Optimal control of two interacting service stations

Optimal controls described by switching curves in the two dimensional state space are shown to exist for the optimal control of a Markov network with two service stations and linear cost. The controls govern routing and service priorities. Finite horizon and long run average cost problems are considered. An example is given which shows that nonconvex value functions can arise for slightly more general networks. A single station control problem with nonconvex value functions is then considered to indicate how switch structure might be established more generally.