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On the Analysis of the Discrete-Time Geom(n)/G(n)/1/N Queue

Published online by Cambridge University Press:  27 July 2009

M. L. Chaudhry  and
U. C. Gupta
M. L. Chaudhry
Affiliation:
Department of Mathematics and Computer Science, Royal Military College of CanadaKingston, Ontario, Canada, K7K 5L0
U. C. Gupta
Affiliation:
Department of Mathematics, Indian Institute of Technology, Kharagpur 721302, India
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Extract

In this paper, we discuss the late-arrival discrete-time Geom(n)/G(n)/1/N queue with state-dependent arrival and service processes. Whereas the interarrival times are geometrically distributed, service times are conditioned on the system length at the moment of service initiation. The model has wide applications in computer-communications systems, broadband integrated service digital network, asynchronous transfer mode, and so on. The analysis of the model has been carried out, using the supplementary variable technique, and the final results are presented in the form of recursive equations that can be easily implemented on any personal computer. In addition, relations among state probabilities at prearrival, postdeparture, and random epochs have been developed. To demonstrate the effectiveness of our method, some numerical examples have been presented for service-time distributions such as geometric, deterministic, arbitrary, and mixed. The results obtained in this paper should be found useful by system designers who wish to control the congestion by adjusting the service rate if the arrival traffic changes.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 10 , Issue 3 , July 1996 , pp. 415 - 428
Copyright
Copyright © Cambridge University Press 1996

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References

1.Bruneel, H. & Kim, B.G. (1993). Discrete-time models for communication systems including ATM. Boston: Kluwer Academic Publishers.CrossRefGoogle Scholar
2.Chaudhry, M.L. & Gupta, U.C. (1996). Performance analysis of the discrete-time GI/Geom/1/N queue. Journal of Applied Probability 33: 239–255.CrossRefGoogle Scholar
3.Gravey, A., Louvion, J.R., & Boyer, P. (1990). On the Geom/D/l and Geom/D/l/n queues. Performance Evaluation 11: 117–125.CrossRefGoogle Scholar
4.Hunter, J.J. (1983). Mathematical techniques of applied probability. Vol. II: Discrete time models: Techniques and applications. New York: Academic Press.Google Scholar
5.Kijima, N. & Makimoto, N. (1982). Computation of the quasi-stationary distribution in M(n)/Gl/l/K and GI/M(n)/1/Kqueues. Queueing Systems 11: 255–272.CrossRefGoogle Scholar
6.Louchard, G. & Latouche, G. (1983). Probability theory and computer science. New York: Academic Press.Google Scholar
7.Takagi, H. (1993). Queueing analysis—A foundation of performance evaluation, Vol. 2: Finite systems. New York: North-Holland.Google Scholar
8.Takagi, H. (1993). Queueing analysis—A foundation of performance evaluation, Vol. 3: Discretetime systems. New York: North-Holland.Google Scholar