A reversible erlang loss system with multitype customers and multitype servers

Ivo Adan, Cor Hurkens, Gideon Weiss

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We consider a memoryless Erlang loss system with servers = {1, J}, and with customer types = {1, I}. Servers are multitype, so that server j can serve a subset of customer types C(j). We show that the probabilities of assigning arriving customers to idle servers can be chosen in such a way that the Markov process describing the system is reversible, with a simple product form stationary distribution. Furthermore, the system is insensitive; these properties are preserved for general service time distributions.

Original languageEnglish
Pages (from-to)535-548
Number of pages14
JournalProbability in the Engineering and Informational Sciences
Issue number4
StatePublished - Oct 2010

Bibliographical note

Funding Information:
The authors would like to thank Scott Provan for many stimulating discussions on this problem. The authors would like to thank Frank Kelly and Peter Whittle for discussions of insensitivity. Research by I. Adan was supported in part by the Netherlands Organization for Scientific Research (NWO). Research by G. Weiss was supported in part by Israel Science Foundation Grants 454/05 and 711/09; hospitality of the Newton Institute of Mathematical Sciences is gratefully acknowledged.

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Management Science and Operations Research
  • Industrial and Manufacturing Engineering

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