Question

Students arrive at the Administrative Services Office at an average of one every 15 minutes, and their requests take on average 10 minutes to be processed. The service counter is staffed by only one clerk, Judy Gumshoes. Assume Poisson arrivals and exponential service times.

How much time, on average, does a student spend waiting in line?
Prepare for VUT calculation
a (avg. inter- arrival time) s (avg. service time) m (number of servers) u (avg. utilization) CV, (coef. of var.-arrival) CV, (coef. of var.- service)


Show VUT calculation and final answer to the question:

Answer 1

The average waiting time for a student in line is 3 minutes.

Step-by-step explanation:

The average waiting time for a student in line can be calculated using the formula VUT (average waiting time) = 1 / (m - u). In this case, the average inter-arrival time (s) is 15 minutes and the average service time (s) is 10 minutes. Since there is only one server (m = 1), the average utilization (u) can be calculated as u = s / s. The average utilization is 10 / 15 = 0.67.

Using the formula VUT = 1 / (m - u), we can calculate the average waiting time as VUT = 1 / (1 - 0.67) = 3 minutes.