Stochastic Networks and Spatial Queueing Systems

9800606 Serfozo这个研究项目的目的是开发制造和通信系统的随机过程模型。在制造系统中，零件订单或材料在处理它们的工作站或中转区之间移动。预期的模型将描述生产率、排队所浪费的时间、瓶颈位置、满足最后期限和资源需求(机器、工具和人员)的概率行为。类似地，在计算机或电信网络中，数据分组、读/写交易和电话呼叫在计算机、缓冲器操作员或交换站的网络之间移动。这些模型将描述延迟、忙碌信号和过载的概率。主要的关注点将是无线通信(或移动电话)的“空间排队模型”，即客户在空间而不是固定网络中移动。该分析将使用一般空间上的空时点过程和马尔可夫过程的当代理论来寻找平面上的空间客户需求、服务时间以及由于客户位置而导致的需求和服务中的依赖关系的适当公式。待开发的模型将有助于制造和通信系统的初步规划和设计，或用于改进现有系统。它们将提供信息，以比较几个原型系统，选择最佳运行规则，并找到成本最低的系统。例如，在无线通信系统中的何处放置发射站(天线或集中器)，以及采用什么交换程序来保证移动和固定客户所需的服务水平。这些模型将有助于在正常运营策略、任务完成时间、运营成本、客户对无线系统的需求和人员要求的情况下预测系统过载。其他用途还包括制定通信系统标准和制定制造合同。

9800606 Serfozo The aim of this research project is to develop stochastic process models of manufacturing and communications systems. In a manufacturing system, parts orders or material move among workstations or staging areas where they are processed. The intended models will describe the probabilistic behavior of production rates, wasted time due to queueing, locations of bottlenecks, meeting deadlines and resource needs (machines, tools, and personnel). Similarly, in a computer or telecommunications network, data packets, read/write transactions and telephone calls move among a network of computers, buffers operators or switching stations. The models will describe probabilities of delays, busy signals and overloads. A major focus will be on "spatial queueing models" for wireless communications (or cellular phones), where customers move in a space rather than a fixed network. The analysis will use contemporary theories of space-time point processes and Markov processes on general spaces to find appropriate formulations of spatial customer demands in the plane, service times and dependencies in the demands and services due to customer locations. The models to be developed will be useful for initial planning and design of manufacturing and communications systems, or for the improvement of existing systems. They will provide information for comparing several prototype systems, selecting optimal operating rules and finding least-cost systems. For instance, where to place transmission stations (antennas or concentrators) in a wireless communications system and what switching procedures to adopt that will guarantee a desired level of service for mobile and fixed customers. The models will help in predictions of system overloads under normal operating policies, job completion times, operating costs, customer demands for wireless systems and personnel requirements. Other uses are in setting standards for communications systems and fashioning manufacturing contracts.