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A note on the virtual waiting time in the stationary PH/M/c+D queue

Published online by Cambridge University Press:  30 March 2016

Ken'ichi Kawanishi
Affiliation:
Gunma University
Tetsuya Takine
Affiliation:
Osaka University
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Abstract

In this paper we consider the stationary PH/M/c queue with deterministic impatience times (PH/M/c+D). We show that the probability density function of the virtual waiting time takes the form of a matrix exponential whose exponent is given explicitly by system parameters.

Type
Short Communications
Copyright
Copyright © 2015 by the Applied Probability Trust 

References

Choi, B. D., Kim, B. and Zhu, D. (2004). MAP/M/c queue with constant impatient time. Math. Operat. Res. 29, 309325.CrossRefGoogle Scholar
Sakuma, Y. and Takine, T. (2015). Multi-class M/PH/1 queues with deterministic impatience times. Submitted.Google Scholar
Swensen, A. R. (1986). On a GI/M/c queue with bounded waiting times. Operat. Res. 34, 895908.CrossRefGoogle Scholar
Tijms, H. C. (1994). Stochastic Models: An Algorithmic Approach, John Wiley, Chichester.Google Scholar
Van Loan, C. F. (1978). Computing integrals involving the matrix exponential. IEEE Trans. Automatic Control 23, 395-404.CrossRefGoogle Scholar

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