A single queue with mutually replacing m servers

Abstract

Customers arriving in a Poisson stream are served one by one exponentially by the m servers 81, 82, ... .S,«. A server who has just completed a service either continues the next service or is replaced by another server. The replacement of server at each service completion is governed by a probabilistic criterion of availability of servers. Transient solutions in terms of Laplace transforms of the probability generating functions are obtained and among some special cases the earlier known results of Madan (1990) for the case of 2 servers are deduced. The steady state solutions and the mean queue lengths have been explicitly for some particular cases.