a) Explain the following concepts and notation in queueing theory: i) M/M/1 queue ii) Little's Law iii) Utilisation of the server iv) Sojourn time of a customer (4 marks) b) Which of the following M/M/1 queues will have an equilibrium 3 and in each case give an explanation i) Server has a service rate of 2 customers/minute and the arrival rate is 3 customers/minute ii) Mean service time is 2 minutes and the mean interarrival time is 3 minutes iii) Server has service rate of 2 customers/minute and the mean interarrival time is 3 minutes (3 marks) c) In the cases from b) above which have an equilibrium i) Find the average server utilisation u ii) Determine the mean queue length (including the customer in service) iii) Use Little's law to find the mean sojourn time of a customer in the queue in minutes. (3 marks)