Stochastic Networks in the Heavy Traffic Regime: Algorithms, Approximations and Applications

该项目旨在研究交通繁忙情况下的随机处理网络。重点将是建立建设性的近似方法的performanceanalysis问题中出现的随机处理网络的区域，以及扩展scopeof随机网络框架的新领域的应用。该项目将追求三重目标：将重业务理论的适用性扩展到随机排队网络的均衡运行（稳态）制度，建立一个性能分析框架的大规模呼叫中心模型在繁忙的交通制度，并建立一个通用框架的modelingstochastic排队过程与共享资源在繁忙的交通制度。如果成功，研究结果将产生以下重要影响。对于交通繁忙状态下的随机网络领域，它将使分析网络平衡的启发式方法成为一种理论，从而使扩散过程与平衡状态下的随机网络之间建立正式的联系。在大规模呼叫中心模型领域，它将提供在繁忙的业务状况下，这类系统的性能的一般和实用的方法，没有对呼叫量分布的统计特性的限制性假设。最先进的技术只能处理exponentiallydistributed调用长度的特殊情况。如果成功的话，该项目还将提供分析呼叫中心在非平稳制度，这是呼叫中心运营的主要制度的方法。非平稳性问题将通过获得大规模呼叫中心模型的弛豫时间的界限来解决。最后，通过利用马尔可夫随机场理论等方法的组合，将考虑在繁忙的交通状况下具有共享资源的调度模型的系统理论，具有建设性的性能分析方法的特定目标。具有共享资源的随机系统广泛存在于通信网络、计算机系统和商业过程等领域。然而，这种过程的建设性和一般性的理论是缺乏的。该项目可能是朝着建立这样一种理论的方向迈出的重要一步.

This project proposes to study research on stochastic processing networks in the heavy trafficregime. The focus will be on the creation of constructive approximations methods for the performanceanalysis questions arising in the area of stochastic processing networks, as well as extending the scopeof the stochastic networks framework to the new domains of applications. The project will pursue athree-fold goal: extending the applicability of the heavy traffic theory to stochastic queueing networksoperating in the equilibrium (steady-state) regime, creating a performance analysis framework for largescale call center models in the heavy traffic regime, and creating a general framework for modelingstochastic queueing processes with shared resources in the heavy traffic regime.If successful, the results of the research will have the following important implications. For thefield of stochastic networks in the heavy traffic regime it will make heuristic approaches of analyzingnetworks in equilibrium, into a theory and thus making a formal connection between diffusion processesand the underlying stochastic networks in the equilibrium regime. In the area of large scale callcenter models it will provide general and practical methods for the performance of such systems inthe heavy traffic regime, without the restrictive assumptions on the statistical properties of the calllengths distribution. The state of the art techniques can only handle the special case of exponentiallydistributed call lengths. If successful the project will also provide methods for analyzing call centersin the non-stationary regime, which is the predominant regime of call center operations. The nonstationarityissue will be addressed by obtaining bounds on the relaxation times of large scale callcenter models. Finally, by utilizing a combination of methods, such as the theory of Markov randomfields, a systematic theory of queueing models with shared resources in the heavy traffic regime will beconsidered, with a specific goal of constructive performance analysis methods. Stochastic systems withshared resources appear in a variety of fields, including communication networks, computer systemsand business processes. Yet constructive and general theory of such processes is lacking. The projectwill be an important step in the direction of building such a theory.