A ‘money shop' tax adviser operates a ‘no appointments necessary' system whereby customers arrive at the shop when they wish and wait for a consultation. The adviser works alone and the times she takes to serve customers vary exponentially with amean of 15 minutes. Customer arrivals are distributed according to the Poisson distribution with a mean of 2.5 per hour.
(a) Work out the traffic intensity of the system.
(b) There are four chairs that customers can sit on while waiting for a consultation. Find the probability that one or more customers will have to stand while they are waiting.
(c) Calculate the mean length of the queue.
(d) Determine the mean waiting time in the queue.