Question 3 (8 marks) At a small airport, arriving passengers arrive as a Poisson process of rate 1 per minute and each such passenger is assigned uniformly at random (independent of the length of the queues) to one of & servers (that each serve the customers in their queue in the order in which they arrived). Service times at each queue are Exponential random variables with mean 2.5 minutes (independent of everything else). Let N." denote the number of customers in queue i = 1, . .. . k at time t, and M = )_l N."). (a) Is this system an M/M/k queue? Why or why not? (b) How large does & have to be to ensure that the queuing system is stable (i.e. that no matter how many customers are currently in the system, with probability 1 it will eventually become empty)