Question

Academic advisor Mandy Ng helps students improve their personal statements for applying to top universities. One student at a time is allowed in her office and Mandy takes precisely 25 minutes to evaluate each student's preliminary statement. On average 2.2 students per hour go to her office and they spend on average 160 minutes to get a final version (time waiting in queue plus time in Mandy's office having her evaluate their statements). On average, how many students are waiting outside of Mandy's office

Answer 1

4.95 students

Explanation:

Given that :

Arrival Rate = λ = 2.2 students per hour

Service Time = 25 minutes per student = 25 / 60 = 0.4167 hours

Time in system = W = 160 minutes

W in hours = 160/60 = 2.67 hours

According to Little's law,

Average queue length, L = λ*Wq ;

Wq = Waiting time in queue

Waiting time in queue = Wq = Time in System - Service time = 2.67 - 0.4167 = 2.2533 hours

Hence, average queue length :

2.2 * 2.2533 = 4.95726

On average, 4.95 students are waiting outside Mandy's office