Generalized transport-logistic problem as class of dynamical systems
Mathematical Models and Computer Simulations, 2015, vol. 27, no. 12, pp. 65–87
Abstract
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Dynamical systems on network with discrete set of states and discrete time are considered. Sites, channels and particles are forming an abstract model of mass transport, information and so on, on the one hand, and another, they are forming dynamical system of deterministic or stochastic type. State of the system in the following discrete instant of time $S(T+1)$ is defined by transformation of the state at the moment $S(T)$ with given rules $L$, $S(T+1)=L(S(T))$. In this case, $S(T+1)$ does not necessarily belong to the admissible states set $A$. Then "judicial system" is activated, i.e. operator $P$ such that projects $S(T+1)$ to $A$. Thus, $S(T+1)=\{L(S(T))$, if $L(S(T))$ belongs $A$; $PL(S(T))$, if $L(S(T))$ does not belong $A\}$. Properties of these systems are researched, and applications for transport problems are discussed.

Bugaev A. S., Buslaev A. P., Kozlov V. V., Tatashev A. G., Yashina M. V., Generalized transport-logistic problem as class of dynamical systems, Mathematical Models and Computer Simulations, 2015, vol. 27, no. 12, pp. 65–87

Traffic modeling: monotonic total-connected random walk on a network
Mathematical Models and Computer Simulations, 2013, vol. 25, no. 8, pp. 3–21
Abstract
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Monotonic (particles move in the same direction) and total-connected (particles that occupy neighboring cells move synchronized) random ($p<1$) and deterministic ($p=1$) walks on closed networks, which consist of circles, are considered. An algorithm has been developed that allows to calculate the duration of the time interval after that all the particles will be contained in the unique cluster. It is proved that such the interval is finite in the considered model. Some statements are proved that allow to found the velocity of movement if deterministic movement occurs on the follows structures: two rings (two closed sequences of cells) that have a common cell; a closed sequence of rings each of that has two common cells with two the neighboring rings; a two-dimensional network structure in that each cell has common cells with four the neighboring rings; a similar infinite network.

Keywords:

stochastic models; random walk; traffic flows

Citation:

Bugaev A. S., Buslaev A. P., Kozlov V. V., Tatashev A. G., Yashina M. V., Traffic modeling: monotonic total-connected random walk on a network , Mathematical Models and Computer Simulations, 2013, vol. 25, no. 8, pp. 3–21

Some mathematical and information aspects of traffic modeling
T-Comm: Telecommunications and Transport, 2011, no. 4, pp. 29–31
Abstract
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Transport, communications and mathematics (in wider understanding - natural sciences) it becomes more and more obvious to despite different "age" of these three components. If the mathematics in Russia (USSR) was always, at least, since that moment as to Russia were invited L.Eyler (1976) and D. Bernulli (1725) that a traffic (traffic) as the appreciable phenomenon and an acute problem, appeared in the early nineties after opening of borders and a mass import of cars. With transition to market economy and small business mobility of the population, need for multipurpose cars and load of a street road network sharply increased.

Citation:

Bugaev A. S., Buslaev A. P., Kozlov V. V., Yashina M. V., Some mathematical and information aspects of traffic modeling, T-Comm: Telecommunications and Transport, 2011, no. 4, pp. 29–31

Distributed problems of monitoring and modern approaches to traffic modeling
2011 14th IEEE International IEEE Conference on Intelligent Transportation Systems (ITSC), 14th International IEEE Conference on Intelligent Transportation Systems-ITSC, 2011, pp. 477–481
Abstract

The paper discusses some mathematical models of traffic flow. We have introduced the concept of a stationary r-connected traffic flow on k-lane road as a development of the hydrodynamic approach and cellular automata method. A client-server based software “SSSR”-system, using smart-phone programming, for evaluating a distance of safety in continuous traffic was developed. A series of experiments were carried out using the SSSR-system, the results showing good agreement with those obtained by Greenshields in 1933. Other problems of traffic monitoring and control by the programmed SSSR-system are discussed. We also introduce a few open problems.

Citation:

Bugaev A. S., Buslaev A. P., Kozlov V. V., Yashina M. V., Distributed problems of monitoring and modern approaches to traffic modeling, 2011 14th IEEE International IEEE Conference on Intelligent Transportation Systems (ITSC), 14th International IEEE Conference on Intelligent Transportation Systems-ITSC, 2011, pp. 477–481