Minimizing Congestion in Single-Source, Single-Sink Queueing Networks
43 Pages Posted: 18 Nov 2021 Last revised: 25 Aug 2022
Date Written: November 6, 2021
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: Suggested Citation