Analysis and Approximation of Dual Tandem Queues with Finite Buffer Capacity

TL;DR

This paper introduces a novel analysis method for dual tandem queues with finite buffers, modeling system performance through virtual interruptions and providing an approximation for mean queue time.

Contribution

It develops an innovative approach using reduction methods and virtual interruptions to analyze finite buffer tandem queues, revealing how system service rate depends on arrival rate.

Findings

System service rate is less than or equal to the bottleneck rate.

Virtual interruptions depend on arrival rates.

An approximation for mean queue time is proposed.

Abstract

Tandem queues with finite buffer capacity commonly exist in practical applications. By viewing a tandem queue as an integrated system, an innovative approach has been developed to analyze its performance through the insight from reduction method. In our approach, the starvation at the bottleneck caused by service time randomness is modeled and captured by interruptions. Fundamental properties of tandem queues with finite buffer capacity are examined. We show that in general system service rate of a dual tandem queue with finite buffer capacity is equal or smaller than its bottleneck service rate, and virtual interruptions, which are the extra idle period at the bottleneck caused by the non-bottlenecks, depend on arrival rates. Hence, system service rate is a function of arrival rate when the buffer capacity of a tandem queue is finite. Approximation for the mean queue time of a dual tandem queue has been developed through the concept of virtual interruptions.