8. Two streams of customers arrive to a system each according to a Poisson process. Each stream is independent of the other and both steams have the same parameter 2. Assume that the service time for each customer is independent and identically distributed with an exponential distribution with parameter u. 8.1 Consider system A in which we treat the system as two identical M/M/1 queues, each operating independently. If we denote the average number of customers in one of the MM/1 sub-systems as Ni, and N, as the average number in the other M/M/1 sub-system, then NA = Ni + N. Find 14. 8.2 Consider system B in which the two streams of customers are merged together into a single MM/1 system but the rate of the server is increased so that the server is now able to reduce the service time for each customer to an 1.1.d. exponential random variable with rate 2u. Find the average number of customers in system B, NB. 8.3 For what values of , and u is system A stable? Repeat for system B. 8.4 Show that TB