  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, i.e., congestion-prone confined-space
service facilities, such as grocery stores. We propose a novel metric
($R_0^{\mathsf{sys}}$) inspired by $R_0$, the "basic reproduction number"
concept from epidemiology, which measures the transmissibility of infectious
diseases. We derive the $R_0^{\mathsf{sys}}$ 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.
