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

Question

Burrito King (e new fast-food franchise opening up nationwide) has successfully automated burrto production for its drive-up fast-food establishments. The Burro-Master 9000 requires a constant 10 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 4 seconds. To help determine the amount of space needed for the line at the drive-up window a. What is the average waiting line length (in cars)? (Do not round intermediate calculations. Round your answer to 2 decimal places.) ine cars 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.) e. What is the expect decimal places.) ed average time in the system, in minutes? (Do not round intermediate calculations. Round your answer to 2 minutes

Explanation / Answer

Ans:- Customer arrival rate = one every 4 seconds = 15 per minute = lambda

Service rate of burritos = one every 10 seconds = 6 per minute = Mu

a) Length of waiting line = lambda^2/((mu)*(mu-lambda))

= 15^2/6 *9= 225/54 = 4.167

b) Cars at the window = lambda/((mu)*(mu-lambda)) = 15/54 = 0.278

Cars in the line = 4.167

Hence,cars in the system including at the window and in the line = 4.167+0.278 = 4.445

c) Expected average time in the system = 1/(lambda-mu) = 1/9 minutes = 0.11 minutes

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