© 1998 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.

IEEE Transactions on Networking
Volume 6 Number 5, October 1998

On Variations of Queue Response for Inputs with the Same Mean and Autocorrelation Function

Page 588.

Abstract:

This paper explores the variations in mean queue length for stationary arrival processes with the same mean and autocorrelation functions, or equivalently, the same mean and power spectrum. Three types of processes, namely, two-state Markov-modulated Poisson processes, periodic-sequence modulated Poisson processes and processes generated by randomly filtering a white noise process, are investigated. Results show that the mean queue length can vary substantially for the first type of process, and can vary moderately for the second type of process, as the parameters of the processes are varied, subject to a specified mean and autocorrelation function. However, the mean queue lengths for the third type of arrival processes are determined by the input mean and autocorrelation functions. The results suggest that queueing performance can be hard to predict from spectral data alone when the power in low frequencies is large.

References

1. S. Q. Li and C. L. Hwang, "Queue response to input correlation functions: Discrete spectral analysis," IEEE/ACM Trans. Networking, vol. 1, pp. 522-533, Oct. 1993
2. --, "Queue response to input correlation functions: Continuous spectral analysis," IEEE/ACM Trans. Networking, vol. 1, pp. 678-692, Dec. 1993
3. C. L. Hwang and S. Q. Li, "On the convergence of traffic measurement and queueing analysis: A statistical-match queueing (SMAQ) tool," in Proc. IEEE Infocom'95, Apr. 1995, pp. 602-613.
4. Y. Kim and S. Q. Li, "Timescale of interest in traffic measurement for link bandwidth allocation design," in Proc. IEEE Infocom'96, Mar. 1996, pp. 738-748.
5. S.-Q. Li and J. D. Pruneski, "The linearity of low frequency traffic flow: An intrinsic I/O property in queueing systems," IEEE/ACM Trans. Networking, vol. 5, pp. 429-443, June 1997.
6. M. F. Neuts, Matrix Geometric Solutions in Stochastic Models.Baltimore, MD: The Johns Hopkins Univ. Press, 1981.
7. --, Structured Stochastic Matrices of the M/G/1 Type and Their Applications.New York: Marcel-Dekker, 1989.
8. J. N. Daigle, Y. Lee, and M. N. Magalha˜es, "Discrete time queues with phase dependent arrivals," IEEE Trans. Commun., vol. 42, pp. 606-614, Feb.-Apr. 1994.
9. A. Elwalid, D. Heyman, T. V. Laksman, D. Mitra, and A. Weiss, "Fundamental bounds and approximations for ATM multiplexers with applications to video conferencing," IEEE J. Select. Areas Commun., pp. 1004-1016, Aug. 1995.
10. W. E. Leland, M. Taqqu, W. Willinger, and D. V. Wilson, "On the self-similar nature of ethernet traffic (extended version)," IEEE/ACM Trans. Networking, vol. 2, pp. 1-15, Feb. 1994.