Optimal control of arrivals in tandem queues of constant service time

We propose an optimal schedule for multiple classes of arrivals in a queueing system consisting of queues in tandem. The arrival process for each class is Poisson with different rates, and the service times are constant. A theoretical result is presented by Linear Programming of sample-path arguments, together with duality theory. The approach shows a powerful analytical tool which facilitates the procedure in analysis of optimization in queueing control problems and a possibility of future study in other similar problems.