Analysis of a G/M/K/O queueing loss system with heterogeneous servers and retrials

Consider a G/M/K/O queueing loss system with K heterogeneous servers, exponentially distributed service times, no waiting room, a stationary counting arrival process, and an ordered entry. The ordered entry rule implies that, if the servers are indexed from 1 to K, units first arrive at the first server, then at the second server, and finally at the Kth server. In this queueing system, units that find the servers busy are not lost. Those units re-try to receive service by merging with the incoming units to be reconsidered for service by one of the free servers. This queueing system is analysed in terms of approximating the flows of units inside the system by a two parameter method. An example is introduced and approximation results are compared with those from a simulation study.