On evaluation of the mean service cycle time in tandem queueing systems

TL;DR

This paper derives formulas for calculating the average cycle time in tandem queueing systems with both infinite and finite buffers, considering the statistical properties of interarrival and service times.

Contribution

It provides a theoretical framework for exact evaluation of mean cycle times in tandem queues, including systems with finite buffers and blocking.

Findings

Mean cycle time exists for tandem queues with i.i.d. times.

Finite variance allows explicit calculation of mean cycle time.

Results extend to systems with finite buffers and blocking.

Abstract

The problem of exact evaluation of the mean service cycle time in tandem systems of single-server queues with both infinite and finite buffers is considered. It is assumed that the interarrival and service times of customers form sequences of independent and identically distributed random variables with known mean values. We start with tandem queues with infinite buffers, and show that under the above assumptions, the mean cycle time exists. Furthermore, if the random variables which represent interarrival and service times have finite variance, the mean cycle time can be calculated as the maximum out from the mean values of these variables. Finally, obtained results are extended to evaluation of the mean cycle time in particular tandem systems with finite buffers and blocking.