Monotonicity results for MR/GI/1 queues

Nicole Bäuerle

26 citations0/0 files storedJournal of Applied Probability

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Advanced Queuing Theory Analysis Probability and Statistical Research Probability and Risk Models

Abstract

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.

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References

1962The stability of a queue with non-independent inter-arrival and service times 1986Comparison Methods for Queues and Other Stochastic Models.1984Comparison Methods for Queues and Other Stochastic Models 1993Regularity of Stochastic Processes: A Theory Based on Directional Convexity 1986Upper Bounds for Single Server Queues with Doubly Stochastic Poisson Arrivals 1989Queues with nonstationary inputs 1994MR/GI/1 queues by positively correlated arrival stream 1991Monotonicity results for queues with doubly stochastic Poisson arrivals: Ross's conjecture

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1996Some results about the expected ruin time in Markov-modulated risk models 1997Comparison Results for Markov-Modulated Recursive Models

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