Question: Consider the optimal routing problem discussed in Lecture 3 and shown in the figure below. We have a system with two M/M/1 queues. The total

Consider the optimal routing problem discussed in Lecture 3 and shown in the figure below. We have a system with two M/M/1 queues. The total arrival rate to the system is jobs/sec and each job is routed to server 1 with probability p and routed to server 2 with probability 1 p. Assuming that 1 = 2 jobs/sec and 2 = 1 jobs/sec, we have shown in the lectures that mean response time (for any job) is given by E[T] = p 2 p 1 p 1 (1 p) (1) For any (0, 1), find the routing probability p that minimizes the mean response time E[T] given in (1) numerically or analytically, and then plot the optimal p value as a function of . What is the behavior of the optimal p value as approaches 1 and give an intuitive explanation of the results you observe

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