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. How many students, on the average, will be waiting in line at any one time?
A) 0.9 students
B) 1.5 students
C) 3 students
D) 4 students
E) 36 students

Question

Quizplus · Accepted Answer

The average number of students waiting in line can be calculated using the formula $L_q = \frac{\lambda^2}{\mu(\mu - \lambda)}$, where $\lambda$ is the arrival rate and $\mu$ is the service rate. Plugging in $\lambda = 12$ students per hour and $\mu = 20$ students per hour, we get $L_q = \frac{12^2}{20(20 - 12)} = \frac{144}{160} = 0.9$ students.

Students Arrive Randomly at the Help Desk of the Computer