# Waiting line analysis

Student 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, who works eights hours per day. Assume Poisson arrivals and exponential service times.

A. What percentage of time is Judy idle?

B. How much time, on average, does a student spend waiting in line?

C. How long is the (waiting) line on average?

D. What is the probability that an arriving student (just before entering the Administrative Services Office) will find at least one other student waiting in line?

A cafeteria serving line has a coffee urn from which customers serve themselves. Arrivals at the urn follow a Poisson distribution at the rate of three per minute. In serving themselves, customers take about 15 seconds, exponentially distributed.

A. How many customers would you expect to see on the average at the coffee urn?

B. How long would you expect it to take to get a cup of coffee?

C. What percentage of time is the urn being used?

D. What is the probability that three or more people are in the cafeteria?

E. If the cafeteria installs an automatic vendor that dispenses a cup of coffee at a constant time of 15 seconds, how does this change your answer to A and B?

https://brainmass.com/math/complex-analysis/waiting-line-analysis-327474

#### Solution Summary

Waiting line analysis is modeled.