Question: Consider the following queueing system. In this system, arrivals and departures are according to Poisson distribution with average arrival rate A, and departure rate

Consider the following queueing system. In this system, arrivals and departures are according to Poisson M A3 Queue 1 Queue 2 Queue 3 H H H3 (a) What is the probability that Queue 1, Queue 2, and Queue 3 have N-3,

Consider the following queueing system. In this system, arrivals and departures are according to Poisson distribution with average arrival rate A, and departure rate u, for Queue i, where i = 1,2,3. These three queues are independent from each other. Assume that the arrival rates are; A = 2, A2 = 4, A3 = 4 packets/second, and the departure rates are; 1 = 10, = 5, 3 = 5 packets/second. M A3 Queue 1 Queue 2 Queue 3 H H H3 (a) What is the probability that Queue 1, Queue 2, and Queue 3 have N-3, N2=2, and N3=10 packets, respectively? (b) Assume that the maximum number of packets that all queues can have is 100 packets. What is the probability that Queue 1, Queue 2, and Queue 3 have N-3, N2-2, and N3-10 packets, respectively?

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