1. 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.
b) The average time a customer waits in line.
c) The average time a customer is in the shop.
d) The average number of customers in the shop.
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. Weary travelers arrive at Will Rogers International Airport, pick up their luggage, stumble to their cars, and proceed to the parking lot attendant to pay for their parking. Traveler interarrival times are exponentially distributed, as are the service times of the attendant. On average, travelers arrive every 25 seconds. The attendant can process three travelers per minute, and processing rates follow a Poisson distribution.
Use the information in Scenario B.2. What is the average number of customers in the system?
fewer than or equal to 3.0
greater than 3.0 but fewer than or equal to 5.0
greater than 5.0 but fewer than or equal to 7.0
greater than 7.0