Many-Server Queueing Systems with Heterogeneous Strategic Servers in Heavy Traffic

TL;DR

This paper develops a measure-valued mean-field game framework to analyze strategic, heterogeneous servers in many-server queues, revealing new optimal regimes influenced by server discomfort and routing policies.

Contribution

It introduces a novel measure-valued mean-field game approach to model individual server choices, abilities, discomfort, and routing in large service systems, extending existing literature.

Findings

Asymptotic characterization of Nash equilibria in large systems.

Identification of conditions where quality-and-efficiency-driven regimes are optimal.

First demonstration that discomfort can shift optimal regimes in queueing systems.

Abstract

In most service systems, the servers are humans who desire to experience a certain level of idleness. In call centers, this manifests itself as the call avoidance behavior, where servers strategically adjust their service rate to strike a balance between the idleness they receive and effort to work harder. Moreover, being humans, each server values this trade-off differently and has different capabilities. Drawing ideas on mean-field games we develop a novel framework relying on measure-valued processes to simultaneously address strategic server behavior and inherent server heterogeneity in service systems. This framework enables us to extend the recent literature on strategic servers in four new directions by: (i) incorporating individual choices of servers, (ii) incorporating individual abilities of servers, (iii) modeling the discomfort experienced by servers due to low levels of idleness, and (iv) considering more general routing policies. Using our framework, we are able to asymptotically characterize asymmetric Nash equilibria for many-server systems with strategic servers. In simpler cases, it has been shown that the purely quality-driven regime is asymptotically optimal. However, we show that if the discomfort increases fast enough as the idleness approaches zero, the quality-and-efficiency-driven regime and other quality driven regimes can be optimal. This is the first time this conclusion appears in the literature.