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Michael Maloney, a mechanic at CAT Williams, installs new mufflers at an average of 20 minutes each, according to an exponential distribution. Customers seeking this service arrive at the shop on the average of 2 per hour, following a Poisson distribution. They are served on a first in, first out basis and come from a very large (infinite) population of possible customers
a. What are the arrival and service rates?
b. What is the average number of customers in the system?
c. What is the average waiting time in the system?
d. What is the average waiting time in the queue?
e. What is the probability that the mechanic is busy? (hint: utilisation rate)
f. Determine the system utilisation rate if there are three mechanics.
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