Scheduling and Control of Queueing Networks: 14 (Institute of Mathematical Statistics Textbooks, Series Number 14)
Cambridge University Press, 10/14/2021
EAN 9781108415323, ISBN10: 1108415326
Hardcover, 200 pages, 22.9 x 15.2 x 2.5 cm
Language: English
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.