Consider a graph with nodes 1, 2,...,n and the arcs (i,j), ij,,,1,, n. (See Section 3.6.2 for appropriate definitions.) Suppose that a particle moves along this graph as follows: Events occur along the arcs (i,j) according to independent Poisson processes with rates 2.

An event along arc (i,j) causes that are to become excited. If the particle is at node i at the moment that (i,j) becomes excited, it instan- taneously moves to node j; i,j = 1,..., n. Let P, denote the proportion of time that the particle is at node j. Show that Hint: Use time reversibility.