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Decomposition property in a discrete-time queue with multiple input streams and service interruptions

  • Fumio Ishizaki (a1)

Abstract

This paper studies a discrete-time single-server queue with two independent inputs and service interruptions. One of the inputs to the queue is an independent and identically distributed process. The other is a much more general process and it is not required to be Markov nor is it required to be stationary. The service interruption process is also general and it is not required to be Markov or to be stationary. This paper shows that a stochastic decomposition property for the virtual waiting-time process holds in the discrete-time single-server queue with service interruptions. To the best of the author's knowledge, no stochastic decomposition results for virtual waiting-time processes in non-work-conserving queues, such as queues with service interruptions, have been obtained before and only work-conserving queues have been studied in the literature.

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Corresponding author

Postal address: Department of Information and Telecommunication Engineering, Nanzan University, 27 Seirei, Aichi 489-0863, Japan. Email address: fumio@ieee.org

References

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[1] Cassandras, C. G., and Lafortune, S. (1999). Introduction to Discrete Event Systems. Kluwer, Boston, MA.
[2] Chaudhry, M. L. (2000). On numerical computations of some discrete-time queues. In Computational Probability, ed. Grassmann, W. K., Kluwer, Dordrecht, pp. 365408.
[3] Glasserman, P., and Gong, W.-B. (1991). Time-changing and truncating k-capacity queues from one k to another. J. Appl. Prob. 28, 647655.
[4] Ishizaki, F., Takine, T., Takahashi, Y., and Hasegawa, T. (1994). A generalized SBBP/G/1 queue and its applications. Performance Evaluation 21, 163181.
[5] Ott, T. J. (1984). On the M/G/1 queue with additional inputs. J. Appl. Prob. 21, 129142.
[6] Ott, T. J. (1987). The single-server queue with independent GI/G and M/G input streams. Adv. Appl. Prob. 19, 266286.
[7] Takagi, H. (1993). Queueing Analysis: A Foundation of Performance Evaluation, Vol. 3, Discrete-Time Systems. North-Holland, Amsterdam.
[8] Takine, T., and Hasegawa, T. (1995). On the single-server queue with independent MAP/G and M/GI inputs streams. Commun. Statist. Stoch. Models 11, 227234.

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