An application of modern control theory to a time-dependent queuing system for optimal operation

‘ Bang-bang ’ optimal closed-loop service policy for a time dependent M/M/l queuing system is derived using optimal control theory. The policy is based on probabilistic (and not stochastic) behaviour of the queue. Computational results are obtained for an illustrative example with non-bang-bang service policy using the conjugate gradient algorithm with bounded control variables. It is interesting to note that the optimal service policy is not sensitive to the arrival rate but to the mean service cost of a customer.