Multiple channel queues in heavy traffic. II: sequences, networks, and batches

Abstract

This paper is a sequel to [7], in which heavy traffic limit theorems were proved for various stochastic processes arising in a single queueing facility with r arrival channels and s service channels. Here we prove similar theorems for sequences of such queueing facilities. The same heavy traffic behavior prevails in many cases in this more general setting, but new heavy traffic behavior is observed when the sequence of traffic intensities associated with the sequence of queueing facilities approaches the critical value (ρ = 1) at appropriate rates.