In 2014 cars arrived randomly to a drive-through Starbucks with a single window

Question

In 2014 cars arrived randomly to a drive-through Starbucks with a single window having an average line length of 10 cars, which includes the car being served. The service time of a car follows a Venti distribution at the average rate of 20 cars per hour with a standard deviation of 1 minute. Then in January, 2015, Starbucks raised its prices. Thereafter, the cars still arrive randomly, but the line averages only 5 cars with the same Venti service distribution as in 2014 (a) Determine the arrival rate of cars in both 2014 and 2015 (b) Determine the proportion of its business that Starbucks lost from 2014 to 2015

Explanation / Answer

a) The arrival rate of cars in 2014

arrival Rate = Service Rate, the line length turn out to be unending substantial the more extended you run the model.

we were ascertaining the entry rate every moment. A hour has a hour and a day has 24 hours. In this manner, the quantity of minutes in a day are 24 x 60 = 1,440.

20 cars / 24 = 0.8333

The arrival rate of cars in 2014 = 0.8 cars per hour

The arrival rate of cars in 2015

= 5 cars / 24 = 0.2 cars per hours

b) The propotion of its business that Starbucks lost from 2014 to 2015

= average rate of cars arrival in 2014 - avg. rate of cars arrival in 2015

= 20 - 5 = 15

this is 25 % propotion of business lost Starbucks from 2014 to 2015

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