Interactions in Queues: A Stochastic Analysis

了解我们如何与他人分享空间从未如此重要。 自2019冠状病毒病大流行开始以来，公众更加了解他们的周围环境，并在可能的情况下尽量保持社交距离。 该奖项支持旨在了解客户如何在服务系统中相互交互的基础研究。 这项研究将使企业和个人能够了解客户在空间中相互互动的时间将如何影响新冠肺炎等传染病的传播。 该项目将影响服务系统管理人员的运营决策，使他们能够了解如何限制客户在系统中花费的时间将有助于这些客户和公众的健康和安全。 特别是，该项目可以影响对传染病如何在人们无法保持社交距离的环境中传播的理解，例如公共交通系统。 它还包括有针对性的外联工作，以扩大历史上的黑人学院和大学（HBCU）的学生参与研究。本计画将研究新的随机模式，以代表服务系统中顾客的互动与重叠时间。 研究目的是帮助服务系统管理人员和公众了解加入各种服务系统的风险状况，其中社交距离是不可能的。 该分析将独特地使用来自嵌入理论和随机过程的工具来开发新的见解，以描述在指定的时间段内与其他客户交互的概率。 随机定价模型将被用来描述客户之间的相互作用，并制定严格的描述连续客户之间的相互作用的时间。 该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

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.