Students arrive randomly at the help desk of the computer lab. There is only one service agent, and the time required for inquiry varies from student to student. Arrival rates have been found to follow the Poisson distribution, and the service times follow the negative exponential distribution. The average arrival rate is 12 students per hour, and the average service rate is 20 students per hour. A student has just entered the system. How long is she expected to stay in the system?
A) 0.125 minute
B) 0.9 minute
C) 1.5 minutes
D) 7.5 minutes
E) 0.075 hour

Question

Quizplus · Accepted Answer

The expected time a student stays in the system can be calculated using the formula for the average time in the system (T) in a M/M/1 queue: T = 1 / (μ - λ), where μ is the service rate and λ is the arrival rate. Given μ = 20 students per hour and λ = 12 students per hour, T = 1 / (20 - 12) = 1 / 8 hours. Converting to minutes, T = 7.5 minutes.

Students Arrive Randomly at the Help Desk of the Computer