Question

During finals week, students arrive randomly at the help desk of the computer lab. There is only one technician due to budget cuts, and the time required to provide service varies from student to student. The average arrival rate is 15 students per hour, and the average service rate is 20 students per hour. Arrival rates have been found to follow the Poisson distribution, and the service times follow the exponential distribution. What is the average time spent waiting in line for each student?"

Answer 1

Answer:

The average time spent waiting in line for each student is 2.25 students.

Explanation:

Use Lq with a single server formula.

λ = Avg arrival rate  = 15 std/hr

μ= Avg server rate (individual server capacity) = 20 std/hr

Μ = # of servers/line (identical capacities)

= λ$^{2}$/μ(μ- λ)

=15$^{2}$ / 20(20-15)

= 225/100

=2.25 students.