Single-Server Queue with Markov-Dependent Inter-Arrival and Service Times |
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Authors: | Adan IJBF Kulkarni VG |
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Affiliation: | (1) Department of Mathematics and Computer Science, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands;(2) Department of Operations Research, University of North Carolina, CB 3180, Chapel Hill, NC 27599, USA |
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Abstract: | In this paper we study a single-server queue where the inter-arrival times and the service times depend on a common discrete
time Markov chain. This model generalizes the well-known MAP/G/1 queue by allowing dependencies between inter-arrival and service times. The waiting time process is directly analyzed by
solving Lindley's equation by transform methods. The Laplace–Stieltjes transforms (LST) of the steady-state waiting time and
queue length distribution are both derived, and used to obtain recursive equations for the calculation of the moments. Numerical
examples are included to demonstrate the effect of the autocorrelation of and the cross-correlation between the inter-arrival
and service times.
An erratum to this article is available at . |
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Keywords: | autocorrelation cross-correlation semi-Markov queue single server queue waiting time |
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