Scheduling and Control of Queueing Networks

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.

• 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.