Jackson Networks with Feedbacks at Nodes. Consider a Jackson process under the usual assumption that, whenever it is in state x, the time to the next departure from node i is exponentially distributed...

Jackson Networks with Feedbacks at Nodes. Consider a Jackson process under the usual assumption that, whenever it is in state x, the time to the next departure from node i is exponentially distributed with rate φ­_i(x_i), but the routing is a little different. Assume that an item departing from node i enters node j with probability ¯p_ij , independently of everything else, where the probability ¯p_ii of a feedback may be positive. Justify that theresulting process X(t) is a CTMC and specify its transition rates q(x, Tijx) and exponential sojourn rate q(x) in state x.