General Solution of Queueing Model with Batch Renewal Arrival by Two Approaches

Queueing models with finite capacity and batch arrival or batch service processes are widely recognised as powerful tools for representing transportation networks, flexible manufacturing systems and predicting their performance. Although a considerable progress has been made in the field of analysis of a queue with single server and batch service in the literature, more work is needed to study more realistic type of queues with both batch arrival and service processes. This paper gives two general solutions to queues with continuous time batch renewal processes. Which are dual embedded Markov chains and supplementary variable technique respectively, and the two approaches are shown essentially equivalent.