On Poisson Queue with Two Heterogeneous Servers

A Poisson queue with two heterogeneous servers has been considered. Some objections to the use of classical queue discipline are raised, chief among them being the violation of the “first-in first-out” principle, because of heterogeneity of servers. Two alternative queue disciplines are considered, one with a slight and the other with a greater modification of the classical one. The second one takes care of the objections raised against the classical one, while the first is still of interest because of its operational simplicity. Under the first one the steady state and the Laplace transform of the transient state probability distribution of the queue length have been derived. Also different types of busy periods have been defined. Under the second one, only steady-state results have been obtained. An application has been indicated.