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Response Time Distributions in Networks of Queues

In: Queueing Networks

Author

Listed:
  • Michael Grottke

    (University of Erlangen-Nuremberg)

  • Varsha Apte

    (IIT Bombay)

  • Kishor S. Trivedi

    (Duke University)

  • Steve Woolet

    (IBM Corporation)

Abstract

This chapter addresses the issue of determining the response time distribution in networks of queues. Four different techniques are described and demonstrated. A two step numerical approach to compute the response time distribution for closed Markovian networks with general connectivity, a technique for determining the approximate (exact under certain conditions) response time distribution of a defined subset of open M/M/c/b Markovian networks using predefined continuous timeMarkov chain (CTMC) “response time blocks,” an expansion of “response time blocks” to openMarkovian networks with general phase type (PH) service time distributions, and an approach for handling non Markovian networks having M/G/1 priority and PH/G/1 queues. These techniques are shown to give accurate results with much smaller CTMCs or semi Markov processes than exact analysis.

Suggested Citation

  • Michael Grottke & Varsha Apte & Kishor S. Trivedi & Steve Woolet, 2011. "Response Time Distributions in Networks of Queues," International Series in Operations Research & Management Science, in: Richard J. Boucherie & Nico M. Dijk (ed.), Queueing Networks, chapter 14, pages 587-641, Springer.
    • Handle: RePEc:spr:isochp:978-1-4419-6472-4_14
    DOI: 10.1007/978-1-4419-6472-4_14
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    Cited by:

    1. Hum, Sin-Hoon & Parlar, Mahmut & Zhou, Yun, 2018. "Measurement and optimization of responsiveness in supply chain networks with queueing structures," European Journal of Operational Research, Elsevier, vol. 264(1), pages 106-118.

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