Construct a transition model with a specified equilibrium
A monthly membership model records members assigned to two library branches
Use the state order central branch, neighbourhood branch and write state populations as a column. In T, a column is the current state and a row is the next state
\[S=\begin{bmatrix} 720 \\ 840 \end{bmatrix}\]
The entries marked ? are the missing transition entries in one source-state column
\[T=\begin{bmatrix} ? & 0.15 \\ ? & 0.85 \end{bmatrix}\]
The supplied rate is \(0.15\) from neighbourhood branch to central branch
At equilibrium, the flow from central branch to neighbourhood branch equals the flow from neighbourhood branch to central branch