Scheduling and Control of Queueing Networks

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.