Interactions in Queues: A Stochastic Analysis

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It has never been more important to understand how we share space with others. Ever since the start of the Covid-19 pandemic, the general public is more aware of their surroundings and try to social distance when possible. This award supports fundamental research intended to understand how customers interact with one another in service systems. This research will enable businesses and individuals to understand how the time that customers interact with each other in spaces will influence the spread of infectious diseases such as Covid-19. This project will influence the operational decision making of service system managers so they can understand how limiting the time that customers spend in systems will contribute to the health and safety of those customers and the general public. In particular, this project can impact the understanding of how infectious diseases spread in settings where people are not able to social distance such as public transportation systems. It also includes targeted outreach efforts to broaden participation of Historically Black Colleges and Universities (HBCU) students in research. This project will study new stochastic models for representing interactions and overlap times of customers in service system settings. The research objective is to aid service system managers and the public understand the risk profile of joining various service systems where social distancing is not possible. The analysis will uniquely use tools from queueing theory and stochastic processes to develop new insights for describing the probability of interacting with other customers for a specified time duration. Stochastic queueing models will be used to describe the interactions between customers and develop rigorous descriptions of the time of interaction between consecutive customers. The rigorous analysis of the interactions will be compared with stochastic simulation as well as observational data from real-world transportation systems.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.