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A REVERSIBLE ERLANG LOSS SYSTEM WITH MULTITYPE CUSTOMERS AND MULTITYPE SERVERS

Published online by Cambridge University Press:  14 September 2010

Ivo Adan ,
Cor Hurkens  and
Gideon Weiss
Ivo Adan
Affiliation:
Department of Mathematics and Computer Science, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands Department of Quantitative Economics, University of Amsterdam, 1000 GG Amsterdam, The Netherlands E-mail: iadan@win.tue.nl
Cor Hurkens
Affiliation:
Department of Mathematics and Computer Science, Eindhoven University of Technology, 5600 MB, Eindhoven, The Netherlands E-mail: wscor@win.tue.nl
Gideon Weiss
Affiliation:
Department of Statistics, The University of Haifa, Mount Carmel 31905, Israel E-mail: gweiss@stat.haifa.ac.il
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Abstract

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.

Information

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 24 , Issue 4 , October 2010 , pp. 535 - 548
Copyright
Copyright © Cambridge University Press 2010

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References

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