This paper studies a diffusion control problem motivated by challenges faced by public health agencies who run clinics to serve the public. A key challenge for these agencies is to motivate individuals to participate in the services provided. They must manage the flow of (voluntary) participants so that the clinic capacity is highly utilized, but not overwhelmed. The organization can deploy costly promotion activities to increase the inflow of participants. Ideally, the system manager would like to have enough participants waiting in a queue to serve as many individuals as possible and efficiently use clinic capacity. However, if too many participants sign up, resulting in a long wait, participants may become irritated and hesitate to participate again in the future. We develop a diffusion model of managing participant inflow mechanisms. Each mechanism corresponds to choosing a particular drift rate parameter for the diffusion model. The system manager seeks to balance three different costs optimally: i) a linear holding cost that captures the congestion concerns; ii) an idleness penalty corresponding to wasted clinic capacity and negative impact on public health, and iii) costs of promotion activities. We show that a nested-threshold policy for deployment of participant inflow mechanisms is optimal under the long-run average cost criterion. In this policy, the system manager progressively deploys mechanisms in increasing order of cost, as the number of participants in the queue decreases. We derive explicit formulas for the queue length thresholds that trigger each promotion activity, providing the system manager with guidance on when to use each mechanism.

翻译：本文研究由公共卫生机构在运营诊所服务公众时所面临挑战引发的扩散控制问题。这些机构的关键挑战在于激励个体参与所提供服务。他们必须管理（自愿）参与者的流入，使诊所容量得到充分利用但避免超负荷。组织可部署成本高昂的推广活动以增加参与者流入。理想情况下，系统管理者希望等待队列中有足够参与者以服务尽可能多的个体并高效利用诊所容量。然而，若报名人数过多导致等待时间过长，参与者可能产生抵触情绪并在未来犹豫是否再次参与。我们构建了参与者流入机制管理的扩散模型。每种机制对应选择扩散模型中特定的漂移率参数。系统管理者需最优平衡三种不同成本：i)表征拥堵问题的线性持有成本；ii)对应诊所容量浪费及公共卫生负面影响的闲置惩罚；iii)推广活动成本。我们证明，在长期平均成本准则下，嵌套阈值策略对于部署参与者流入机制是最优的。该策略中，系统管理者根据队列中参与者数量减少情况，按成本递增顺序逐步部署机制。我们推导出触发每项推广活动的队列长度阈值显式公式，为系统管理者提供何时使用何种机制的指导。