Response Time Distributions in Networks of Queues

Michael Grottke (), Varsha Apte (), Kishor S. Trivedi () and Steve Woolet ()
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Michael Grottke: University of Erlangen-Nuremberg
Varsha Apte: IIT Bombay
Kishor S. Trivedi: Duke University
Steve Woolet: IBM Corporation

Chapter 14 in Queueing Networks, 2011, pp 587-641 from Springer

Abstract: 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.

Keywords: Arrival Rate; Sojourn Time; Service Time Distribution; Wait Time Distribution; Response Time Distribution (search for similar items in EconPapers)
Date: 2011
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DOI: 10.1007/978-1-4419-6472-4_14

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