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) Little's Formula: the no in the system (Q) = arrival rate * avg time the customer spends in the system 2014 Q = 10 cars avg time the customer spends in the system = 1 hour/20 cars = 0.05 hours Hence, Arrival rate = 200 cars/hour 2015 Q = 5 cars avg time the customer spends in the system = 1 hour/20 cars = 0.05 hours Hence, Arrival rate = 100 cars/hour b) Since the arrivall rate decresed from 200 to 100 customers per hour, the proportion of its business lost from 2014 to 2015 = ((200-100)/200)*100 = 50%

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.