Essays on Service System Design: Efficiency, Fairness, and Safety

Abstract

This dissertation focuses on the congested service system design with efficiency, fairness, and safety. In particular, we study the prioritization in the presence of self-ordering opportunities in designing Omni-channel service systems with efficiency and fairness, and in order to design safe service systems with congestion, we propose a novel queueing-theoretic framework for evaluating disease transmission risks in service facilities during a pandemic. Then we extend the analysis for deriving this novel metric to a queueing network setting with variations and provide examples. In the first essay, motivated by the popularity of mobile-order-and-pay applications, especially in fast-casual food restaurants and coffee shops, we study omni-channel service systems---where customers can employ mobile applications for self-ordering---with respect to sojourn times, throughput, and social welfare. Our models are two-stage queues with two customer classes: walk-ins and mobiles. We identify Pareto efficient prioritization policies, highlighting trade-offs between each class's mean sojourn times. We allow customers to make strategic joining decisions based on their anticipated delays under an information structure where walk-ins observe partial queue length information. We draw from a wide array of techniques, including steady-state, transient, busy period, hitting-time analyses, and matrix analytic methods. We showcase the significance of prioritization on the system throughput and social welfare. We demonstrate settings where the (typically beneficial) transformation of a traditional service system to an omni-channel reduces throughput. Our analysis highlights the importance of prioritization policy choice for an efficient transition to an omni-channel service system. The throughput-optimal policy choice is highly dependent on the operational parameters and on customer patience levels; implementing a wrong policy can yield a significant loss in throughput and, hence, profitability. In the second essay, 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. 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. We also extend the analysis of the system-specific basic reproduction rate to the setting where the service systems with congestion can be modeled as queueing networks with adequate service capacity. We study the systematic way of deriving the system-specific basic reproduction rates and give examples for different models, including the theoretic models along with their variations and a realistic grocery store model.