EAGER: Mathematical Models for Large-Scale Service Systems

这笔赠款为开发大型服务系统的数学模型和分析方法提供资金，例如客户联系中心和医院，这些系统有许多并行工作的“服务器”(例如，代理或护士)。这些模型将被用于开发算法，以确定最佳人员配置水平，并进行实时延误估计，以用于人员配置和发布延误公告。这些算法将通过与计算机模拟进行比较来进行评估。模型将是多服务台排队系统，它捕捉了现实服务系统的基本特征，如到达和服务时间的随机性，但不是完全的操作复杂性，因为它们只有一个大的同质服务池和单一类别的同质客户。将特别强调可能对性能有很大影响但使这些模型难以分析的现实特征，包括时变到达率、客户遗弃和非指数概率分布。为了解决这些复杂性，将利用渐近方法，导致流体和扩散近似。如果成功，这项研究的结果将最终导致服务系统的设计和管理的改进，导致更有效的操作。长期目标是为服务系统中的资源分配(例如人员配置)建立健全的科学基础，以平衡客户经历的拥堵成本和提供资源的成本。其目标是开发新的设计原则、控制策略和数学方法，以提高系统性能。如果成功，这项研究将证明渐近方法作为一种有效降低大规模随机系统复杂性的方法的优势。其目的是表明，有可能将大规模的挑战转化为优势。因此，拟议的工作将有助于运筹学和应用概率以及服务企业系统的计算工具和方法。

This grant provides funding for the development of mathematical models and analysis methods for large-scale service systems, such as customer contact centers and hospitals, which have many "servers" working in parallel (e.g., agents or nurses). These models will be applied to develop algorithms to determine optimal staffing levels and to perform real-time delay estimation to use in staffing and making delay announcements. These algorithms will be evaluated by making comparisons to computer simulations. The models will be many-server queueing systems, which capture essential features of realistic service systems such as randomness in the arrival and service times, but not the full operational complexity because they have only a single large pool of homogeneous servers and a single class of homogeneous customers. Special emphasis will be given to realistic features that can have a big impact on performance but make these models difficult to analyze, including time-varying arrival rates, customer abandonment and non-exponential probability distributions. To address these complications, asymptotic methods will be exploited, leading to fluid and diffusion approximations.If successful, the results of this research will ultimately lead to improvements in the design and management of service systems, leading to more efficient operations. The long-term goal is to establish a sound scientific basis for resource allocation (e.g., staffing) in service systems, which balances the cost of the congestion experienced by customers and the cost of providing the resources. The goal is to develop new design principles, control policies and mathematical methods for improving system performance. If successful, the research will demonstrate the advantage of the asymptotic approach as a way to effectively reduce the complexity of large-scale stochastic systems. The aim is to show that it is possible to transform the challenge of large scale into an advantage. The proposed work will thus contribute to the computational tools and methodologies of operations research and applied probability as well as service enterprise systems.