The Generalized M/G/k Blocking System with Heterogeneous Servers

This paper studies the equilibrium behaviour of the generalized M/G/k blocking system with heterogeneous servers. Such a service 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 they do not return later (i.e. they are ‘blocked’). Whenever there are n (n = 0, 1, 2,..., k) servers occupied, each arriving customer balks with probability 1 - fn+1(fk+1 = 0) and each server works at a rate gn. Among other things, a generalization of the Erlang B-formula is given and also it is shown that the equilibrium departure process from the system is Poisson.