Question

Burrito King (a new fast-food franchise opening up nationwide) has successfully automated burrito production for its drive-up fast-food establishments. The Burro-Master 9000 requires a constant 50 seconds to produce a batch of burritos. It has been estimated that customers will arrive at the drive-up window according to a Poisson distribution at an average of one every 75 seconds. To help determine the amount of space needed for the line at the drive-up window, answer the following questions.

a. What is the average waiting line length (in cars)? (Do not round intermediate calculations. Round your answer to 2 decimal places.) Average line length

b. What is the average number of cars in the system (both in line and at the window)? (Do not round intermediate calculations. Round your answer to 2 decimal places.) Average number of cars

c. What is the expected average time in the system, in minutes? (Do not round intermediate calculations. Round your answer to 2 decimal places.) Expected average time

Answer 1

Arrival rate / minute = 60/75= 0.80 per minute

Service rate / minute = 60 / 50 = 1.2 per minute

a & B) Utilization = a/s = 0.8 / 1.2 = 0.667

b) Average number of cars in system = L = a / (s-a) = 0.8 / 0.4 = 2.00 cars

a) Average cars waiting lenght of line, Lq = p * L = 0.667*2 = 1.33 cars

c) Total time in the system, W (Includes wait time + service time) = 1 / (s-a) = 1/ 0.40 = 2.50 minutes