Burrito King (a new fast-food franchise opening up nationwide) has successfully

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 45 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 60 seconds. To help determine the amount of space needed for the line at the drive-up window

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.)

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

Explanation / Answer

a = 60 seconds = 60/60 min = 1 minutes
p = 45 seconds = 45/60 min = .75 minutes
m =1
u = 45/60 = .75 min
CVa = 1
CVb = 0
Tq = (1^2 +0^2)/2 x 0.75/(1-0.75)x 0.75 = 1.125
a. average waiting line length (in cars) = Tq/a = 1.125/ 1= 1.125 cars
b. average number of cars in the system (both in line and at the window) = Tq + p/a = 1.125 +.75 min /1 = 1.875 cars
c. expected average time in the system, in minutes = Tq + p = 1.125 +.75 min = 1.875 min.

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