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Palm Calculus, Reallocatable GSMP and Insensitivity Structure

In: Queueing Networks

Author

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  • Masakiyo Miyazawa

    (Tokyo University of Science)

Abstract

This chapter discusses Palm calculus and its applications to various processes including queues and their networks. We aim to explain basic ideas behind this calculus. Since it differs from the classical approach using Markov processes, we scratch from very fundamental facts. The main target of Palm calculus is stationary processes, but we are also interested in its applications to Markov processes. For this, we consider piece-wise deterministic processes and reallocatable generalized Markov processes, RGSMP for short, and characterize their stationary distributions using Palm calculus. In particular, the insensitive structure of RGSMP with respect to the lifetime distributions of its clocks is detailed. Those results are applied to study the insensitive structure of product form queueing networks with respect to service requirement distributions.

Suggested Citation

  • Masakiyo Miyazawa, 2011. "Palm Calculus, Reallocatable GSMP and Insensitivity Structure," International Series in Operations Research & Management Science, in: Richard J. Boucherie & Nico M. Dijk (ed.), Queueing Networks, chapter 0, pages 141-215, Springer.
    • Handle: RePEc:spr:isochp:978-1-4419-6472-4_4
    DOI: 10.1007/978-1-4419-6472-4_4
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