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 50 seconds. To help determine the amount of space needed for the line at the drive up window. Burrito king would like to know the expected average time in the system, the average line length (in cars) and the average number of cars in the system (both in line and at the window).

Explanation / Answer

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 Poison distribution at an
average of one every 50 seconds. To help determine the amount of space needed for the
line at the drive-up window, Burrito King would like to know the expected average time
in the system, the average line length (in cars), and the average number of cars in the
system (both in line and at the window).
Solution:
We have = 45 and = 50
Expected average time is given by:WQ = LQ / + 1/
= 4.05/45 + 1/50
= 0.11
Average line length is given by:LQ =
=
= 2025/500s
= 4.05 cars
Average number of cars in the system is given by:LS = LQ + /
= 4.05 + (45/50)
= 4.05 + 0.9
= 4.95 cars

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