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Busy period of a finite queue with phase type service

Published online by Cambridge University Press:  14 July 2016

Stig I. Rosenlund
Stig I. Rosenlund*
Affiliation:
University of Stockholm
*
∗Now at the University of Gothenburg, Sweden.
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Abstract

An M/G/1 service system with finite waiting room is studied. A customer is served by one server in two phases, during the first of which a place in the waiting room is occupied. Starting from a determinant expression for the Laplace-Stieltjes transform of the busy period given in [2] we obtain contour integral expressions for the transform and the expectation, thereby generalising a result by Cohen [1]. This is effected by developing the determinants along the first row.

Keywords

QUEUEFINITE WAITING ROOMPHASE TYPE SERVICEBUSY PERIODDETERMINANT CALCULUSINVENTORY
Type
Short Communications
Information
Journal of Applied Probability , Volume 12 , Issue 1 , March 1975 , pp. 201 - 204
Copyright
Copyright © Applied Probability Trust 1975 

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References

[1] Cohen, J. W. (1971) On the busy periods for the M/G/1 queue with finite and with infinite waiting room. J. Appl. Prob. 8, 821–827.Google Scholar
[2] Rosenlund, S. I. (1973) An M/G/1 model with finite waiting room in which a customer remains during part of service. J. Appl. Prob. 10, 778–785.CrossRefGoogle Scholar
[3] Råed, L. (1972) A model for interaction of a Poisson and a renewal process and its relation with queuing theory. J. Appl. Prob. 9, 451–456.Google Scholar
[4] Tomko, J. (1967) A limit theorem for a queue when the input rate increases indefinitely. (In Russian) Studia Sci. Math. Hung. 2, 447–454.Google Scholar