Which of the following M/M/1 queues will have an equilibrium 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)