Minimizing Congestion in Single-Source, Single-Sink Queueing Networks

43 Pages Posted: 18 Nov 2021 Last revised: 25 Aug 2022

See all articles by Fabian Ying

Fabian Ying

University of Oxford - Mathematical Institute

Alisdair Wallis

Tesco PLC

Mason Porter

University of California, Los Angeles (UCLA)

Sam Howison

University of Oxford

Mariano Beguerisse-Diaz

University of Oxford - Mathematical Institute

Date Written: November 6, 2021

Abstract

Motivated by the modeling of customer mobility and congestion in supermarkets, we study queueing networks with a single source and a single sink. We assume that walkers traverse a network according to an unbiased random walk, and we analyze how network topology affects the total mean queue size $Q$, which we use to measure congestion. We examine network topologies that minimize $Q$ and provide proofs of optimality for some cases and numerical evidence of optimality for others. Finally, we present greedy algorithms that add and delete edges from a network to reduce $Q$, and we apply these algorithms to a supermarket store layout. We find that these greedy algorithms, which typically tend to add edges to the sink node, are able to significantly reduce $Q$. Our work helps improve understanding of how to design networks with low congestion and to amend networks to reduce congestion.

Keywords: queueing networks, random walks, congestion, human mobility, complex systems

JEL Classification: C02

Suggested Citation

Ying, Fabian and Wallis, Alisdair and Porter, Mason and Howison, Sam and Beguerisse-Diaz, Mariano, Minimizing Congestion in Single-Source, Single-Sink Queueing Networks (November 6, 2021). Available at SSRN: https://ssrn.com/abstract=3958094 or http://dx.doi.org/10.2139/ssrn.3958094

Fabian Ying

University of Oxford - Mathematical Institute ( email )

Radcliffe Observatory, Andrew Wiles Building
Woodstock Rd
Oxford, Oxfordshire OX2 6GG
United Kingdom

Alisdair Wallis

Tesco PLC

Mason Porter (Contact Author)

University of California, Los Angeles (UCLA) ( email )

405 Hilgard Avenue
Box 951361
Los Angeles, CA 90095
United States

Sam Howison

University of Oxford ( email )

Mathematical Institute
andrew Wiles Building, Woodstock Road
Oxford, OX2 6GG
United Kingdom

Mariano Beguerisse-Diaz

University of Oxford - Mathematical Institute ( email )

Andrew Wiles Building
Radcliffe Observatory Quarter (550)
Oxford, OX2 6GG
United Kingdom

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