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A dynamical communication system on a network. (English) Zbl 1297.68024
Summary: A dynamical system is introduced and investigated. The system contains $$N$$ vertices. The vertices send messages at discrete time instants according to a given rule. A conflict of two vertices takes place if the vertices try to send messages to each other at the same instant. Each vertex sends a message to another vertex at every step if no conflict takes place. In case of a conflict, only one of the two competing vertices sends a message. Deterministic and stochastic conflict resolution rules are considered. We investigate the average number of messages sent by a vertex per a time unit, called the productivity of this vertex, the total productivity of the system and other characteristics. The productivity of vertices depends on the initial state of the system, and the criterion of efficiency is the expected average productivity of vertices provided all possible initial states of the system are equiprobable. An ergodic version of the system is also considered in which any particle moves with approximately equal to 1 probability provided there is no conflict.

##### MSC:
 68M10 Network design and communication in computer systems 68Q10 Modes of computation (nondeterministic, parallel, interactive, probabilistic, etc.) 60J20 Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.) 37N99 Applications of dynamical systems
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##### References:
 [1] V.V. Kozlov, A.P. Buslaev, A.G. Tatashev, On synergy of total connected flows on chainmails, in: CMMSE2013 24-27 June, 2013. Proceedings, Vol. 3 (2013) 861-873. [2] A.P. Buslaev, A.G. Tatashev, M.V. Yashina, Qualitative properties of dynamical system on toroidal chainmail, in: AIP Conference. Proceedings, 1558 (2013) 1144-1147. [3] A.P. Buslaev, A.G. Tatashev, A system of pendulums on a regular polygon, in: SIMUL2013. The Fifth International Conference on Advances in System Simulation, October 27-November 1, 2013 Proceedings, 36-39. [4] Bugaev, A. S.; Buslaev, A. P.; Kozlov, V. V.; Tatashev, A. G.; Yashina, M. V., Modeling of traffic. monotonic random walk on a network, Matematicheskoe modelirovanie, 25.8, 3-21, (2013), (in Russian) · Zbl 1356.60113 [5] Kozlov, V. V.; Buslaev, A. P.; Tatashev, A. G., Monotonic walks on a necklace and a colored dynamical vector, Int. J. Comput. Math., 915964, (2014) [6] Kozlov, V. V.; Buslaev, A. P.; Tatashev, A. G., Behavior of pendulums on a regular polygon, J. Commun. Comput., 11, 30-38, (2014) [7] Kozlov, V. V.; Buslaev, A. P.; Tatashev, A. G.; Yashina, M. V., Dynamical honeycomb networks, (Traffic and Granular Flow 2013, (2013), Springer Germany (Julich)), in press [8] Kozlov, V. V.; Buslaev, A. P.; Tatashev, A. G., Traffic modelling random walks on a networks. models and traffic applications, 1-300, (2013), Lambert Academic Publishing [9] Feller, A., An introduction to probability theory and its applications, (1968), John Wiley New York · Zbl 0155.23101
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