A Queuing System with Service-Time Distribution of Mixed Chi-Squared Type
- 1 April 1959
- journal article
- Published by Institute for Operations Research and the Management Sciences (INFORMS) in Operations Research
- Vol. 7 (2) , 174-179
- https://doi.org/10.1287/opre.7.2.174
Abstract
In this paper Kendall's technique of the embedded Markov chain (Kendall, D. G. 1953. Stochastic processes in the theory of queues. Ann. Math. Stat. 24 338–354.) is applied to a queuing system with general independent input and a wide class of service-time distributions. The matrix of transition probabilities is found to be formally identical with that discussed in our earlier study (Wishart, D. M. G. 1956. A queuing system with χ2 service-time distribution. Ann. Math. Stat. 27 768–779.), which will be taken as read in the present paper. Using the results of reference 9 we can write down the equilibrium distribution of waiting-times for customers in the more general system in terms of the roots of a transcendental equation. An example is considered that arose in Bailey's study of hospital systems (Bailey, N. T. J. 1952. A study of queues and appointment systems in hospital out-patient departments. J. Roy. Stat. Soc. B14 185–199.).Keywords
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