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.
The cafeteria is considering installing an automatic vendor that dispenses a cup of coffee at a constant time of 15 seconds. If customers still arrive at the same rate, answer the following questions:
How many customers would be in line now?
How many customers would you expect to see at the coffee urn (waiting and being served)?
How long would you expect to wait in line to get a cup of coffee?
How long would you expect it to take to get a cup of coffee total?