The analysis of batch sojourn-times in polling systems

TL;DR

This paper analyzes the distribution and mean of batch sojourn-times in cyclic polling systems with general service and switch-over times, comparing different service disciplines through exact formulas and numerical analysis.

Contribution

It provides exact Laplace-Stieltjes transform expressions and an efficient mean value analysis method for batch sojourn-times in polling systems with various service disciplines.

Findings

Exact expressions for batch sojourn-time distributions.

Efficient mean sojourn-time calculation method.

Service discipline performance varies with system parameters.

Abstract

We consider a cyclic polling system with general service times, general switch-over times, and simultaneous batch arrivals. This means that at an arrival epoch, a batch of customers may arrive simultaneously at the different queues of the system. For the locally-gated, globally-gated, and exhaustive service disciplines, we study the batch sojourn-time, which is defined as the time from an arrival epoch until service completion of the last customer in the batch. We obtain for the different service disciplines exact expressions for the Laplace-Stieltjes transform of the steady-state batch sojourn-time distribution, which can be used to determine the moments of the batch sojourn-time, and in particular, its mean. However, we also provide an alternative, more efficient way to determine the mean batch sojourn-time, using Mean Value Analysis. Finally, we compare the batch sojourn-times for the different service disciplines in several numerical examples. Our results show that the best performing service discipline, in terms of minimizing the batch sojourn-time, depends on system characteristics.