Question

1.

Rock Valley Airport is beginning to experience flight congestion and backups on the one runway that is used exclusively for landings. A plane can land and be cleared in 7.3 minutes on average. Planes waiting to land are asked to circle the airport.

On average 4.6 planes arrive at the airport per hour. What is the utilization-factor U of this runway? (Two decimal places.)

2.

Rock Valley Airport is beginning to experience flight congestion and backups on the one runway that is used exclusively for landings. A plane can land and be cleared in 7.6 minutes on average. Planes waiting to land are asked to circle the airport.

On average 3.9 planes arrive at the airport per hour. Assume system V=1.

On average, how many minutes do planes circle the airport waiting for clearance to land?

(Hint: this is the WT. Use WT = V*U*PT. Get U using the same procedure for the last questsion. The V factor is almost always assumed to be 1. The procedure is similar to the face painting example in the lecture.)

Answer 1

1.

Arrival Rate = 4.6 planes per hour

Processing time = 7.3 minutes

Capacity = 1/Processing Time

Capacity = 1/7.3 planes per minute

Capacity = 60/7.3 planers per hour

Capacity = 8.21917

Utilization = Arrival Rate/ Capacity

Utilization = 4.6/8.21917

Utilization (u) = 0.559666

Utilization U-Factor = u/(1-u)

Utilization U-factor = 0.559666/(1-0.559666)

Utilization U-factor = 1.27

2.

Arrival Rate = 3.9 planes per hour

Processing time (PT) = 7.6 minutes

Capacity = 1/Processing Time

Capacity = 1/7.6 planes per minute

Capacity = 60/7.6 planers per hour

Capacity = 7.8947368

Utilization = Arrival Rate/ Capacity

Utilization = 3.9/7.8947368

Utilization (u) = 0.494

Utilization U-Factor = u/(1-u)

Utilization U-factor = 0.494/(1-0.494)

Utilization U-factor = 0.97628

Given V = 1

Waiting time (WT) = V × U × PT

WT = 1 × 0.97628 × 7.6

WT = 7.41976 minutes

WT = 7.42 minutes (rounded off to 2 decimals)

Waiting time = 7.42 minutes