标题： 使用具有部分信息的无限服务器队列进行占用预测 显示英文标题

标题： Using infinite server queues with partial information for occupancy prediction

摘要： 受英格兰和威尔士看守监狱人口需求预测的驱动，本文描述了一种使用无限服务器队列研究服务系统的的方法，其中系统具有非空的初始状态，且初始存在的个体的经过时间未知。 通过将人口分为初始内容和新到达者，我们可以分别或联合应用于这些子群体的各种技术，以实现短期队列长度预测以及更长期的考虑，如管理拥堵和分析潜在干预措施的影响。 本文的重点是具有非齐次泊松到达过程的$M_t/G/\infty$队列的瞬态行为，我们的分析考虑了各种可能的简化，包括近似。 我们使用公开数据在贝叶斯框架中说明该方法以进行模型推断。 显示英文摘要

摘要： Motivated by demand prediction for the custodial prison population in England and Wales, this paper describes an approach to the study of service systems using infinite server queues, where the system has non-empty initial state and the elapsed time of individuals initially present is not known. By separating the population into initial content and new arrivals, we can apply several techniques either separately or jointly to those sub-populations, to enable both short-term queue length predictions and longer-term considerations such as managing congestion and analysing the impact of potential interventions. The focus in the paper is the transient behaviour of the $M_t/G/\infty$ queue with a non-homogeneous Poisson arrival process and our analysis considers various possible simplifications, including approximation. We illustrate the approach in that domain using publicly available data in a Bayesian framework to perform model inference.