# Statistics: Queueing Problem

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A fast food outlet has an average of 8 cars at the drivethrough during "lunch rush" 11am-1pm. On average, 2 cars per min. arrive at the resaurant parking lot, and consider the drivethrough but 25% of the time, an arriving car does not actually enter the drive-through line (i.e. it "balks"). Assume no car enters the line without completing the drive-through service (i.e. there is no "reneging").

a.) On average, how much time does a car spend at the drive-through?

b.) The current average processing time at the drive through is 3 min. The manager wants to reduce this processing time to 2 min. If the arrival rate, the probability of "balking" and the time in the drive through line remain the same, how many cars would be at the drive-through on average, with the new processing time?

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##### Solution Summary

The processing times of cars in a drive-through are analyzed.

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(a). How much time does a car spend at the drive through?

Assume that there are 8 cars there at one given time during lunch.

The rate of arrival for cars on the parking lot is 2 cars per minute.

Since 25% of those cars that arrive on the parking lot do not enter the drive through, then

The arrival rate not entering the drive ...

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