Analysis of Closed Unreliable Queueing Networks with Batch Service

Abstract

In this article, we study closed queuing networks with batch services of customers. Each node in the queueing network is an infinite capacity single-server queueing system under a RANDOM discipline. Customers move among the nodes following a routing matrix. We assume queueing systems in the network operate under the general batch service rule. The lower and upper bounds for the batch size are given. The batch service time is exponentially distributed. We presents an analysis of the queueing network using a Markov chain with continuous time. The qenerator matrix is constructed for the underlying Markov chain. We obtain expressions for the performance measures. In addition, we consider an unreliable case and propose an approximation. Some numerical examples are provided. The results can be used for the performance analysis manufacturing systems, production lines, trucking, ship locks.