A queueing‐theoretic framework for evaluating transmission risks in service facilities during a pandemic

Abstract

We propose a new modeling framework for evaluating the risk of disease transmission during a pandemic in small-scale settings driven by stochasticity in the arrival and service processes, that is, congestion-prone confined-space service facilities. We propose a novel metric, system-specific basic reproduction rate, inspired by the "basic reproduction rate" concept from epidemiology, which measures the transmissibility of infectious diseases. We derive our metric for various queueing models of service facilities by leveraging a novel queueing-theoretic notion: sojourn time overlaps. We showcase how our metric can be used to explore the efficacy of a variety of interventions aimed at curbing the spread of disease inside service facilities. Specifically, we focus on some prevalent interventions employed during the COVID-19 pandemic: limiting the occupancy of service facilities, protecting high-risk customers (via prioritization or designated time windows), and increasing the service speed (or limiting patronage duration). We discuss a variety of directions for adapting our transmission model to incorporate some more nuanced features of disease transmission, including heterogeneity in the population immunity level, varying levels of mask usage, and spatial considerations in disease transmission.

Impacts of the COVID‐19 pandemic on grocery retail operations: An analytical model

“…Kang et al. ( 2022 ) use queueing‐theoretic metrics to measure infectious disease transmissibility inside congestion‐prone service facilities to explore the efficacy of various interventions, such as limiting the occupancy of service facilities and prioritizing high‐risk customers.…”

Managing pandemics: A POM perspective and directions for future research

“…Two of the papers in this special issue focus on studying the spread of pandemics. These include: “Sojourn Time & Transmission Risk” (Kang et al., 2023) and “A Multiwave SIR Based Model for Learning Waves” (Perakis et al., 2023).…”

“…Kang et al. (2023) study disease transmission in small‐scale service settings prone to congestion (e.g., grocery stores, transportation hubs, and entertainment venues) during a pandemic. They extend the concept of the “basic reproduction rate,” used to assess disease transmission, to the “system‐specific basic reproduction rate.” They calculate the expected number of susceptible customers an infectious customer will infect during a single sojourn in a service facility (assuming all other customers are susceptible).…”

“…Two of the papers in this special issue focus on studying the spread of pandemics. These include: "Sojourn Time & Transmission Risk" (Kang et al, 2023) and "A Multiwave SIR Based Model for Learning Waves" (Perakis et al, 2023). Kang et al (2023) study disease transmission in smallscale service settings prone to congestion (e.g., grocery stores, transportation hubs, and entertainment venues) during a pandemic.…”

“…These include: "Sojourn Time & Transmission Risk" (Kang et al, 2023) and "A Multiwave SIR Based Model for Learning Waves" (Perakis et al, 2023). Kang et al (2023) study disease transmission in smallscale service settings prone to congestion (e.g., grocery stores, transportation hubs, and entertainment venues) during a pandemic. They extend the concept of the "basic reproduction rate," used to assess disease transmission, to the "system-specific basic reproduction rate."…”