Question

Burger World is considering opening a drive-through window for customer service. Management estimates that customers will arrive at the rate of 15 per hour. The server who will staff the drive-up window can service customers at the rate of one every three minutes.

Assuming Poisson arrivals and exponential service, find:

40. Utilization of the teller

A) 45%

B) 55%

C) 65%

D) None of the above

41. Average number of customers in the waiting line

A) 2.25

B) 5.22

C) 2.00

D) None of the above

42. Average number of customers in the system

A) 1.00

B) 2.00

C) 3.00

D) 4.00

43. Average waiting time in the line (in minutes)

A) 7 minutes

B) 8 minutes

C) 9 minutes

D) None of the above

44. Average waiting time in the system, including service (in minutes)

A) 9 minutes

B) 10 minutes

C) 11 minutes

D) None of the above

Answer 1

Arrival Rate = 15 per hour

Service Rate = 60/3 = 20 per hour

40.

Utilization = Arrival Rate / Service Rate = 15/20 = 0.75 = 75%

41.

Average Customer in line Lq = Arrival Rate^2 / (Service Rate*(Service Rate - Arrival Rate))

Lq = 225/(20*(20-15))

Lq = 225/100

Lq = 2.25

42.

Average Customer in system Ws = Arrival Rate / (Service Rate - Arrival Rate)

Ls = 15/(20-15)

Ls = 15/5

Ls = 3.00

43.

Average Waiting Time in Line Wq = Arrival Rate/(Service Rate*(Service Rate - Arrival Rate)

Wq = 15/(20*(20-15))

Wq = 15/100

Wq = 0.15 hours

Wq = 0.15*60 = 9 minutes

44.

Average Waiting Time in System Ws = 1/(Service Rate - Arrival Rate)

Ws = 1/(20-15)

Ws = 1/5

Ws = 0.2 hours

Ws = 0.2*60 = 12 minutes