission for a single resource. We show that using time-invariant workload descriptions grossly underutilizes the network capacity. In Section 3, we develop efficient admission control for CM flow descriptions that are piecewise linear, but are not necessarily time-invariant. In Section 4, we propose an average-rate interpolation workload model that provides a more precise representation of the workload than that provided by any time-invariant description. In Section 5, we evaluate the performance of our flow description model and compare its performance to the time-invariant description. Section 6 presents conclusions and discusses future extensions of our work.

Section snippets

Admission control framework

Fig. 1 illustrates a typical stored continuous media application. The continuous media is stored at the server in a disk subsystem. A client sends a request for the transmission of continuous media via the attached network. The server then retrieves the continuous media from the disk subsystem for timely transmission over the network. In order to meet the end-to-end service guarantees, it is necessary that sufficient resources are available at all the links on the path between the server and

Efficient admissibility conditions

In this section, we develop efficient admissibility conditions that can be used to perform admission control based on the EDF schedulability conditions in Theorem 1. First we develop admissibility conditions for any general workload function. Based on these new admissibility conditions, we derive special admissibility conditions for the set of all piecewise linear workload functions which allows efficient admission control.

Time-dependent workload characterization

The results in Fig. 4 indicate that a significant increase in network utilization is possible by using the exact workload information instead of the “time-invariant” empirical envelope. Note that the computational complexity of the admissibility condition in Theorem 3 depends on the number of linear segments needed to represent the workload function. Thus the computational requirements in checking the admissibility conditions can be quite high when using the exact workload function which has as

Comparison with time-invariant model

We evaluate the benefits of the average-rate interpolation workload model via simulation using the workloads introduced in Section 2. Two types of arrival patterns are considered. In the bunched arrival pattern, all requests arrive before any request receives service. In the staggered arrival pattern, requests arrive dynamically according to some arrival process. We use an “average-rate” based interpolation workload function with 14 segments and compare the performance using this function to

Conclusion and future work

In this paper, we have taken a different approach to address the admission control problem for stored video. Instead of restricting ourselves to the set of time-invariant workload functions, we consider more general descriptions. We have shown that any time-invariant description of the workload for compressed video significantly overestimates the exact workload. By considering more general workload functions that benefit from the availability of detailed workload information, we are able to

Acknowledgements

We would like to thank Prof. Zhi-Li Zhang of the University of Minnesota for many helpful comments and discussions during the course of this work.

Sambit Sahu received his B.S. degree in Mathematics from Indian Institute of Technology, Kharagpur, India and M.E. degree in Electrical Communication Engineering from Indian Institute of Science, Bangalore, India. He is currently a member of the Computer Networks Research Group led by Professors Don Towsley and Jim Kurose at the University of Massachusetts at Amherst. He was a Reseach Intern with the Network Architecture and Analysis Group at IBM T.J. Watson Research Center in 1995, and with

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Cited by (1)

Sambit Sahu received his B.S. degree in Mathematics from Indian Institute of Technology, Kharagpur, India and M.E. degree in Electrical Communication Engineering from Indian Institute of Science, Bangalore, India. He is currently a member of the Computer Networks Research Group led by Professors Don Towsley and Jim Kurose at the University of Massachusetts at Amherst. He was a Reseach Intern with the Network Architecture and Analysis Group at IBM T.J. Watson Research Center in 1995, and with the IP group at Sprint Advanced Technology Laboratories in 1999. His research interests include end-to-end quality of service issues with the multimedia streaming applications in the Internet.

Victor Firoiu received his Diploma of Engineer from the Department of Computer Science at the Polytechnic Institute of Bucharest, Romania in 1987, and his M.S. and Ph.D. from the Department of Computer Science at the University of Massachusetts in 1995 and 1998, respectively. He was a member of the Computer Networks Research Group led by Professors Don Towsley and Jim Kurose. He was a Research Intern with the Broadband Networking Group at IBM T.J. Watson Research Center in 1995 and 1996. He joined Nortel Networks in 1998, where he is managing the QoS and Performance Engineering Group.

Don Towsley holds a B.A. in Physics (1971) and a Ph.D. in Computer Science (1975) from University of Texas. From 1976 to 1985 he was a member of the faculty of the Department of Electrical and Computer Engineering at the University of Massachusetts, Amherst. He is currently a Distinguished Professor at the University of Massachusetts in the Department of Computer Science. He has held visiting positions at IBM T.J. Watson Research Center, Yorktown Heights, NY (1982–1983); Laboratoire MASI, Paris, France (1989–1990); INRIA, Sophia-Antipolis, France (1996); and AT & T Labs  Research, Florham Park, NJ (1997). His research interests include networks, multimedia systems, and performance evaluation. He currently serves on the Editorial board of Performance Evaluation and has previously served on several editorial boards including those of the IEEE Transactions on Communications and IEEE/ACM Transactions on Networking. He was a Program Co-chair of the joint ACM SIGMETRICS and PERFORMANCE’92 conference. He is a member of ACM, ORSA and the IFIP Working Groups 6.3 and 7.3. He has received the 1998 IEEE Communications Society William Bennett Paper Award and two best conference paper awards from ACM SIGMETRICS in 1987 and 1996. Last, he has been elected Fellow of both the ACM and IEEE.

Jim Kurose received his Ph.D. degree in computer science from Columbia University. He is currently Professor and Chair of Computer Science at the University of Massachusetts. Prof. Kurose has been a Visiting Scientist at IBM Research and at INRIA and EURECOM, both in Sophia-Antipolis, France. His research interests include real-time and multimedia communication, tranport protocols, network and operating system support for servers, and modeling and performance evaluation. Dr. Kurose is the past Editor-in-Chief of the IEEE Transactions on Communications and of the IEEE/ACM Transactions on Networking. He has been active in the program committees for IEEE Infocom, ACM SIGCOMM, and ACM SIGMETRICS conferences for a number of years. Dr. Kurose is proud of the teaching awards he has received for both on-campus and distance learning courses. He is a Fellow of the IEEE, and a member of ACM, Phi Beta Kappa, Eta Kappa Nu, and Sigma Xi.

This work was supported in part under National Science Foundation grants NCR-9508274 and CDA-9502639. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation. An earlier version of this paper was presented at the Performance and Control of Network Systems II Conference, in: Wai Sum Lai, Robert B. Cooper (Eds.), Proceedings of SPIE (The International Society for Optical Engineering), Vol. 3530, Boston, Mass., 2–4 November 1998.

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