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Monotonicity Results for MR/GI/1 Queues
Journal of Applied Probability
Vol. 34, No. 2 (Jun., 1997), pp. 514-524
Published by: Applied Probability Trust
Stable URL: http://www.jstor.org/stable/3215390
Page Count: 11
You can always find the topics here!Topics: Customers, Random variables, Markov chains, Matrices, Mathematical vectors, Stochastic models, Mathematical monotonicity, Mathematical theorems, Markov processes, Probability distributions
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This paper considers queues with a Markov renewal arrival process and a particular transition matrix for the underlying Markov chain. We study the effect that the transition matrix has on the waiting time of the nth customer as well as on the stationary waiting time. The main theorem generalizes results of Szekli et al. (1994a) and partly confirms their conjecture. In this context we show the importance of a new stochastic ordering concept.
Journal of Applied Probability © 1997 Applied Probability Trust