A REVERSIBLE ERLANG LOSS SYSTEM WITH MULTITYPE CUSTOMERS AND MULTITYPE SERVERS

We consider a memoryless Erlang loss system with servers S = {1, . . . , J}, and with customer types C = {1, . . . , I}. Servers are multitype, so that server j can serve a subset of customer typesC( j).We showthat 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.