Analysis and Approximation of Dual Tandem Queues with Finite Buffer Capacity

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.