Modelling and Control of Dynamic Flows in Communication Networks

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.