30. Consider a graph with nodesI mage and theI mage arcsI mage. (See Section 3.6.2 for appropriate definitions.) Suppose that a particle moves along this graph as follows: Events occur along the arcs Image according to independent Poisson processes with ratesI mage.

An event along arcI mage causes that arc to become excited. If the particle is at node i at the moment thatI mage becomes excited, it instantaneously moves to nodeI mage. Let denote the proportion of time that the particle is at node j. Show that