Double-circuit system with clusters of different lengths and unequal arrangement of two nodes on the circuits

We study a system that fulfills the class of driving systems developed by A. P. Buslaev (Buslaev networks). In this system, in each of two closed loops there is a segment called a cluster, and it moves at a constant speed if there are no delays. The lengths of the clusters are $l_1$ and $l_2$. There are two common points of the contours, called nodes. Delays in the movement of clusters are due to the fact that two clusters cannot pass through a node at the same time. The contours have the same height, the glazing is accepted. The nodes divide each contour into parts, the length of one of which is equal to $d_i$, and the other $1-d_i$, $i=1,2$, — contour number. Studies of the spectrum of average speeds of systems, i. e. set of pairs of results $(v_1,v_2)$, where $v_i$ — cluster of average movement speed $i$ taking into account delays, for different initial states and fixed values $l_1$, $l_2$, $d_1$, $d_2$. 12 scenarios of system behavior have been identified, and for each of these manifestations sufficient conditions for its implementation have been found, and each of these observed spectra contains one or two pairs of average velocities.