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The steady state of a multi-server mixed queue

Published online by Cambridge University Press:  01 July 2016

N. B. Slater
University of Hull
T. C. T. Kotiah*
University of Hull
Now at Southern Illinois University, Edwardsville.


In a multi-server queueing system in which the customers are of several different types, it is useful to define states which specify the types of customers being served as well as the total number present. Analogies with some problems in statistical mechanics are found fruitful. Certain generating functions are defined in such a way that they satisfy a system of linear equations. Solution of the associated eigenvector problem shows that the steady-state probabilities for states in which all the servers are busy can be represented by a weighted sum of geometric probabilities.

Research Article
Copyright © Applied Probability Trust 1973 

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The final version of this paper was prepared for the printer by Dr. J. W. Thompson after Professor Slater's death on 31 January 1973.


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