This paper is concerned with single server queueing systems with renewal service process and Poisson arrivals modulated by a finite-state Markov chain. Exponential martingales are associated with a chain embedded at service completion epochs in the stochastic process describing the joint...

We give some probabilistic conditions based on coupling for a functional of a Poisson point process to be differentiable in the intensity [lambda] of this process in a neighborhood of the origin. These conditions are exemplified on various queueing theory problems, and compared with other...

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