2. In the small network depicted below, two external Poisson sources generate packets with rates 4 and 3 packets per second, respectively. All sources generate packets with exponentially distributed lengths with the same mean. All nodes have infinite queue capacity and can process 8 packets per second each. A packet leaving node 1 joins node 2 with a probability of 0.6 and leaves the system with probability 0.4. Similarly, a packet leaving node 2 joins node 1 with probability 0.5 and leaves the system with probability 0.5. 21=4 P1d=0.4 H1=8 P21=0.5 H,=8 P12=0.6 2 P2d=0.5 1,=3 (a) Calculate steady state probability P(n1, n2) that queues 1 and 2 have n1 and n2 packets, respectively. (10pt) (b) What is the average packet delay in the system? (8pt) (c) Assume that a packet enters the system at queue 1. How many transmissions (on the average) does it undergo before it leaves the system? Express your answer in terms of P12, Pid, P21, and p2d. (7pt)