A Diffusion Approximation for Bulk Queues

In this paper the steady-state queue size behavior of single-server queues with bulk-arrival and batch-service, referred to as bulk queues, is approximated by a diffusion process using the instantaneous return approach. Diffusion approximation solutions for various queue size statistics are developed and evaluated for a number of special “Markovian-like” bulk queues. The approximate solutions are found to be robust for queues under heavy traffic, and in certain cases, under other traffic conditions.