A Model of a Finite Buffer Shared by Queues with Batched Poisson Arrivals

We study a model of a finite buffer shared by M ([x]) / M/ 1 queues. Customer arrivals in each queue are modeled as a batched Poisson process with an arbitrary batch size distribution. The model is a generalization of the Kamoun and Kleinrock model of a packet switch buffer memory shared by M/M/1 queues. A sufficient condition is found, involving quite general buffer sharing policies, for equilibrium state probability distribution to have the product form. For the special case of the geometrically distributed batches and complete sharing buffer policy, we obtain closed form solutions for the normalization constant. The solutions emerge from a few system load configurations and lead to efficient computational procedures for the performance characteristics.