A maximum entropy optimization approach to tandem queues with generalized blocking

We study a general blocking scheme for an open tandem queueing network with finite intermediate buffers. The service time at each node as well as interarrival time at the first node is assumed to be exponentially distributed. The interarrival and service time at each intermediate node of the tandem queue, under the general blocking scheme, depend upon three parameters at each node, namely, the maximum number of raw jobs, the upper limit on the number of finished but blocked jobs and the buffer capacity. This three-parameter analysis was introduced by Cheng and Yao (1993), and was shown, using Monte Carlo simulations, to provide good results. Our analysis is also based on this three-parameter approach, but with a different view. We first decompose the tandem queue into a group of two-node subsystems in order to derive a set of equations for the effective interarrival and service time distributions at each node. Each of these two-node subsystems is treated as a finite capacity queueing system with population size constraints. Then we apply the principle of maximum entropy to evaluate different parameters such as the blocking probabilities, starvation probabilities, etc., of each subsystem. We propose a step-by-step algorithm along with its convergence properties. A comparison of numerical results with the simulation results is also discussed.