Optimal control of admission to a multiserver queue with two arrival streams

The problem of finding an optimal admission policy to an M/M/c queue with one controlled and one uncontrolled arrival stream is addressed There are two streams of customers that are generated according to independent Poisson processes with constant arrival rates. The service time probability distribution is exponential and does not depend on the class of the customers. Upon arrival a class 1 customer may be admitted or rejected, while incoming class 2 customers are always admitted. A state-dependent reward is earned each time a new class 1 customer enters the system. When the discount factor is small, there exists a stationary admission policy of a threshold type that maximizes the expected total discounted reward over an infinite horizon. A similar result is also obtained when considering the long-run average reward criterion. The proof relies on a new device that consists of a partial construction of the solution of the dynamic programming equation. Applications arising from teletraffic analysis are proposed