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The queue GI/M/s with customers of different types or the queue GI/Hm/s

Published online by Cambridge University Press:  01 July 2016

Jos H. A. De Smit
Jos H. A. De Smit*
Affiliation:
Twente University of Technology
*
∗Postal address: Department of Applied Mathematics, Twente University of Technology, P.O. Box 217, 7500 AE Enschede, The Netherlands.
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Abstract

We study the queue GI/M/s with customers of m different types. An arriving customer is of type i with probability pi and the types of different customers are independent. A customer of type i requires a service time which is exponentially distributed with parameter bi. This model is equivalent to the queue GI/Hm/s, where Hm denotes a mixture of m different exponential distributions. We are primarily interested in the distributions of waiting times and queue lengths. Using a probabilistic argument we reduce the problem to the solution of a system of Wiener-Hopf-type equations. This system is solved by a factorization method. Thus we obtain explicit results for the stationary distributions of waiting times and queue lengths.

Keywords

MULTISERVER QUEUEQUEUE WITH CUSTOMERS OF DIFFERENT TYPESHYPEREXPONENTIAL SERVICE TIMESSYSTEM OF WIENER-HOPF-TYPE EQUATIONSMATRIX FACTORIZATIONMATRIX GENERALIZATION OF ROUCHÉ'S THEOREM
Type
Research Article
Information
Advances in Applied Probability , Volume 15 , Issue 2 , June 1983 , pp. 392 - 419
Copyright
Copyright © Applied Probability Trust 1983 

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References

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