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Journal Article

The Queue GI/M/s with Customers of Different Types or the Queue GI/Hm/s

Jos H. A. De Smit
Advances in Applied Probability
Vol. 15, No. 2 (Jun., 1983), pp. 392-419
DOI: 10.2307/1426442
Stable URL: http://www.jstor.org/stable/1426442
Page Count: 28
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
The Queue GI/M/s with Customers of Different Types or the Queue GI/Hm/s
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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.

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