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A Queuing System with a Branching Process Arrival Stream, the Case of Short-Range Dependence

Published online by Cambridge University Press:  27 July 2009

Teunis J. Ott
Teunis J. Ott
Affiliation:
Bellcore, 445 South Street, Morristown, New Jersey 07960
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Abstract

In a previous paper, we defined and studied a branching process input stream that can be used to model the organization of packets (in packetized communication) in messages. In this paper we derive a central result on the effect that such streams have on a packet switch (or queue) and further study one particular model (the case of so-called short-range dependence), where the distribution of the number of packets in a buffer can explicitly be found (albeit in the form of a transform). The solution to this particular model suggests an approximation for the average buffer content in the general case.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 7 , Issue 4 , October 1993 , pp. 515 - 528
Copyright
Copyright © Cambridge University Press 1993

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References

1.Anick, D., Mitra, D., & Sondhi, M.M. (1982). Stochastic theory of data handling. Bell System Technical Journal 61: 1871–1894.Google Scholar
2.Bhargava, A., Humblet, P., & Hluchyj, M.G. (1989). Queueing analysis of continuous bit stream transport packet networks. Proceedings Globecom 1989, pp. 25.6.1–25.6.5.CrossRefGoogle Scholar
3.Elwalid, A.I. & Mitra, D. (1991). Analysis and design of rate-based congestion control for high speed networks, I: Stochastic fluid models, access regulation. Questa 9: 29–63.Google Scholar
4.Elwalid, A.I., Mitra, D., & Stern, T.E. (1991). Statistical multiplexing of Markov modulated sources: Theory and computational algorithms. Proceedings ITC-13, Copenhagen, 06 1991.Google Scholar
5.Hluchyj, M.G. & Karol, M.K. (1988). Queueing in space-division packet switching. Proceedings Globecom 1988, pp. 334–343.CrossRefGoogle Scholar
6.Kendall, D.G. (1956). Some problems in the theory of queues. Journal of the Royal Statistical Society, Series B 13: 151–185.Google Scholar
7.Kino, I. & Miyazawa, M. (to appear). The stationary work in system of a G1/G/1 gradual input queue. Journal of Applied Probability.Google Scholar
8.Miyazawa, M. & Yamazaki, G. (1992). Loss probabilities of a burst arrival finite queue with synchronized service. Probability in the Engineering and Informational Sciences 6: 201–216.Google Scholar
9.Ott, T.J. (1993). A versatile packet arrival process and its second order properties. Probability in the Engineering and Informational Sciences 7: 495–513.CrossRefGoogle Scholar
10.Ott, T.J. (1993). A queuing system with a branching process arrival stream, the case of intermediate-range dependence. Bellcore Internal Publication, Morristown, NJ.Google Scholar
11.Ott, T.J. & Shanthikumar, J.G. (1991). On a buffer problem for packetized voice with an N-periodic strongly interchangeable input process. Journal of Applied Probability 28: 630–646.CrossRefGoogle Scholar
12.Roberts, J.W. & Virtamo, H.T. (1991). The superposition of periodic cell arrival streams in an ATM multiplexer. IEEE Transactions on Communications 39(2): 298–303.Google Scholar
13.Sigman, K. & Yamazaki, G. (1992). Fluid models with burst arrivals: A sample path analysis. Probability in the Engineering and Informational Sciences 6: 17–27.CrossRefGoogle Scholar