2. (The M/M/2 Queue, 15 marks) Suppose that customers arrive at a service station with 2-servers in accordance with a Poisson process having rate A. The service time for each server with respect to each customer is independently exponentially distributed with mean 1/ (i.e., the service time is i.i.d. exponential with parameter ). Then, this M/M/2 queue forms a birth and death process. Show that this birth and death process has the birth rates { , n 0} and death rates {n, n > 0} respectively as An = A, n 0 nu, n = 1,2 Pn= 2, n > 2. (Recall that A is the transfer rate from state n to n + 1, and n is the transfer rate from state n + 1 to state n; state n at time t means that there are n customers in the queue system at time t.)