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The departure process from the GI/G/1 Queue

Published online by Cambridge University Press:  14 July 2016

Thomas L. Vlach  and
Ralph L. Disney
Thomas L. Vlach
Affiliation:
University of Michigan
Ralph L. Disney
Affiliation:
University of Michigan
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Abstract

The departure process from the GI/G/1 queue is shown to be a semi-Markov process imbedded at departure points with a two-dimensional state space. Transition probabilities for this process are defined and derived from the distributions of the arrival and service processes. The one step transition probabilities and a stationary distribution are obtained for the imbedded two-dimensional Markov chain.

Type
Short Communications
Information
Journal of Applied Probability , Volume 6 , Issue 3 , December 1969 , pp. 704 - 707
Copyright
Copyright © Applied Probability Trust 

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References

[1] King, R. A. (1967) The Covariance Properties of the Departure Process from Single Channel Queues. Doctoral Dissertation, University of Michigan.Google Scholar
[2] Neuts, M. F. (1965) Discussion in [4].Google Scholar
[3] Prabhu, N. U. (1967) Queues and Inventories. John Wiley and Sons, Inc., New York.Google Scholar
[4] Smith, W. L. and Wilkinson, W. E. (1965) Proceedings of the Symposium on Congestion Theory. University of North Carolina Press, Chapel Hill.Google Scholar
[5] Vlach, T. L. (1968) Recurrence-type random variables in the GI/G/1 queue. Submitted for publication.Google Scholar