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A dynamical system is considered such that, in this system, particles move ona toroidal lattice of the dimension $N_1\times N_2$ according to a version ofthe rule of particle movement in Biham--Middleton--Levine traffic model.Particles of the first type move along rows, and the particles of the secondtype move along columns. A particle can change its type. The probability that,at a step, a particle changes the type equals $q.$ It has been proved that, ifwhether $q>0$ or $q=0$ and there are at least one particle of the first typeand there is at least one particle of the second type, then a necessarycondition for a state of free movement to exist is that the greatest divisor of$N_1$ and $N_2$ be not less than~3. The system is represented as an algebraicstructure over a set of matrices corresponding to states of the system. Thetheorems are formulated in terms of the algebraic structures and terms of thedynamical systems. The model is also presented as a Buslaev net. The spectrumof the net $2\times 2$ has been found.

Necessary Condition for Self-organization in the BML Model with Stochastic Direction Choice