During an interview, you have been asked to demonstrate your ability to use Little's Law for personal situations, such as waiting in a TSA Line for Spring Break. The following information is provided:

While waiting in the TSA, you determine there are an average of 12,375 passengers waiting to be processed.
The average flow rate is 125 persons per minute. What is the average time a ticket buyer can expect to wait in line?

Using Little's Law, the average time a ticket holder can expect to wait in line is ________ minutes.

Question

During an interview, you have been asked to demonstrate your ability to use Little's Law for personal situations, such as waiting in a TSA Line for Spring Break.  The following information is provided:

While waiting in the TSA, you determine there are an average of 12,375 passengers waiting to be processed.
The average flow rate is 125 persons per minute.  What is the average time a ticket buyer can expect to wait in line?

Using Little's Law, the average time a ticket holder can expect to wait in line is ________ minutes.

BlackTom AI · Accepted Answer

First, restate the scenario and identify the variables involved: we are applying Little's Law, which relates the average number in the system (L), the arrival rate (λ), and the average time in the system (W) via L = λW. For this problem, the average number waiting to be processed is given as L = 12,375 passengers, and the average flow rate is λ = 125 passengers per minute.

Next, rearrange the formula to solve for the average time in line: W = L / λ. This substitution gives W = 12,375 / 125 minutes.

Proceed to the division: 12,375 ÷ 125 = 99. To check units, dividing passengers by passengers per minute yields minutes, which is consistent with the time dimension we seek.

Consider any potential ambiguities: Little's Law can apply to the system as a whole or just the queue depending on definitions, but here the problem explicitly uses 'waiting to be processed' as the L term and 'flow rate' as λ, which aligns with W = L/λ in minutes.

As a quick sanity check, if 125 passengers are processed each minute, and there are 12,375 passengers waiting, then it takes roughly 99 minutes to clear or service that backlog at the current rate, which matches the computed value.

SCO 3001 (004/005/006) First Exam - Spring 2025

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