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.
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. In classical queueing scheduling, the optimal policy often takes the form of a priority rule, which commits at any time hundred percent of the resource, the server(s), to the job class with the highest priority. Although the priority rule is known to optimize certain efficiency-oriented performance measures, such as average delay or mean queue length, it may be neither practical nor desirable in certain applications. For instance, in many service systems, the real-time allocation of resources is obligated to observe some notion of "fairness" among the various classes of jobs or customers. Furthermore, classical queueing scheduling is limited to simple models such as a single server or a stand-alone service facility as opposed to a network. In particular, the models do not allow features such as concurrent occupancy of multiple resources that are distributed and inter-connected in a network, what’s known as a stochastic processing network. The main goal of the project is two-fold, to study the dynamic allocation of resources that are networked, and to focus on control rules that are beyond the class of priority rules, with a broader set of objectives, such as those that take into account some measures of fairness. The main findings/outcomes of the project include a complete characterization of the diffusion limiting regime of the aforementioned network under proportional fair resource control, and the limit is theoretically justified as providing bona fide asymptotics for the original network. These results hence indicate that a large-scale, heaviiy-utilized set of networked resources can be most effectively studied and controlled using the diffusion limits established in this project, and to address objectives that involve fairness measures. More specifically, the intellectual merit of the project lies in its contribution to the analytical and computational tools to the study of dynamic resource allocation schemes in processing networks. Furthermore, results from this project have brought out the importance of a class of control rules that explicitly take into account fairness measures --- such measures are central to many human-centric service systems, and the corresponding resource control schemes are shown to be optimal in the asymptotic sense (i.e., when the system is large and heavily utilized). As resources in today's world are often interconnected, typically in the form of a complex network (examples include bandwidth and servers on the Internet; beds/wards, operating rooms, ICU's, surgeons and nursing staff in a hospital; and as such networks are prevalent in the service industries), the broader impacts of this project include its helping to solve an important and challenging problem of our time.
