A double-server double-class queue with constant retrial policy in reducing delay in healthcare delivery.

Abstract

We consider in this paper a double-server double-class retrial queues. Servers, when free, help serve patients awaiting in the buffers of other servers. Patients arrive at both queues according to Poisson processes. Each station is fed by a renewal input with general independent identically distributed inter-arrival times and general identically independent distributed service times possibly different in the two stations. All service times are exponential, with rates depending on the queues. The cost to be minimized involve cost per unit time that a patient spends in the system. We find a sufficient conditions including all possible parameter choices such as arrival rates, retrial rates and service rates. We further present conditions for scheduling new arrivals, under which server assignment to either queue-1 or queue-2 is cost optimal.