On average 6 customers per hour arrive at a single-server facility centre according to a Poisson distribution. The average service time for each customer is 5 minutes and the customer population is large. (a) On the average, how many customers per hour will be served by the centre if the service distribution is Poisson as well. (b) Determine the mean queue length and the expected waiting time in the queue when the service distribution is Erlang with k 4. (c) Determine the mean queue length and the expected waiting time in the queue when the service distribution is constant. (d) If in an unexpected situation the arrival rate is increased to 12 customers per hour, given that the service time has a general distribution, what would be the minimum number of service providers required in the centre? (e) If there were c = 5 servers working in the centre according to an exponential service distribution, what would be the fraction of time that a particular server is idle? (You only need to define the probability in terms of Po, not the exact value.)