Question

2. A barber owns a one-chair shop. At barber college, he was told that his customers would exhibit a Poission arrival distribution and that he would provide an exponential service distribution. His market survey data indicate that customers arrive at the rate of two per hour and that it takes him an average of 20 minutes to give a haircut. Based on these figures, find the following:

a. The average number of customers waiting in line. (2 pts)

b. The average time a customer waits in line (2 pts)

c. The average time a customer is in the shop. (2 pts)

d. The average number of customers in the shop. (2 pts)

e. The barber would like to increase his utilization to .85. Given he cannot speed up giving haircuts, how often would customers have to arrive for him to achieve his goal? (round to two decimal places). (2 pts)

Answer 1

As per policy only first four parts will be answered

arrival rate, lamda = 2 per hour

Service rate, mu = 60/20 = 3 per hour

Therefore, utilization ration, rho = lamda/mu = 2/3 = 0.667

a) Number of customers waiting in line, Lq = rho2/ (1-rho) = 0.445 / 0.33 = 1.33

b) The average time a customer waits in line, Wq = Lq/lamda = 1.33/2 = 0.66 hour = 40 minutes

c) The average time a customer is in the shop, W = 1/ (mu-lamda) = 1 hour

d) The average number of customers in the shop, L = W* Lamda = 1*2 = 2 Customers