Technical Note—Optimal Service Policies, Just after Idle Periods, in Two-Server Heterogeneous Queuing Systems

We consider a two-server queuing system in which the service time distributions of the two servers are different. Customer arrivals are Poisson distributed. Customers renege if their wait in queue exceeds T (a random time). Customers arriving when the system is empty can be served by either of the two servers. Under policy i, they are served by server i, i = 1, 2. Our objective is to find the policy that maximizes the number of customers served. Let server 1's service time be stochastically less than server 2's service time. Intuitively, the optimal policy is policy 1; a counter-example shows that this is not always true.