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The author considers a queueing network with types of customers, Poisson arrivals, type dependent routing and state dependent service. A number of stochastic aspects relating to sojourn times are investigated. Included are limiting state distributions imbedded at customer move times, mean sojourn times, and sojourn time distributions along overtake-free paths. It is shown that Reich's results extend to overtake-free paths yielding limiting sojourn time distributions which correspond to the sum of exponential independent stages of sojourn in individual nodes. The analysis is based solely on considerations of population distributions through conditioning on customers' itineraries in the network.

Original languageEnglish (US)
Pages (from-to)223-244
Number of pages22
JournalMathematics of Operations Research
Issue number2
StatePublished - 1982
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Computer Science Applications
  • Management Science and Operations Research

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