Probability in the Engineering and Informational Sciences

Table of Contents - 2010 - Volume 24, Issue 04  

Research Article

A REVERSIBLE ERLANG LOSS SYSTEM WITH MULTITYPE CUSTOMERS AND MULTITYPE SERVERS

Ivo Adana1a2, Cor Hurkensa3 and Gideon Weissa4

a1 Department of Mathematics and Computer Science, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands

a2 Department of Quantitative Economics, University of Amsterdam, 1000 GG Amsterdam, The Netherlands E-mail: iadan@win.tue.nl

a3 Department of Mathematics and Computer Science, Eindhoven University of Technology, 5600 MB, Eindhoven, The Netherlands E-mail: wscor@win.tue.nl

a4 Department of Statistics, The University of Haifa, Mount Carmel 31905, Israel E-mail: gweiss@stat.haifa.ac.il

Abstract

We consider a memoryless Erlang loss system with servers S0269964810000161_inline1 = {1, …, J}, and with customer types S0269964810000161_inline2 = {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.