A large clothing store offers a ‘no quibble' returns policy under which shoppers can return unwanted goods to the store and receive their money back. They have to take their unwanted goods to a returns desk where there is one server. Customers arrive at the desk according to a Poisson distribution with a mean of 24 per hour and service times at the desk are exponentially distributed with a mean of two minutes.
(a) What is the traffic intensity in the returns system?
(b) What is the probability that there are more than three customers queuing?
(c) What is the mean waiting time?
(d) What is the mean queue length?