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# Queueing Problem

Service station cars arive randomly at a rate of 1 car every 30 min. the average time to change oil on a car is 20 min. both the time between arrivals and service time can be modeled using the negative exponential Poisson distribution. This shop only has one garage and one oil change person on duty at any given time.

a) On average what would the length of the line be?

b) On average how long would each car spend at the oil change outlet?

c) On average how long would each driver have to wait before receiving service

d) If the owner wants to lease some new equipment for the oil change outlet so that the average customer spends 15 minutes in the system what level or speed of service rate must the oil change crew deliver?

e) If the owner values his custermers time in the system at \$30 per hour and the oil change garage is open 12 hours a day what is most that he shuld be willing to pay (as a daily lease coat) to achieve the 15 minute time in system goal listed above?

#### Solution Summary

A queueing problem is solved. The average length of the lines are determined.

\$2.19