Burrito King (a new fast-food franchise opening up nationwide) has successfully
ID: 3072634 • Letter: B
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 ...... 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.)
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 ..... minutes
Explanation / Answer
We have, the single-server model with Poisson arrival and constant service time.
And we are given
Mean arrival rate = 1/ 75 per second or 60/75 = 0.8 per minute.
Mean service rate = 1/50 per seconds or 60/50 = 1.2 per minute.
Now, for the single-server model with Poisson arrival and constant service time.
a) Expected queue length Lq = 2 / 2( - )
= (0.8)2 / 2*1.2 (1.2 - 0.8)
= 0.64 / 0.96
= 0.6667 cars
Hence, he average waiting line length is 0.6667 cars.
b) Expected line length Ls = Lq + /
= 0.6667 + 0.8/1.2
= 0.6667 + .6667
= 1.3334
Hence, average number of cars 1.3334.
c) Expected average time in the system Ws = Ls /
= 1.3334 / 0.8
= 1.66675 minutes
Hence, expected average time 1.66675 minutes.
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