2. Eat & Gas convenience store operates a two-pump gas station. The lane leading to the pumps...

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2. Eat & Gas convenience store operates a two-pump gas station. The lane leading to the pumps can house at most 3 cars, excluding those being serviced. Arriving cars go elsewhere if the lane is full. The distribution of arriving cars is Poisson with mean 20 per hour. The time to fill up and pay for the purchase is exponential with mean 6 minutes.

Determine the following:

(a) Percentage of cars that will seek business elsewhere.

(b) Percentage of time one pump is in use.

(c) Percent utilization of the two pumps.

(d) Probability that an arriving car will not start service immediately but will find an empty space in the lane.

(e) Capacity of the lane that will ensure that, on the average, no more than 10% of the arriving cars are turned away.

(f) Capacity of the lane that will ensure that the probability that both pumps are idle is

.05 or less.

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