6. The figure below shows a cascade of two M/M/1 nodes in which packets arrive at...

Transcribed Image Text:

6. The figure below shows a cascade of two M/M/1 nodes in which packets arrive at rate a packets per second. Service rates of both nodes are and 2 packets per second. At the output of node 1, packets exit with probability p = 0.1; otherwise, they are driven into node 2 and then fed back to node 1. System Under Study Probability of Exit = 0.10 (a) Find the average delay E[T] incurred on a packet, including the delay from circulations, as a function of p, a, #1, and 2. (b) Assume a = 10,000 and = 2=200,000 packets per second. Compute E[T;]. 7. Consider the following network with five flows: fo, f1, f2, f3, f4. Assume all three links each has unit capacity. Flow 3 Flow 4 Link 1 Link 2 Link 3 Epo Flow 0 Flow 1 Flow 2 (a) Use the progressive filling algorithm to find a max-min fair allocation. (b) Find a proportionally fair allocation. 6. The figure below shows a cascade of two M/M/1 nodes in which packets arrive at rate a packets per second. Service rates of both nodes are and 2 packets per second. At the output of node 1, packets exit with probability p = 0.1; otherwise, they are driven into node 2 and then fed back to node 1. System Under Study Probability of Exit = 0.10 (a) Find the average delay E[T] incurred on a packet, including the delay from circulations, as a function of p, a, #1, and 2. (b) Assume a = 10,000 and = 2=200,000 packets per second. Compute E[T;]. 7. Consider the following network with five flows: fo, f1, f2, f3, f4. Assume all three links each has unit capacity. Flow 3 Flow 4 Link 1 Link 2 Link 3 Epo Flow 0 Flow 1 Flow 2 (a) Use the progressive filling algorithm to find a max-min fair allocation. (b) Find a proportionally fair allocation.