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Customers arrive on average every 30 minutes to an auto repair shop with only one mechanic. The inter-arrival times are exponentially distributed. Repair times are variable with a mean of 25 minutes and a standard deviation of 20 minutes. The mechanic works on one vehicle at a time from beginning to end and takes in any waiting vehicles on a first-come first-served basis. The shop consists of a small garage and an adjacent parking lot. The garage itself has room for only one vehicle at a time, so waiting vehicles are kept in the parking lot where there are always plenty of spaces available. Assume customers never balk or renege.
[1] How long (in minutes) do vehicles wait on average exclusively in the adjacent parking lot?
[2] What is the average number of vehicles one would expect to nd exclusively in the garage? (In other words, at any given time, what is the probability of nding a vehicle in the garage?)
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