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A monotonicity result for the workload in Markov-modulated queues

  • Nicole Bäuerle (a1) and Tomasz Rolski (a2)

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.

Corresponding author
Postal address: Department of Mathematics VII, University of Ulm, D-89069 Ulm, Germany. Email address:
∗∗ Postal address: Mathematical Institute, University of Wroclaw, 50384 Wroclaw, Poland.
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Work supported in part by KBN under grant 2 PO3A 04608(1995–97).

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Journal of Applied Probability
  • ISSN: 0021-9002
  • EISSN: 1475-6072
  • URL: /core/journals/journal-of-applied-probability
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