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 30 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 55 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.)

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.)

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

Answer 1

The assumptions in single-server queue theory include: -

Unlimited calling population may enter the queue

Arrivals are random and independent but average number of arrival does not change.

Single waiting line and arriving customers are patient customers who can wait in the queue before they can be served regardless of the length of the line.

Arrivals are served on FIFO basis

Service time of one customer may vary from that of another customer.

Single server and service time is as per the negative exponential probability distribution.

Average service rate is greater than average arrival rate.