Abstract
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.
Highlights
Group arrival and batch service queues have many applications in manufacturing, service operations, computer and telecommunication systems.R
Since most of these systems have finite buffer capacity, it is of interest to study queueing systems with finite queue size
In computer and telecommunication systems, routers and switches that regulate the transmission of information packages have finite buffer capacity
Summary
Group arrival and batch service queues (usually called bulk queues) have many applications in manufacturing, service operations, computer and telecommunication systems. In computer and telecommunication systems, routers and switches that regulate the transmission of information packages have finite buffer capacity In many of these applications, the arrival and service rate depend on the state of the queue. The batch service time can depend on the batch size; typically larger batches require more service time In all these applications, it is helpful to be able to compute relevant performance measures, such as average time in system, moments of the number of customers in queue and loss probabilities for arriving groups of customers, or individual customers within a group. It is helpful to be able to compute relevant performance measures, such as average time in system, moments of the number of customers in queue and loss probabilities for arriving groups of customers, or individual customers within a group This allows operators to determine optimal system configuration, good admission control policies, or optimal batch sizing policies.
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