Suppose Ethernet physical addresses are chosen at random (using true random bits). (a) What is the probability that on a 1024-host network, two addresses will be the same? (b) What is the probability that the above event will occur on one or more of 220 networks? (c) What is the probability that, of the 230 hosts in all the networks of (b), some pair has the same address? Hint: The calculation for (a) and (c) is a variant of that used in solving the so-called Birthday Problem: Given N people, what is the probability that two of their birthdays (addresses) will be the same? The second person has probability 1-3 of having a 365 different birthday from the first, the third has probability 1 of having a different birthday from the first two, and so on. The probability that all birthdays are different is thus 2 N (1-365) × (1-365) ×---×(1-965¹) (₁ which for smallish N is about 1 - 1+2+...+(N − 1) 365 - 2 365

Assume that an end-to-end communications system is made up of three networks with date rate in Mbps ρ1, ρ2, and ρ3, respectively. Ignoring the other delay components, what is the total end-to-end delay to transmit a packet size of λ?

You are employed as a network engineer and have been asked to analyze a communication network to determine the current data rates and ensure that the links aren’t at risk of “reaching capacity.” In the following figure of the network, the sender is transmitting data at a total rate of 100+50 = 150 megabits per second (Mbps). The data is transmitted from the sender to the receiver over a network of five different routers. These routers are labeled A, B, C, D, and E. The connections and data rates between the routers are labeled as , , , , and .   Directions   In this project, you will analyze the communication network and solve for the unknown data rates using a variety of techniques. The system can be modeled mathematically as a system of linear equations by writing an equation for each node/router in the network. Each of these equations can be written by noting that the sum of inputs must equal the sum of outputs.   To complete the project, work on the problems described below. As you…