Newell and Jeff are the two barbers in a barber shop they own and operate. They provide two chairs for customers who are waiting to begin a haircut, so the number of customers in the shop varies between 0 and 4. For n = 0, 1, 2, 3, 4, the probability Pn that exactly n customers are in the shop is P0 = 1/16, P1 = 4/16, P2 = 6/16, P3 = 4/16, P4 = 1/16.
(a) Calculate L. How would you describe the meaning of L to Newell and Jeff?
(b) For each of the possible values of the number of customers in the queueing system, specify how many customers are in the queue. Then calculate Lq. How would you describe the meaning of Lq to Newell and Jeff?
(c) Determine the expected number of customers being served.
(d) Given that an average of 4 customers per hour arrive and stay to receive a haircut, determine W and Wq. Describe these two quantities in terms meaningful to Newell and Jeff.
(e) Given that Newell and Jeff are equally fast in giving haircuts, what is the average duration of a haircut?