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An M/G/1 model with finite waiting room in which a customer remains during part of service

Published online by Cambridge University Press:  14 July 2016

Stig I. Rosenlund
Stig I. Rosenlund*
Affiliation:
University of Stockholm
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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 phases, during some of which a place in the waiting room is occupied. The busy period length distribution is obtained from a system of integral equations leading to a linear system in Laplace-Stieltjes transforms. An asymptotic expression, for large intensity of arrival, for the expectation of this length is given. An efficiency measure giving the long run customer loss ratio is obtained. The model is shown to apply to an inventory and a container traffic problem.

Keywords

QUEUEFINITE WAITING ROOMPHASE TYPE SERVICEBUSY PERIOD LENGTHCUSTOMER LOSS RATIOCONTAINERINVENTORYLINEAR EQUATIONS IN LAPLACE TRANSFORMS
Type
Research Papers
Information
Journal of Applied Probability , Volume 10 , Issue 4 , December 1973 , pp. 778 - 785
Copyright
Copyright © Applied Probability Trust 1973 

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References

[1] Rosenlund, S. I. (1972) An M/G/1 queue model with limited queue size for the servicing of containers with a random number of units in each. Research Report No. 67, Institute of Mathematical Statistics and Actuarial Mathematics, University of Stockholm.Google Scholar
[2] Råde, 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
[3] Råde, L. (1972) Thinning of a renewal point process by an inhibitory Poisson process with cumulative effect. Department of Mathematics Publications, 1972–6, Chalmer's Institute of Technology and the University of Göteborg.Google Scholar