CAREER: Scheduling of Multiclass Queueing Networks via Fluid Models

由于高度复杂的制造、通信和计算机系统的出现，对更复杂和现实的数学模型来分析和控制这些系统的需求增加了。一个特别突出的例子是在半导体晶圆制造中看到的，其中一个工厂可能会制造多个产品，这些产品要经过数百个步骤组成的迷宫路线。诸如可重入路由、不同的处理速度、设置时间和机器停机时间等因素使得此类系统特别难以评估和控制。排队中的流体模型可以被认为是原始多类排队网络的松弛，它可以为复杂可重入系统的操作提供重要的见解。提出的研究计划包括探索多类排队模型的高效调度的流体模型技术。首先，我们提出开发鲁棒和高效的算法来解决流体模型控制问题。然后，我们将开发将流体控制问题的解决方案转化为原始可行的近最优调度的技术。最后，我们将使用实际尺寸和范围的实际晶圆厂数据来测试我们方法的适用性，并利用与国际SEMATECH的晶圆厂数据和基准模拟模型的合作伙伴关系。拟议的教育计划与研究计划相结合，涉及运筹学建模和排队理论的本科课程和研究生课程的新课程开发和软件开发。

Due to the advent of highly complex manufacturing, communication, and computer systems, there has been an increased need for more complex and realistic mathematical models to analyze and control such systems. A particularly striking example is seen in semiconductor wafer fabrication, where one facility may manufacture multiple products which traverse a labyrinthine route consisting of hundreds of steps. Factors such as reentrant routing, varied processing speeds, setup times, and machine downtimes make such systems particularly difficult to evaluate and control.Fluid models in queueing can be thought of as a relaxation of an original multiclass queuing network which can provide crucial insight into the operation of complex reentrant systems. The proposed research plan involves exploring fluid model techniques for efficient scheduling of multiclass queuing models. First we propose developing robust and efficient algorithms for solving a fluid model control problem. Then we will develop techniques for translating the solution to the fluid control problem into a feasible near-optimal schedule for the original. Finally, we will test the applicability of our methods using realistic wafer fab data of practical size and scope, drawing on a partnership with International SEMATECH for fab data and benchmark simulation models. The proposed education plan is tied in with the research plan and involves new course development and software development for undergraduate courses and graduate courses in operations research modeling and queueing theory.