Research Initiation: Queueing Theroetic Analysis and Optimization of Parallel Processing Systems

并行处理系统将从排队理论的角度研究，在工作随机输入流的平稳性和遍历性的一般假设下。作业具有一些复杂的内部结构，由多个基本任务组成，这些任务必须由一个处理器系统根据某些规范执行。经典的排队理论问题的稳定性，渐近平稳性等，以及控制理论问题的最优动态调度的任务处理器，以优化系统的性能，例如，最大限度地提高吞吐量。分析将集中在并行处理的基本原型模型上，捕捉大型并行处理系统的基本操作特征。这项研究对于理解并行处理系统在基本数学水平上的操作，以及基于坚实的数学方法建立优化其性能的技术是很重要的，这与目前主要的启发式实践相反。

Parallel processing systems will be studied from a queueing theoretic point of view, under general assumptions of stationarity and ergodicity of the random input flow of jobs. The jobs have some complex internal structure, consisting of multiple elementary tasks, that have to be executed by a system of processors, according to some specifications. The classical queueing theoretic problems of stability, asymptotic stationarity etc. will be addressed, as well as control theoretic problems of optimal dynamic scheduling of jobs to processors in order to optimize the performance of the system, for example, maximize the throughput. Analysis will focus on basic prototypical models of parallel processing, capturing the essential operational characteristics of large classes of parallel processing systems. The research is important for understanding the operation of parallel processing systems at a fundamental mathematical level and establishing techniques to optimize their performance, based on a solid mathematical methodology, contrary to the largely heuristic current practice.