Analysis And Optimization Of Flow Control And Dynamic Scheduling Problems In Queueing Systems

This text presents a modern theory of analysis, control, and optimization for dynamic networks. Mathematical techniques of Lyapunov drift and Lyapunov optimization are developed and shown to enable constrained optimization of time averages in general stochastic systems. The focus is on communication and queueing systems, including wireless networks with time-varying channels, mobility, and randomly arriving traffic. A simple drift-plus-penalty framework is used to optimize time averages such as throughput, throughput-utility, power, and distortion. Explicit performance-delay tradeoffs are provided to illustrate the cost of approaching optimality. This theory is also applicable to problems in operations research and economics, where energy-efficient and profit-maximizing decisions must be made without knowing the future. Topics in the text include the following: - Queue stability theory - Backpressure, max-weight, and virtual queue methods - Primal-dual methods for non-convex stochastic utility maximization - Universal scheduling theory for arbitrary sample paths - Approximate and randomized scheduling theory - Optimization of renewal systems and Markov decision systems Detailed examples and numerous problem set questions are provided to reinforce the main concepts. Table of Contents: Introduction / Introduction to Queues / Dynamic Scheduling Example / Optimizing Time Averages / Optimizing Functions of Time Averages / Approximate Scheduling / Optimization of Renewal Systems / Conclusions

This text presents a modern theory of analysis, control, and optimization for dynamic networks. Mathematical techniques of Lyapunov drift and Lyapunov optimization are developed and shown to enable constrained optimization of time averages in general stochastic systems. The focus is on communication and queueing systems, including wireless networks with time-varying channels, mobility, and randomly arriving traffic. A simple drift-plus-penalty framework is used to optimize time averages such as throughput, throughput-utility, power, and distortion. Explicit performance-delay tradeoffs are provided to illustrate the cost of approaching optimality. This theory is also applicable to problems in operations research and economics, where energy-efficient and profit-maximizing decisions must be made without knowing the future. Topics in the text include the following: - Queue stability theory - Backpressure, max-weight, and virtual queue methods - Primal-dual methods for non-convex stochastic utility maximization - Universal scheduling theory for arbitrary sample paths - Approximate and randomized scheduling theory - Optimization of renewal systems and Markov decision systems Detailed examples and numerous problem set questions are provided to reinforce the main concepts. Table of Contents: Introduction / Introduction to Queues / Dynamic Scheduling Example / Optimizing Time Averages / Optimizing Functions of Time Averages / Approximate Scheduling / Optimization of Renewal Systems / Conclusions

"This thesis deals with dynamic control of multi-class single-server queues. In a broad class of such systems, fixed-priority rules, although static, have been shown to be optimal among dynamic schedules. This result however rests on the independence between the order of service and the pattern of arrivals, an assumption which is violated when flow control is exercised. We seek to characterize the optimal scheduling in the presence of flow control, when both scheduling and flow control are optimized jointly." --

Applications of queueing network models have multiplied in the last generation, including scheduling of large manufacturing systems, control of patient flow in health systems, load balancing in cloud computing, and matching in ride sharing. These problems are too large and complex for exact solution, but their scale allows approximation. This book is the first comprehensive treatment of fluid scaling, diffusion scaling, and many-server scaling in a single text presented at a level suitable for graduate students. Fluid scaling is used to verify stability, in particular treating max weight policies, and to study optimal control of transient queueing networks. Diffusion scaling is used to control systems in balanced heavy traffic, by solving for optimal scheduling, admission control, and routing in Brownian networks. Many-server scaling is studied in the quality and efficiency driven Halfin–Whitt regime and applied to load balancing in the supermarket model and to bipartite matching in ride-sharing applications.

This book is a collection of research papers in optimization and approximation dedicated to Professor Minyi Yue of the Institute of Applied Mathematics, Beijing, China. The papers provide a broad spectrum of research on optimization problems, including scheduling, location, assignment, linear and nonlinear programming problems as well as problems in molecular biology. The emphasis of the book is on algorithmic aspects of research work in optimization. Special attention is paid to approximation algorithms, including heuristics for combinatorial approximation problems, approximation algorithms for global optimization problems, and applications of approximations in real problems. The work provides the state of the art for researchers in mathematical programming, operations research, theoretical computer science and applied mathematics.

In order to include setup times, we create a logic-based Benders decomposition model for a static representation of the queueing network. Our model is able to find optimal schedules up to 5 orders of magnitude faster than the only other model in the literature. A hybrid model is then developed for the dynamic problem and shown to achieve the best mean flow time while also guaranteeing maximal capacity.The central thesis of this dissertation is that insight from queueing analysis can effectively guide standard (combinatorial) scheduling algorithms in dynamic environments. Scheduling is generally concerned with complex combinatorial decisions for static problems, whereas queueing theory simplifies the combinatorics and focuses on dynamic systems. We examine a queueing network with flexible servers under queueing and scheduling techniques. Based on the strengths of queueing analysis and scheduling, we develop a hybrid model that guides scheduling with results from the queueing model.

Each number is the catalogue of a specific school or college of the University.

Control and Dynamic Systems, Volume 37: Advances in Industrial Systems provides an overview of the state of knowledge in industrial systems. This volume contains nine chapters and begins with a paper on the objective measures used to characterize the performance of computers which control critical processes. This is followed by separate chapters on the design of automotive power train control systems; control techniques in the pulp and paper industry; developments production scheduling research and practice; a general model-based failure detection and diagnosis methodology; and the application of model-predictive control techniques to problems with several input and output variables. Subsequent chapters deal with techniques for dealing with the problem of providing a complete, coherent, and reliable data base from a collection of switch and breaker status data and measurements; systematic approaches to modifying a finite element model; and optimization techniques in industrial chemical systems. The contributions in this volume will provide a unique and significant reference source for practicing professionals as well as those involved with advancing the state of the art.