Suppose that 2000 students enter (and later leave) a classroom building over the 20 hours in which it is open. On average, there are 200 students in the building.

Assuming the classroom building is operating in steady-state, which of the following statements are true?

Question

Suppose that 2000 students enter (and later leave) a classroom building over the 20 hours in which it is open.  On average, there are 200 students in the building.

Assuming the classroom building is operating in steady-state, which of the following statements are true?

BlackTom AI · Accepted Answer

This problem uses basic queueing/steady-state reasoning.
Option 1: The arrival rate at the building is 120 students per hour. To find the arrival rate, divide the total number of arrivals by the total open time: 2000 arrivals / 20 hours = 100 students per hour. Therefore, 120 per hour is incorrect.
Option 2: Students spend an average of 120 minutes in the building. Using Little’s Law (L = λW), where L is the average number in the system, λ is the arrival rate, and W is the average time in the system, we have L = 200 and λ = 100 per hour. Solving for W gives W = L/λ = 200 / 100 = 2 hours, which is 120 minutes. This matches the statement, so this option is correct.
Option 3: The average number of students in the building is 100. We’re told that on average there are 200 students in the building (L = 200). So stating 100 is incorrect.
Option 4: The building must have at least 5 classrooms. From the given information (arrivals, time in system, and steady-state average occupancy), there is no data tying these figures to the number of classrooms or capacity. Therefore, concluding a minimum of 5 classrooms is not justified.
Option 5: None of the answers are correct. Since option 2 is correct, this statement is false.
In summary, the only statement supported by the data and Little’s Law is that the average time spent in the building is 120 minutes. The other options either miscompute λ, misstate L, make unsupported capacity claims, or claim all are incorrect despite the evidence pointing to option 2.

MGMT 101 LEC ONL: MANA... Weekly Quiz 7: Analysis of Queues

Suppose that 2000 students enter (and later leave) a classroom building over the 20 hours in which it is open. On average, there are 200 students in the building. Assuming the classroom building is operating in steady-state, which of the following statements are true?

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