Using infinite server queues with partial information for occupancy prediction
针对英格兰和威尔士监狱人口需求预测，提出利用无限服务台队列研究服务系统，通过分离初始人口和新到达者，结合贝叶斯框架进行短期队列长度预测和长期管理分析。
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 Mt/G/∞ 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.