Journal of Applied Probability

A monotonicity result for the workload in Markov-modulated queues

Nicole Bäuerle and Tomasz Rolski

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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.

Article information

J. Appl. Probab. Volume 35, Number 3 (1998), 741-747.

First available in Project Euclid: 17 September 2002

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60K25: Queueing theory [See also 68M20, 90B22]

Markov-modulated queue stationary workload increasing convex ordering supermodular function


Bäuerle, Nicole; Rolski, Tomasz. A monotonicity result for the workload in Markov-modulated queues. J. Appl. Probab. 35 (1998), no. 3, 741--747. doi:10.1239/jap/1032265221.

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