Economies-of-scale in resource sharing systems: tutorial and partial review of the QED heavy-traffic regime

TL;DR

This paper provides a tutorial and partial review of the QED heavy-traffic regime in multi-server queueing systems, focusing on resource pooling and economies-of-scale for large capacity systems.

Contribution

It offers a detailed explanation of the mathematical foundations of the QED regime in many-server systems, bridging theory and practical system design insights.

Findings

QED regime enables high utilization with manageable delays.

Mathematical concepts for Markovian many-server systems are detailed.

Partial survey of advanced topics related to load balancing and queueing networks.

Abstract

Multi-server queueing systems describe situations in which users require service from multiple parallel servers. Examples include check-in lines at airports, waiting rooms in hospitals, queues in contact centers, data buffers in wireless networks, and delayed service in cloud data centers. These are all situations with jobs (clients, patients, tasks) and servers (agents, beds, processors) that have large capacity levels, ranging from the order of tens (checkouts) to thousands (processors). This survey investigates how to design such systems to exploit resource pooling and economies-of-scale. In particular, we review the mathematics behind the Quality-and-Efficiency Driven (QED) regime, which lets the system operate close to full utilization, while the number of servers grows simultaneously large and delays remain manageable. Aimed at a broad audience, we describe in detail the mathematical concepts for the basic Markovian many-server system, and only provide sketches or references for more advanced settings related to e.g. load balancing, overdispersion, parameter uncertainty, general service requirements and queueing networks. While serving as a partial survey of a massive body of work, the tutorial is not aimed to be exhaustive.