Question

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 8.0 minutes on average. Planes waiting to land are asked to circle the airport.

On average 3.8 planes arrive at the airport per hour. Assume system V=1.

On average, how many planes will be circling the airport waiting for clearance to land?

(Hint: this is the queue length, or WIP of the queue. Consider the queue itself as a subsystem. Waiting time (e.g., last question) is therefore Time-in-System in this subsystem and is therefore the CT in the queue. Output rate from the queue is the same TH. Simply apply the Little's Law. Make sure use the same time unit for calculation. The procedure is similar to the face painting example in the lecture.)

Answer 1

Arrival Rate = 3.8 planes per hour

Processing time (PT) = 8 minutes

Capacity = 1/Processing Time

Capacity = 1/8 planes per minute

Capacity = 60/8 planers per hour

Capacity = 7.5

Utilization = Arrival Rate/ Capacity

Utilization = 3.8/7.5

Utilization (u) = 0.506666

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

Utilization U-factor = 0.506666/(1-0.506666)

Utilization U-factor = 1.027027

Given V = 1

Waiting time (WT) = V × U × PT

WT = 1 × 1.027027 × 8

WT = 8.2162 minutes

WT = 8.22 minutes (rounded off to 2 decimals)

Waiting time = 8.22 minutes