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Exploring Macrosystem Models of Communication Flows in GRID Technology Networks

This document presents an extensive analysis of the macrosystem models associated with flows in communication networks, specifically focusing on GRID technology. It explores concepts such as real-time operations, stochastic factors, and the dynamics of transportation flows within systems like Moscow's traffic. The study tackles the probabilistic characteristics of information and computing resources, discussing quasi-stationary states, balance constraints, and transmission costs. Emphasis is placed on the importance of understanding these models for effective control, prediction, and resource management in dynamic systems.

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Exploring Macrosystem Models of Communication Flows in GRID Technology Networks

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  1. Macrosystem models of flows in communication-computing networks(GRID-technology) Yuri S. Popkov Institute for Systems Analysis of the Russian Academy of Sciences popkov@isa.ru

  2. GRID—distributed computer

  3. A B • Real-time operation mode • network as a computer • response time is a random value which depends on the flows in network • random delay • random delay depends on flows in network

  4. Transportation flows in Moscow traffic system (middle of the day) T = 25 min

  5. Change of transportation flows in Moscow traffic system (morning) T = 32 min

  6. Change of transportation flows in Moscow traffic system (evening) T = 29 min

  7. Stochastic factors Inertia GRID — Stochastic network—Dynamic system History Transportation networks (passanger, cargo) Pipe-line networks (oil, gas) Computer networks (Internet, Intranet) Energy networks State GRID Distribution of Information flows Dynamic stochastic network Macrosystem theory

  8. GRID states • Spatial distribution of information and computing resources • relaxation time • Distribution of correspondence flows • relaxation time Problems for study • Formation of quasi-stationary states of corresponding flows • Spatial-temporary evolution of network: interaction between “slow” and “fast” processes in network

  9. Macrostate - correspondence flows GRID phenomenology Network Correspondences Flows Assignment

  10. Information and computing resources Number of information portions Correspondence flows  Number of information portions per time unit Prior probabilities Model of quasi-stationary states Probabilistic characteristics Time interval Flows Volumes Generalized Boltzmann information entropy

  11. Volume of correspondences Model of quasi-stationary states Probabilistic characteristics Throughputs Feasible correspondence flows Generalized Fermi-Dirac information entropy

  12. —transmission cost of an information portion for( ij ) – correspondence Model of quasi-stationary states Feasible sets Cost constraints —transmission cost of an information portion per time unit for i–th resource Balance constraints - demands - throughput constraints –throughput ofk-th arc General model

  13. Classification of the model of quasi-stationary states (MQSS) • MQSS for constant capacity of correspondences • MQSS for variable capacity of correspondences • MQSS for small network loading

  14. Illustration of adequacy of the MQSS(transport network)

  15. Dynamic models of stochastic network Regional structure of network —volume of computing resources ini-th region(slow variables) —information flows between regionsiandj (fast variables) or • Change factors of information and computing resources • ageing (depends onX(t)) • renewal (external influenceU(t)) • information flows (Y(t)) • Change factors of information flows • information and computing resources (X(t)) • demand (Q(t)) • information flows (Y(t))

  16. Dynamic model А. Resource dynamic - positiveness - boundedness Example:

  17. Model types 1. Ageing with constant rate 2. Ageing and renewal with constant rate 3. Renewal with constant rate P – (m x n) matrix; Pi – i –th row of matrixP; Yi – i –th column of matrixY; B. Quasi-stationary states of the information flows distribution

  18. General dynamic model of stochastic network Positive dynamic system with entropy operator

  19. GRID-technology Hardware, software, technical tools and etc. GRID as a system Information and computing resources, information flows, distributed on-line computing Conclusion Interestingly: new class of dynamic systems Why it is necessary to study System properties of GRID? Usefully: active and strategic control, prediction Tools Macrosystem modelling

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