Consider there are three directions $S_1$, $S_2$ and $S_3$ of a road junction.
Suppose $m_i$ is the number of cars coming from $S_i$ direction towards the junction.
Similarly, suppose $n_i$ is the number of cars going to $S_i$ direction via the junction.
Question is to determine how many cars going from $S_i$ to $S_j$ where $i\neq j$. Here $i,j \in \{1,2,3\}$.
Any help is highly solicited.
Simple case: all $m_i$ and $n_j$ are $1$.
Then we have $2$ possibilities. So I think you need more information/requirements.
I would consider a transition matrix with the following equation:
$$\begin{bmatrix}IN1 & IN2 & IN3 \end{bmatrix} \cdot \begin{bmatrix}a_{11} & a_{12} &a_{13} \\a_{21} & a_{22} & a_{23} \\a_{31} & a_{32} & a_{33} \end{bmatrix} = \begin{bmatrix}OUT1 & OUT2 & OUT3 \end{bmatrix}$$
Values $a_{ij}$ are obtained by observation.