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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Bäuerle et al. (1998) studied this question.
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