Non-Asymptotic Performance Analysis of Size-Based Routing Policies

TL;DR

This paper analyzes the performance of size-based routing policies in a two-server system with bounded Pareto job sizes, revealing unbounded mean waiting time ratios under certain conditions and supporting findings with numerical experiments.

Contribution

It provides the first non-asymptotic analysis of SITA and TAGS policies, showing unbounded waiting time ratios and extending results to various Pareto distributions.

Findings

Mean waiting time ratio between TAGS and SITA can be unbounded.

Theoretical results hold for Bounded Pareto distributions with different tail parameters.

Numerical experiments confirm the theoretical analysis.

Abstract

We investigate the performance of two size-based routing policies: the Size Interval Task Assignment (SITA) and Task Assignment based on Guessing Size (TAGS). We consider a system with two servers and Bounded Pareto distributed job sizes with tail parameter 1 where the difference between the size of the largest and the smallest job is finite. We show that the ratio between the mean waiting time of TAGS over the mean waiting time of SITA is unbounded when the largest job size is large and the arrival rate times the largest job size is less than one. We provide numerical experiments that show that our theoretical findings extend to Bounded Pareto distributed job sizes with tail parameter different to 1.