Discrete-Event Control of Stochastic Networks - Multimodularity and Regularity

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 queuing 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.

List of contents

Preface.- Part I: Theoretical Foundations: Multimodularity, Convexity and Optimization; Balanced Sequences; Stochastic Event Graphs.- Part II: Admission and Routing Control: Admission Control in Stochastic Event Graphs; Applications in Queuing Networks; Optimal Routing; Optimal Routing in two Deterministic Queues.- Part III: Several Extensions: Networks with no Buffers; Vacancies, Service Allocation and Polling; Monotonicity of Feedback Control.- Part IV: Comparisons: Comparison of Queues with Discrete-time Arrival Processes; Simplex Convexity; Orders and Bounds for Multimodular Functions; Regular Ordering.- References.- Index.

Summary

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 queuing 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.

Product details

• Authors: Eita Altman, Eitan Altman, Brun Gaujal, Bruno Gaujal, Arie Hordijk
• Publisher: Springer, Berlin
• Languages: English
• Product format: Paperback / Softback
• Released: 01.01.2003
• EAN: 9783540203582
• ISBN: 978-3-540-20358-2
• No. of pages: 313
• Weight: 500 g
• Series: Lecture Notes in Mathematics; (1829) Lecture Notes in Mathematics; Lecture Notes in Mathematics
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Probability theory, stochastic theory, mathematical statistics; Optimierung, B, Optimization, Diskrete Mathematik, Combinatorics, Mathematics and Statistics, Probability Theory and Stochastic Processes, Systems Theory, Control, Discrete Mathematics, Combinatorics & graph theory, Probabilities, Stochastics, Probability Theory, Calculus of Variations and Optimization, Calculus of variations, Calculus of Variations and Optimal Control; Optimization, System Theory, Cybernetics & systems theory