Dynamic Scheduling and Resource Control in Stochastic Processing Networks: Beyond Priority Rules

这个项目的目标是研究超越经典优先级规则的资源控制，并在随机处理网络的一般设置中这样做，允许资源的并发占用和共享等特征。在许多复杂系统的设计和分析中，动态分配资源以服务于不同类型的客户或工作类别是一个中心问题。研究计划是研究系统在一类资源控制下的渐近行为，这类资源控制在每个系统状态中优化一个效用函数(例如，在因特网协议的情况下也普遍存在于许多服务系统中的“公平性”度量)。这将通过推导在流动和扩散标度下的主要性能过程的限制制度来实现，例如工作负荷和拥堵程度。这些限制在评估系统性能时非常有用。它们还建立了效用函数和性能目标之间的联系，效用函数是控制在每个状态下局部(或贪婪地)最大化的，性能目标是通过控制在任何给定的计划范围内全局优化的，无论是有限的还是无限的。该项目的结果有望从两个方面帮助随机处理网络中的动态资源控制规则的设计：给定一个控制方案，可以评估其性能；反之，给定一个性能目标，可以识别一个或几个控制方案来优化目标。更广泛地说，该项目将增加随机网络的数学基础，增强对效用最大化资源分配方案对网络性能影响的理解，并为系统设计和优化带来新的决策工具和计算技术。

The goal of this project is to study resource control that extends beyond the classical priority rules, and to do so in the general setting of stochastic processing networks, allowing features such as concurrent occupancy and sharing of resources. Dynamic allocation of resources to serve different kinds of customers or job classes is a central issue in the design and analysis of many complex systems. The research plan is to investigate the asymptotic behavior of the system under a general class of resource control, which optimizes in each system state a utility function (e.g., a "fairness" measure as in the case of the Internet protocol, also prevalent in many service systems). This will be carried out by deriving the limiting regimes of the main performance processes, such as workloads and congestion levels, under fluid and diffusion scalings. These limits are useful in evaluating the system performance. They also establish the connection between the utility function, which the control maximizes locally (or "greedily") in each state, and the performance objective that is optimized by the control globally over any given planning horizon, finite or infinite.Results from the project are expected to help the design of dynamic resource control rules in stochastic processing networks in two ways: given a control scheme, its performance can be evaluated; and conversely, given a performance objective, one or several control schemes can be identifed to optimize the objective. More broadly, the project will add to the mathematical foundation of stochastic networks, enhance the understanding of the implications of utility- maximizing resource allocation schemes on network performance, and lead to new decision tools and computational techniques for systems design and optimization.