标题： 社区保释基金系统：流极限和近似 显示英文标题

标题： Community Bail Fund Systems: Fluid Limits and Approximations

摘要： 社区保释基金（CBFs）帮助那些被逮捕但无法负担保释金的个人，防止不必要的审前监禁及其有害或有时致命的后果。 通过支付保释金，CBFs允许被告在审判前留在家中并维持生计。 本文介绍了新的随机模型，将排队论与经典保险风险模型相结合，以捕捉CBF中剩余资金的动态。 我们首先分析了一个所有保释请求都被接受的模型。 尽管剩余资金余额可能为负，但该模型为财务不受限制的CBF提供了见解。 然后，我们应用Skorokhod映射确保CBF余额不会为负，并表明Skorokhod映射产生了一个部分满足请求的模型。 最后，我们分析了一个模型，其中如果到达时没有足够的资金满足请求，则可以阻止保释请求。 虽然阻止模型防止了CBF变为负数，但阻止功能给直接随机分析带来了新的分析挑战。 因此，我们证明了阻止模型的功能大数定律或流极限，并表明流极限是一个分布延迟方程。 我们通过仿真评估了我们流极限的质量，并表明流极限准确描述了CBF的大规模随机动态。 最后，我们证明了我们分析的CBF过程的随机排序结果。 显示英文摘要

摘要： Community bail funds (CBFs) assist individuals who have been arrested and cannot afford bail, preventing unnecessary pretrial incarceration along with its harmful or sometimes fatal consequences. By posting bail, CBFs allow defendants to stay at home and maintain their livelihoods until trial. This paper introduces new stochastic models that combine queueing theory with classic insurance risk models to capture the dynamics of the remaining funds in a CBF. We first analyze a model where all bail requests are accepted. Although the remaining fund balance can go negative, this model provides insight for CBFs that are not financially constrained. We then apply the Skorokhod map to make sure the CBF balance does not go negative and show that the Skorokhod map produces a model where requests are partially fulfilled. Finally, we analyze a model where bail requests can be blocked if there is not enough money to satisfy the request upon arrival. Although the blocking model prevents the CBF from being negative, the blocking feature gives rise to new analytical challenges for a direct stochastic analysis. Thus, we prove a functional law of large numbers or a fluid limit for the blocking model and show that the fluid limit is a distributed delay equation. We assess the quality of our fluid limit via simulation and show that the fluid limit accurately describes the large-scale stochastic dynamics of the CBF. Finally, we prove stochastic ordering results for the CBF processes we analyze.