Scheduling and Control of Queueing Networks Institute of Mathematical Statistics Textbooks Series

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.

Notation; Introduction; Part I. The Single Queue: 1. Queues and their simulations, birth and death queues; 2. The M/G/1 queue; 3. Scheduling; Part II. Approximations of the Single Queue: 4. The G/G/1 queue; 5. The basic probability functional limit theorems; 6. Scaling of G/G/1 and G/G/∞; 7. Diffusions and Brownian processes; Part III. Queueing Networks: 8. Product form queueing networks; 9. Generalized Jackson networks; Part IV. Fluid Models of Multi-Class Queueing Networks: 10. Multi-class queueing networks, instability and Markov representations; 11. Stability of MCQN via fluid limits; 12. Processing networks and maximum pressure policies; 13. Processing networks with infinite virtual queues; 14. Optimal control of transient networks; Part V. Diffusion-Scaled Balanced Heavy Traffic: 15. Join the shortest queue in parallel servers; 16. Control in balanced heavy traffic; 17. MCQN with discretionary routing; Part VI. Many-Server Systems: 18. Infinite servers revisited; 19. Asymptotics under Halfin–Whitt regime; 20. Many servers with abandonment; 21. Load balancing in the supermarket model; 22. Parallel servers with skill-based routing; References; Index.

Gideon Weiss is Professor Emeritus in the Department of Statistics at the University of Haifa, Israel. He has previously held tenured positions at Tel Aviv University and at Georgia Tech Industrial and Systems Engineering and visiting positions at Berkeley, MIT, Stanford, NYU, and NUS. He is author of some 90 research papers and served on the editorial boards of leading journals on operations research and applied probability. His work includes significant contributions to the fields of time series, stochastic scheduling, bandit problems, fluid analysis of queueing networks, continuous linear programming, and matching problems.