Queueing Systems with Server Synchronization

该项目关注通过开发增强的劳动力管理技术来改进业务操作。目标是确定在各种产品和服务的不确定需求和处理要求存在的情况下，如何动态地将工人分配到任务中。主要的新颖之处在于在工作者分配中加入了同步约束。例如，完成某些任务可能需要一组工作人员，而其他任务一次只需要一个工作人员。在这两种情况下，工作人员必须同步他们的时间表，因为他们必须同时处理相同或不同的任务。该项目涉及开发易于实现的、健壮的和动态的策略，用于实时地将工作人员分配给任务，同时考虑到工作人员分配的同步约束。潜在的应用领域包括医疗保健交付、作业车间调度、呼叫中心、项目管理和并行计算。如果成功，该奖项将为如何通过更好地利用现有工人和其他资源，以低成本提高大型生产和服务系统的性能提供有价值的见解和具体指导方针。计划中的研究包括将企业建模为排队网络，将工人建模为服务器。研究目标将通过样本路径分析、马尔可夫决策过程、流体极限分析、计算机模拟和线性规划来实现。特别是，对于具有一般拓扑和无限缓冲区的网络，流体限制分析将用于确定服务器在各种可能的服务器配置中应该花费的时间比例。然后将开发任意接近最优的动态服务器分配策略。另一方面，具有有限缓冲区的系统将使用马尔可夫决策过程技术进行分析，其中将存在服务器分配的约束。建议的研究包括对具有灵活的异构服务器的排队系统进行严格的分析和控制，当不同服务器的调度必须同步时（例如，考虑所需的协作或非协作）。重点是最大化系统容量（吞吐量），但也会考虑其他性能度量，包括保持成本。

This project is concerned with improving business operations through the development of enhanced workforce management techniques. The goal is to determine how workers should be assigned dynamically to tasks in the presence of uncertain demand and processing requirements for various products and services. The main novelty is the incorporation of synchronization constraints on worker assignment. For example, the completion of certain tasks may require a team of workers, whereas other tasks require one worker at a time. In both cases, workers must synchronize their schedules in that they must be simultaneously at either the same or different tasks. This project involves the development of easily implementable, robust, and dynamic policies for assigning workers to tasks in real time, taking into account such synchronization constraints on worker assignment. Potential application areas include health care delivery, job shop scheduling, call centers, project management, and parallel computing. If successful, this award will yield valuable insights and concrete guidelines for how the performance of a large class of production and service systems can be improved at low cost by better utilizing the available workers and other resources.The planned research involves modeling businesses as queueing networks and workers as servers. The research objectives will be achieved through sample-path analysis, Markov decision processes, fluid limit analysis, computer simulation, and linear programming. In particular, for networks with general topologies and infinite buffers, fluid limit analysis will be used to identify what fraction of time the servers should spend in the various possible server configurations. Then dynamic server allocation policies that come arbitrarily close to being optimal will be developed. On the other hand, systems with finite buffers will be analyzed using Markov decision process techniques, where there will be constraints on server assignments. The proposed research involves the rigorous analysis and control of queueing systems with flexible, heterogeneous servers when the schedules of different servers must be synchronized (e.g., to account for needed collaboration or non-collaboration). The focus is on maximizing system capacity (throughput), but other performance measures will also be considered, including holding costs.