Exhaustive Parallel Processing. A set of m jobs are processed in parallel until they are all completed. At the completion time, another m jobs instantaneously enter the system and are processed...

Exhaustive Parallel Processing. A set of m jobs are processed in parallel until they are all completed. At the completion time, another m jobs instantaneously enter the system and are processed similarly. This is repeated indefinitely. Assume the times to process jobs are independent witha geometric distribution with mean 1/p. Let Xn denote the number of jobs being processed at time n. Show that Xn is a Markov chain on S = {1,...,m} and specify its transition probabilities (whenever all the jobs in the system are completed simultaneously, the next state is m). Show that the chain is ergodic and that an invariant distribution can be computed by the recursive formula