Analysis of tandem queues with finite buffer capacity

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 insight from Friedman's reduction method. In our approach, the starvation at the bottleneck caused by service time randomness is modeled by interruptions. Fundamental properties of tandem queues with finite buffer capacity are examined. Without the assumptions of phase-type distributions and stochastic independence, we show that, in general, the system service rate of a tandem queue with a finite buffer capacity is equal to 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, the system service rate is a function of arrival rates when the buffer capacity of a tandem queue is finite. Approximations for the mean queue time of a dual tandem queue are developed using the concept of virtual interruptions.