A university models changes in students’ preferred meal-collection hub (A, B or C) from one month to the next. The columns of the transition matrix $T$ represent the current hub, and the rows represent the hub in the following month. The state matrices are column matrices.

$$T= \begin{pmatrix} 0.6&0.2&0.1\\ x&0.5&0.2\\ 0.4-x&0.3&0.7 \end{pmatrix}$$

The initial state matrix and the state matrix one month later are

$$s_0= \begin{pmatrix} 0.50\\ 0.30\\ 0.20 \end{pmatrix}, \qquad s_1= \begin{pmatrix} 0.38\\ 0.34\\ 0.28 \end{pmatrix}.$$

The same transition matrix applies each month, and the resulting Markov chain is regular.