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A dynamical system, called a binary closed chain of contours, is studied. Thedynamica system belongs to the class of Buslaev networks. The system contains$N$ {\it contours.} There two cells and a particle in each contour. There twoadjacent contours for each contour. There is a common point of adjacentcontours. This common point is called a node. The node is located between thecells. In the deterministic version of the system, at any discrete moment, eachparticles moves to the other cell of the contour if there is no delay. Thedelays are due to that two particles may not pass through the common nodesimultaneously. If two particles try to cross the same node, then a {\itcompetition} occurs, and only one of these particles moves in accordance with aprescribed competition resolution rule. In the stochastic version of thesystem, each particle moves with the probability $1-\varepsilon,$ if the systemis in the state such that, in the same state of the deterministic system, thisparticle moves. where $\varepsilon$ is a small value. We have obtained acompetition resolution rule such that the system results in a state such thatall particles move without delays in present time and in the future (a state offree movement), and the system results in the state of free movement over aminimum time. The expectation of the number of the $i$th particle transitionsper a time unit is called the {\it average velocity of this particle,} $v_i,$$i=1,\dots,N.$ For the stochastic version of the system, under the assumptionthat $N=3,$ we have proved the following. For the optimal rule, the averagevelocity of particles is equal to $v_1=v_2=1-2\varepsilon+o(\varepsilon)$$(\varepsilon\to 0).$ For the left-priority rule, which is studied earlier, theaverage velocity of particles equals$v=v_1=v_2=\frac{6}{7}+o(\sqrt{\varepsilon}).$

Optimal Competition Resolution Rule for Buslaev Controlled Binary Chain