This comprehensive treatment of fluid, diffusion, and many-server scaling applies queueing networks and large-scale asymptotics to model and solve core problems such as scheduling in semiconductor wafer fabs, matching Uber drivers to passengers, routing patient flow in emergency rooms, and load balancing in cloud computing. Includes 330 exercises.
This comprehensive treatment of fluid, diffusion, and many-server scaling applies queueing networks and large-scale asymptotics to model and solve core problems such as scheduling in semiconductor wafer fabs, matching Uber drivers to passengers, routing patient flow in emergency rooms, and load balancing in cloud computing. Includes 330 exercises.
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.
Inhaltsangabe
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.
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.
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