Macrosystem models of flows in communication-computing networks (GRID-technology)

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