Optimal Control of Arrivals to Token Ring Networks with Exhaustive Service Discipline

The optimal control of arrivals to a two-station token ring network is analyzed in this paper. By adopting a maximum system throughput under a system time-delay constraint optimality criterion, we study a network optimality problem with the assumption that both stations have global information (i.e., the number of packets at each station). The controlled arrivals are assumed to be state-dependent Poisson streams and have exponentially distributed service time. The optimality problem will be formulated using dynamic programming with a convex cost function. Combining with duality theory, we then show that the optimal control is almost bang-bang and in the special case when both queues have the same service rate and sufficiently large buffers, the optimal control is further shown to be switchover. A nonlinear program is used to numerically determine the optimal local control for the purpose of comparison. The results obtained under global and local information can be used to provide a measure of the tradeoff between maximum throughput efficiency and protocol complexity. Numerical examples illustrating the theoretical results are also provided.