Optimal Control of an M/M/S Queueing System

We consider the problem of determining optimal operating policies for an M/M/S queueing system. The system state (x₁, x₂) is defined by x₁ the number of customers in the system, and x₂ the number of active service channels. The cost structure includes customer holding and service channel operating costs as well as a linear switching cost. We use a continuous-time Markov decision process formulation to obtain an optimal control policy of the control limit form, and present an algorithm for the finite state problem. Finite-transition and infinite-transition with discounting are considered.