Novel heavy-traffic regimes for large-scale service systems

TL;DR

This paper introduces new heavy-traffic regimes for large-scale service systems, providing capacity sizing rules that optimize utilization and limit congestion through novel asymptotic analysis methods.

Contribution

It develops a family of heavy-traffic regimes including moderate and extreme cases, with new asymptotic approximations for performance measures using a specialized saddle point method.

Findings

Heavy-traffic regimes include both moderate and extreme cases.

Capacity rules lead to near 100% utilization with limited congestion.

Asymptotic performance approximations are derived using a novel saddle point approach.

Abstract

We introduce a family of heavy-traffic regimes for large scale service systems, presenting a range of scalings that include both moderate and extreme heavy traffic, as compared to classical heavy traffic. The heavy-traffic regimes can be translated into capacity sizing rules that lead to Economies-of-Scales, so that the system utilization approaches 100% while congestion remains limited. We obtain heavy-traffic approximations for stationary performance measures in terms of asymptotic expansions, using a non-standard saddle point method, tailored to the specific form of integral expressions for the performance measures, in combination with the heavy-traffic regimes.