A monotonicity result for the workload in Markov-modulated queues

Nicole Bäuerle · Tomasz Rolski

41 citations0/0 files storedJournal of Applied Probability

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Advanced Queuing Theory Analysis Stochastic processes and statistical mechanics Probability and Risk Models

Abstract

We consider a single server queue where the arrival process is a Markov-modulated Poisson process and service times are independent and identically distributed and independent from arrivals. The underlying intensity process is assumed ergodic with generator cQ, c > 0. We prove under some monotonicity assumptions on Q that the stationary workload W(c) is decreasing in c with respect to the increasing convex ordering.

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References

1986Comparison Methods for Queues and Other Stochastic Models.1984Comparison Methods for Queues and Other Stochastic Models 1978Average delay in queues with non-stationary Poisson arrivals 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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