Answer to Question #158071 in Economics for Harish

Question

At the Dorchester McDonald’s branch, cars arrive at the Drive-Thru at a rate of 25 per hour, and only one drive-thru till is open. The average time it takes for order and collection is 5 minutes. Assuming that the interarrival time and the service time are both exponentially distributed. Calculate the average number of customers arriving at the till and the average time they must wait before exiting McDonald’s Drive-Thru. You are encouraged to use calculations to prove any challenges if there is any and suggest any solutions, based on the calculations.

(200 words)

Answer 1

Since cars arrive at the r McDonald's branch in Drive-Thru at a speed of 25 per hour, and only one ticket office is open for passage, the base of the compiled exponential function will be equal to the average service speed of one car.

  The average time required for ordering and receiving is 5 minutes, that is,

$$\frac {60}{5}=12$$

cars are served per hour.

So, we will have a function

$$f(x)=(\frac {25}{12})^x$$

Then the average number of customers arriving at the checkout is 2.

  The average waiting time before exiting McDonald's Drive-Thru is 4.3 minutes.