Modelling and Control of Dynamic Flows in Communication Networks

ISBN-13: 9783642832079 / Angielski / Miękka / 2011 / 202 str.

Janusz Filipiak

Opis

In modern communication networks with stored program control the implementation of sophisticated traffic control rules is worthwhile. This allows efficient sharing of existing resources and often defers network extension. Moreover, the flexible control adapts well to changing load conditions during periods of overload and equipment failure. When these benefits become evident, many network administrations start to implement corresponding solutions. This book attempts to provide a systematic approach to the analysis and synthesis of advanced traffic control concepts. Because the book is oriented toward engineering applications, mathematical concepts are often illustrated with examples. The reader is assumed to be familiar with advanced calculus, differential equations and probability theory to engineering level.

Spis treści

0 Introduction.- I: Preliminary Considerations.- 1 The Hierarchy of Communication Network Models.- 2 Various Accuracy Models of the Single Server Queue.- 2.1 Queueing Model.- 2.2 Diffusion Approximation.- 2.3 Dynamic Flow Description.- II: Fundamental Concepts and Methods.- 3 Dynamic Flow Models of Stochastic Service Systems.- 3.1 Model Structure and Characteristics.- 3.2 Reduction of Static and Dynamic Errors.- 3.2.1 Steady-state Characteristics.- 3.2.2 Higher Order Descriptions.- 3.3 Markovian Property at Various Accuracy Levels.- 3.4 Linear Models of Systems without Competition for a Service Facility.- 3.4.1 Random Delay.- 3.4.2 Deterministic Delay.- 3.5 Nonlinear Models of Channels with Queue and Overflow.- 3.5.1 Line-switched Concentrator.- 3.5.2 Buffered Channel.- 3.6 Dynamic Flow Description of Non-Markovian Systems.- 3.6.1 Fixed Service Time.- 3.6.2 Priority Queues.- 3.7 Second-order Dynamic Flow Model.- 4 Control-oriented Network Description.- 4.1 Structural Models of Specimen Networks.- 4.2 Hierarchy of Network Links.- 4.3 Horizontal Structure of a Model.- 4.4 Control Variables and State Equations.- 4.5 Statistical Independence of Traffic Flow.- 4.6 Example: Network without Traffic Control.- 4.7 Example: A Multiprogrammed System.- 5 Model Structure, Fluctuations, and Stability.- 5.1 Bistable Behavior of a Random Access System.- 5.2 Analysis of System Stability in a Parameter Space: Cusp Catastrophe.- 5.3 Network Homeostatic Behavior.- 5.4 High Stability of Mesh-type Networks.- 6 Simple Traffic Control Problem.- 6.1 Adaptive Random Routing.- 6.1.1 Necessary Conditions for Optimality.- 6.1.2 Flow Pattern.- 6.2 Numerical Example.- 6.3 AR Routing Versus JSQ Routing.- 6.4 Simulation Results.- 6.5 An Assignment Problem for Parallel Channels with Rejection of Excess Traffic.- 6.5.1 User-optimal Assignments.- 6.5.2 System-optimal Assignments.- 6.5.3 Saturation State.- 6.6 Implementation.- 7 System-optimal Network Flow Pattern.- 7.1 Formulation of an Optimization Problem.- 7.2 Steady-state Costate Solution.- III: Dynamic Flows Within Specific Networks.- 8 Control of Arrivals to a Random Access System.- 8.1 Structural Perturbations of the Model.- 8.2 Adaptation of System Parameters to Changing Load Conditions.- 8.3 Two-layer Access Control.- 8.4 BSBMA Protocol Implementation.- 8.4.1 Model Verification.- 8.4.2 BSBMA Implementation within the OSI Reference Model.- 8.4.3 Updating of the System Status Information.- 9 Routing and Flow Control in a Packet-switched Network.- 9.1 Model and Optimization Problem.- 9.2 Solution.- 9.3 Properties of the Steady State-costate Solution.- 9.4 Small Loads.- 9.5 Large Loads.- 9.6 Congestion Phenomenon.- 9.7 Medium Loads.- 9.8 An Example.- 9.9 Packet-switched Network with Virtual Channels.- 10 Congestion Offloading Procedure.- 10.1 Model for a Region of Congestion.- 10.2 Switching Times.- 10.3 Unloading Procedure.- 10.4 Example.- 10.5 Further Properties of the Solution.- 11 Adaptive Control of Telephone Traffic.- 11.1 Formulation of a Traffic Control Problem.- 11.2 Steady State-costate Solution for a Line-switched Network.- 11.3 Alternate Routing.- 11.4 Adaptive Routing.- 11.5 Network Control Strategies.- 11.6 Reiteration of Rejected Traffic.- IV: Multistrata Control Models.- 12 Dynamic Load Sharing in Data Networks.- 12.1 Description of the Dynamic Multicommodity Flow.- 12.2 Two-layer Model of Packet-switched Network.- 12.3 Decomposition of the Flow Assignment Problem.- 12.4 Control Law for the Correction Layer.- 12.5 Comments on Multilayer Flow Assignment.- 13 Coordination of Routing by Learning Automata.- 13.1 Routing by Learning Automata in Telephone Networks.- 13.1.1 Modes of Network Operation.- 13.2 Accomplishment of an Optimal Flow Pattern.- 13.2.1 Actual Procedure for Specimen Network.- Appendix A. Basic Concepts of Queueing Theory.- Appendix B. Pontryagin Minimum Principle.- References.