Question

Consider the baggage check-in process of a small airline. Check-in data indicates that from 9am to 10am, 220 passengers checked in. Moreover, based on counting the number of passengers waiting in line, airport management found that the average number of passengers waiting for check-in was 32. Instructions: Round your answer to 1 decimal place. How long did the average passenger have to wait in line?

Answer 1

Using Little's Law, the average waiting time for an airline passenger to check-in was calculated at approximately 8.7 minutes.

Step-by-step explanation:

To calculate how long the average passenger had to wait in line at the small airline's check-in process, we can use Little's Law, which states that the average number of passengers in a system (L) is equal to the average arrival rate (λ) multiplied by the average time a passenger spends in the system (W). The formula is given by L = λW.

In this case, the average number of passengers waiting in line is given as L = 32. The average arrival rate can be calculated by taking the total number of passengers that checked in (220 passengers from 9am to 10am) and dividing it by the time period (1 hour), which gives us λ = 220 passengers/hour. Using these values, we can solve for the average waiting time (W).

The equation becomes 32 = 220 × W. To find W, we divide both sides of the equation by the arrival rate (λ): W = 32 / 220. Performing the calculation yields W ≈ 0.1455 hours. To convert hours to minutes, we multiply by 60: W ≈ 0.1455 hours × 60 minutes/hour ≈ 8.73 minutes. Thus, the average passenger waited approximately 8.7 minutes in line.