Optimal queueing systems controls with finite buffers and with multiple component cost functions

Analytical models of stochastic discrete event dynamic systems are now widely used to control congestion while maintaining throughput in many data communication, computing and production networks. An analytical and tractable framework of an optimal feedback control policy is developed here for queueing networks with limited storage buffers and with sequence-dependent service times. The general response measure used incorporates delay, shortage, and the setup costs. This formulation provides a new perspective to dynamic flow control models that are based on a rational function of the queue lengths of various downstream queues raher than on time. This formulation also enables the derivation of various performance measures for each node. Presented measures include throughput rate, utilization, queue length, starvation intervals and setups. Detailed numerical examples provide some insights into the structure and performance of the optimal policy. It is explicated that the buffer capacity vector has a minimal effect on the routing decisions in the interior of the state space and that the relative value of the buffer spaces declines with the increase in the delay costs. The impact of major resource allocation decisions and of changes in the performance cost measures are also explained.