The M/G/k Blocking System with Heterogeneous Servers

Abstract

This paper considers the M/G/k blocking system under the assumption of servers whose service time distributions differ. Such a system has k servers each with a (possibly) different service time distribution, whose customers arrive in accordance with a Poisson process. They are served, unless all the servers are occupied. In this case they leave and do not return later (i.e. they are "blocked"). A generalization of the Erlang B-formula is given and it is shown that the latter is valid in the case of heterogeneous servers too, provided that all servers have equal mean service times. In the form of an appendix, the Engset formula also is generalized under the above assumption.