Queues with stochastic service rates

Carl M. Harris

Naval Research Logistics Quarterly, 1967, vol. 14, issue 2, 219-230

Abstract: The purpose of this paper is to explore an extension of the output discipline for the Poisson input, general output, single channel, first‐come, first‐served queueing system. The service time parameter, μ, is instead considered a random variable, M. In other words, the service time random variable, T, is to be conditioned by a parameter random variable, M. Therefore, if the distribution function of M is denoted by FM(μ) and the known conditional service time distribution as B(t |μ), then the unconditional service distribution is given by B(t) = Pr {T ≤ t}. = ∫‐∞∞ B(t |μ) dFM(μ). Results are obtained that characterize queue size and waiting time using the imbedded Markov chain approach. Expressions are derived for the expected queue length and Laplace‐Stieltjes transforms of the steady‐state waiting time when conditional service times are exponential. More specific results are found for three special distributions of M: (1) uniform on [1.2]; (2) two‐point; and (3) gamma.

Date: 1967
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Persistent link: https://EconPapers.repec.org/RePEc:wly:navlog:v:14:y:1967:i:2:p:219-230

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