Analysis of dual tandem queues with a finite buffer capacity and non-overlapping service times and subject to breakdowns

Abstract

Tandem queues with a finite buffer capacity are the common structures embedded in practical production systems. We study the properties of tandem queues with a finite buffer capacity and non-overlapping service times subject to time-based preemptive breakdowns. Different from prior aggregation and decomposition approaches, we view a tandem queue as an integrated system and develop an innovative approach to analyze the performance of a dual tandem queue through the insight from Friedman's reduction method. We show that the system capacity of a dual tandem queue with a finite buffer and breakdowns can be less than its bottleneck-sees-initial-arrivals system due to the existence of virtual interruptions. Furthermore, the virtual interruptions depend on job arrival rates in general. Approximate models are derived using priority queues and the concept of virtual interruptions.