Optimal control of arrivals to token ring networks with exhaustive service discipline

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Abstract
The optimal control of arrivals to a two-station token ring network is analyzed. By adopting a maximum system throughput under a system time-delay optimality criterion, a social optimality problem is studied under the assumption that both stations have global information (i.e. the number of packets in each station). The controlled arrivals are assumed to be state-dependent Poisson streams and have exponentially distributed service time. The optimality problem is formulated as a dynamic programming problem with a convex cost function. Using duality theory, it is then shown that the optimal control is switchover when both queues have the same service rate and sufficiently large buffers. Nonlinear programming is used to numerically approximate the optimal local controls for comparison purposes. 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 provided.