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Statistics: Queueing Problem

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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(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 ...

Solution Summary

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

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