Consider a router containing four networked queues, each represented by an M/M/1 model, as shown below. Any percentage number shown on each branch gives the share of the branch from the traffic coming to its branching point. The arrival rate to the system is = 30 packets per sec. The service rates in the nodes are 1 = 50, 2 = 50, 3 = 20, and 4 = 30 packets per sec, respectively. a) Find the arrival rate to each of the four queues. b) Find the average number of packets in each queue. c) Find the average delay for a packet from its arrival to the system until it exits the system.

4 60% 40% 4 60% 40%