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Infinitesimal perturbation analysis for queueing networks with general service time distributions

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Abstract

We study infinitesimal perturbation analysis (IPA) for queueing networks with general service time distributions. By “general” we mean that the distributions may have discrete components. We show that in the presence of service time distributions with discrete components commuting condition (CC) is no longer sufficient for unbiasedness of IPA. To overcome this difficulty, we introduce the notion of separability of real‐valued random variables, and show that separability of service times together with (CC) establishes unbiasedness of IPA for queueing systems with general service time distributions. It turns out that the piecewise analyticity of service times is a sufficient condition for separability.

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  1. Delft University of Technology, Faculty of Information Technology and Systems, P.O. Box 5031, 2600 GA, Delft, The Netherlands E-mail:

    Bernd Heidergott

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  1. Bernd Heidergott
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Heidergott, B. Infinitesimal perturbation analysis for queueing networks with general service time distributions. Queueing Systems 31, 43–58 (1999). https://doi.org/10.1023/A:1019193711052

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