Abstract
We establish the optimal asymptotic decay rate of per-session queue length tail distributions for a two-queue system where a single constant rate server serves the two queues using the Generalized Processor Sharing (GPS) scheduling discipline. The result is obtained using the sample-path large deviation principle and has implications in call admission control for high-speed communication networks.
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References
ATM Forum, ATM User-Network Interface Specification, Version 3.0 (Prentice-Hall, Englewood Cliffs, NJ, 1993).
F. Baccelli and P. Bremaud, Elements of Queueing Theory (Springer, New York, 1990).
D.D. Botvich and N.G. Duffield, Large deviations, the shape of the loss curve, and economies of scale in large multiplexers, Queueing Systems 20 (1995) 293–320.
D. Bertsimas, I.Ch. Paschalidis and J.N. Tsitsiklis, On the large deviations behavior of acyclic networks of G/ G/1 queues, Preprint (1994).
C.S. Chang, Stability, queue length and delay of deterministic and stochastic queueing networks, IEEE Transactions on Automatic Control (May 1994).
C.S. Chang, Sample path large deviations and intree network, Queueing Systems 20 (1995) 7–36.
C.S. Chang, P. Heidelberger, S. Juneja and P. Shahabuddin, Effective bandwidth and fast simulation of ATM intree networks, Performance Evaluation 20 (1994) 45–66.
C.-S. Chang and J.A. Thomas, Effective bandwidth in high-speed digital networks, IEEE Journal on Selected Areas in Communications 13(6) (1995) 1091–1101.
C.-S. Chang and T. Zajic, Effective bandwidths of departure processes from queues with time varying capacities, in: Proceedings of IEEE INFOCOM '95 (1995) pp. 1001–1009.
D. Clark, S. Shenker and L. Zhang, Supporting real-time applications in an integrated service packet network: architecture and mechanism, in: Proceedings of ACM SIGCOMM '92 (1992) pp. 14–26.
R.L. Cruz, A calculus for network delay, part I: Network elements in isolation, IEEE Transactions on Information Theory 37(1) (1991) 114–131.
A. Dembo and T. Zajic, Large deviations: from empirical mean and measure to partial sums process techniques, Preprint (1994).
A. Dembo and O. Zeitouni, Large Deviations Techniques and Applications (Jones and Bartlett Publishers, 1993).
G. de Veciana and G. Kesidis, Bandwidth allocation for multiple qualities of service using generalized processor sharing, revised version, Preprint. An earlier version appeared in: Proceedings of IEEE GLOBECOM '94 (1994).
R.S. Ellis, Entropy, Large Deviations and Statistical Mechanics (Springer, New York, 1985).
P.W. Glynn and W. Whitt, Logarithmic asymptotics for steady-state tail probabilities in a single server queue, J. Appl. Probab. 31 (1994).
R.M. Loynes, The stability of a queue with non-independent inter-arrival and service times, Process. Cambridge Philos. Soc. 58 (1962) 497–520.
J.F. Kurose, Open issues and challenges in providing quality of service guarantees in high-speed networks, ACM Computer Communication Review (1993) 6–13.
F. Lo Presti, Z.-L. Zhang and D. Towsley, Bounds, approximations and applications for a two-queue GPS system, in: Proceedings of IEEE INFOCOM '96 (March 1996) pp. 1310–1317.
A.K. Parekh and R.G. Gallager, A generalized processor sharing approach to flow control in integrated services networks: the single node case, IEEE/ACM Transactions on Networking 1(3) (1993) 344–357.
A.K. Parekh and R.G. Gallager, A generalized processor sharing approach to flow control in integrated services networks: the multiple node case, IEEE/ACM Transactions on Networking 2(2) (1994) 137–150.
A. Shwartz and A. Weiss, Large Deviations for Performance Analysis (Chapman and Hall, New York, 1995).
A. Weiss, An introduction to large deviations for communication networks, IEEE Journal on Selected Areas in Communications 13(6) (1995) 938–952.
O. Yaron and M. Sidi, Performance and stability of communication networks via robust exponential bounds, IEEE/ACM Transactions on Networking 1(3) (1993) 372–385.
O. Yaron and M. Sidi, Generalized processor sharing networks with exponentially bounded burstiness arrivals, in: Proceedings of IEEE INFOCOM '94 (June 1994).
Z.-L. Zhang, Large deviations and the generalized processor sharing scheduling discipline for a general multiple-queue systems, Technical Report UM-CS–95–97, Computer Science Department, University of Massachusetts, Oct. 1995. Available from http://www.cs.umn.edu/~zhzhang/papers.html.
Z.-L. Zhang, Z. Liu, J. Kurose and D. Towsley, Call admission control schemes under the generalized processor sharing scheduling discipline, to appear in Telecommunication Systems.
Z.-L. Zhang, D. Towsley and J. Kurose, Statistical analysis of generalized processor sharing scheduling discipline, IEEE Journal on Selected Areas in Communications 13(6) (1995) 1071–1080.
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Zhang, ZL. Large deviations and the generalized processor sharing scheduling for a two-queue system. Queueing Systems 26, 229–254 (1997). https://doi.org/10.1023/A:1019133208384
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DOI: https://doi.org/10.1023/A:1019133208384