3.3.4 Consider the queueing model of Section 3.4. Now, suppose that at most a single customer arrives during a single period, but that the service time of a customer is a random variable Z with the geometric probability distribution PrfZ D kg D .1????/k????1 for k D 1;2; : : : :

Specify the transition probabilities for the Markov chain whose state is the number of customers waiting for service or being served at the start of each period. Assume that the probability that a customer arrives in a period is and that no customer arrives with probability 1????.