当队列变得具有传染性：分析M/M/1队列中的感染传播
When Lines Become Contagious: Analyzing the Spread of Infection in the M/M/1 Queue
- Cornell University（康奈尔大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文构建并分析M/M/1队列中传染病传播的随机模型，推导了个体感染概率及社区感染人数矩，并用模拟验证了公式的准确性。
AI中文摘要：
在本文中，我们构建并分析了一个用于服务系统中传染病传播的随机模型。我们的模型考虑一个$M/M/1$队列，其中到达人群中有比例为$p$的个体具有传染性，其余人群为易感者。当一个传染性个体在队列中与一个易感顾客重叠时间超过$\ell$个单位时，该易感者就会被感染。我们既提供了关于单个易感顾客如何被感染的个性化视角，也提供了关于一个传染性个体如何感染周围其他人的社区视角。从个性化视角出发，我们推导出易感者被感染的概率以及被至少$k$个不同的人感染的概率。从社区视角出发，我们计算了一个传染性个体所感染的易感顾客数量的均值和高阶矩。最后，我们使用随机模拟来验证我们的分析结果，并表明我们的新公式能够准确描述我们感染随机模型的行为，同时将我们的模型扩展到考虑不同到达和服务机制的情形。
英文摘要：
In this paper, we construct and analyze a stochastic model for infectious disease spread in service systems. Our model considers a $M/M/1$ queue where a proportion, $p$, of the arriving population is infectious and the remaining population is susceptible. When an infectious person overlaps in the queue with a susceptible customer for more than $\ell$ units of time, then the susceptible person becomes infected. We provide both a personalized perspective of how an individual susceptible customer is infected and a community perspective of how one infectious customer can infect the others around them. From the personalized perspective, we derive the probability that a susceptible person becomes infected and the probability they are infected by at least $k$ different people. From the community perspective we compute the mean and higher moments of the number of susceptible customers that are infected by one infectious individual. Finally, we use stochastic simulation to verify our analytical results and show that our new formulas accurately describe the behavior our stochastic model of infection and to expand our model into the consideration of different arrival and service regimes.
