Geodesic
Traffic modeling: monotonic total-connected random walk on a network
Matematičeskoe modelirovanie, Tome 25 (2013) no. 8, pp. 3-21

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Monotonic (particles move in the same direction) and total-connected (particles that occupy neighboring cells move synchronized) random ($p1$) 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. 
@article{MM_2013_25_8_a0,
     author = {A. S. Bugaev and A. P. Buslaev and V. V. Kozlov and A. G. Tatashev and M. V. Yashina},
     title = {Traffic modeling: monotonic total-connected random walk on a network},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {3--21},
     publisher = {mathdoc},
     volume = {25},
     number = {8},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2013_25_8_a0/}
}
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A. S. Bugaev; A. P. Buslaev; V. V. Kozlov; A. G. Tatashev; M. V. Yashina. Traffic modeling: monotonic total-connected random walk on a network. Matematičeskoe modelirovanie, Tome 25 (2013) no. 8, pp. 3-21. http://geodesic.mathdoc.fr/item/MM_2013_25_8_a0/