Vehicles leave an airport parking facility (arrive at parking fee collection booths) at a rate of 500 veh/h (the time between arrivals is exponentially distributed). The parking facility has a policy that the average time a patron spends in a queue waiting to pay for parking is not to exceed 5 seconds. If the time required to pay for parking is exponentially distributed with a mean of 15 seconds, what is the smallest number of payment processing booths that must be open to keep the average time spent in a queue below 5 seconds?

At least 3 processing booths should be open.

Step-by-step explanation:

1 vehicle spends an average of 15 seconds in a booth

In N booths , there will be N/15 vehicles in 1 second

In 1 hr, there will be N/15 * 3600 vehicles

Therefore, there will be a total of 240N vehicles/hour

Actual arrival rate of vehicles at the airport is 500 veh/h

Probability of arrival, P =

P = 500/240N

P = 2.083/N

For the average time spends to be below 5 seconds

, since 500 is the average value.

Solving for N using the quadratic formula with a = 1, b = -2.0832, c = -0.0017

N = 1.0416 ± 1.0424

N = 2.084 or -0.0008

N = 2.084 is the only realistic value here

Therefore, the smallest number of processing booths that must be open should be 3

step-by-step explanation:

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xcvb nm you ugly

  n=   0.0000 - 0.3750 i  

  n=   0.0000 + 0.3750 i

step-by-step explanation:

one of these should be correct