Analysis of finite‐buffer state‐dependent bulk queues

In this paper, we consider a general state‐dependent finite‐buffer bulk queue in which the rates and batch sizes of arrivals and services are allowed to depend on the number of customers in queue and service batch sizes. Such queueing systems have rich applications in manufacturing, service operations, computer and telecommunication systems. Interesting examples include batch oven processes in the aircraft and semiconductor industry; serving of passengers by elevators, shuttle buses, and ferries; and congestion control mechanisms to regulate transmission rates in packet‐switched communication networks. We develop a unifying method to study the performance of this general class of finite‐buffer state‐dependent bulk queueing systems. For this purpose, we use semi‐regenerative analysis to develop a numerically stable method for calculating the limiting probability distribution of the queue length process. Based on the limiting probabilities, we present various performance measures for evaluating admission control and batch service policies, such as the loss probability for an arriving group of customers and for individual customers within a group. We demonstrate our method by means of numerical examples.