Performance balancing size-interval routing policies

Abstract

We study a parallel-queue system with Poisson arrivals, in which a dispatcher sends the incoming traffic to K queues using Size Interval Task Assignment (SITA) policy that aims to equalize the performance of all queues. We study existence and uniqueness of the allocation thresholds for a large set of performance functions of the queues. We also provide a family of performance functions of the queues such that the performance of the system is characterized. For a particular case of the latter family of functions, we show that the performance of the SITA policy we study coincides with the performance of the SITA policy in which the load is balanced. We investigate the optimality of the SITA policy under study and, according to our numerical experiments, for FCFS queues and Bounded Pareto distributed job sizes, the SITA policy we study is almost optimal, when we consider the mean queue length and $\alpha <1$ as well as when we consider the mean slowdown.

Keywords:

• Performance evaluation
• queueing theory
• size-based routing

Acknowledgments

The authors are grateful to the anonymous referees for valuables suggestions that helped to improve the presentation of the paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work has been partially funded by the Project of the Spanish Ministry of Economy and Competitiveness with reference MTM2016-76329-R, the Marie Sklodowska-Curie grant agreement No 777778 and the Consolidated Research Group MATHMODE (IT1294-19).