5.8. As a special case, consider a discrete-time queueing model in which at most a single customer arrives in any period and at most a single customer completes service. Suppose that in any single period, a single customer arrives with probability

a, and no customers arrive with probability 1 -

a. Provided that there are customers in the system, in a single period a single customer completes service with probability f3, and no customers leave with probability 1 - (3. Then X,,, the number of customers in the system at the end of period n, is a random walk in the sense of Section 5.3. Referring to equation (5.9), specify the transition probabilities p;, q;, and r; for i = 0,1.....