Eitan Altman, Bruno Gaujal, Arie Hordijk (auth.)9783540203582, 3540203583
Opening new directions in research in both discrete event dynamic systems as well as in stochastic control, this volume focuses on a wide class of control and of optimization problems over sequences of integer numbers. This is a counterpart of convex optimization in the setting of discrete optimization. The theory developed is applied to the control of stochastic discrete-event dynamic systems. Some applications are admission, routing, service allocation and vacation control in queueing networks. Pure and applied mathematicians will enjoy reading the book since it brings together many disciplines in mathematics: combinatorics, stochastic processes, stochastic control and optimization, discrete event dynamic systems, algebra.
Table of contents :
Introduction….Pages 1-6
Multimodularity, Convexity and Optimization….Pages 11-38
Part I: 2 Balanced Sequences….Pages 39-54
Part I: 3 Stochastic Event Graphs….Pages 55-74
Part II: 4 Admission control in stochastic event graphs….Pages 79-103
Part II: 5 Applications in queuing networks….Pages 105-109
Part II: 6 Optimal routing….Pages 111-118
Part II: 7 Optimal routing in two deterministic queues….Pages 119-149
Part III: 8 Networks with no buffers….Pages 155-181
Vacancies, service allocation and polling….Pages 183-204
Part III: 10 Monotonicity of feedback control….Pages 205-223
Part IV: 11 Comparison of queues with discrete-time arrival processes….Pages 229-241
Part IV: 12 Simplex convexity….Pages 243-259
Part IV: 13 Orders and bounds for multimodular functions….Pages 261-282
Part IV: 14 Regular Ordering….Pages 283-304
References….Pages 305-310
Reviews
There are no reviews yet.