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?"

There are different kinds of calculations as regards to time. Note that average service rate increases, the shape of the negative exponential distribution of service times often is known to be less gently curved as it moves ever closer to the graph start up point.

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

This calculated by:

λ refers to Avg arrival rate. This is denoted as

= 15 std/hr

μ refers to as Avg server rate. This is individual server capacity. It is denoted as

= 20 std/hr

Μ is known as number of servers/line or simply say identical capacities.

Therefore = λ/μ(μ- λ)

Input or fill up all numbers (values) into the equation above;

=15 / 20(20-15)

= 225/100

=2.25

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

See full options below

What is the average time spent waiting in line for each

student? What is the average number of students in the line?

a. 2.25 students

b. 5 students

c. 15 students

d. 20 students

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