A b d B Figure Q3: Network to allow message passing between A and B Q3....

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A b d B Figure Q3: Network to allow message passing between A and B Q3. The message passing network illustrated in Figure Q3 consists of five intermediate nodes, and communication links between those nodes. A message can be successfully passed between A and B if there is a path between them along which all intermediate nodes are functional. To meet service requirements, the network should be designed such that the probability of a message being delivered from A to B exceeds 95%. (a) i. Use set notation to describe the vertex set and the edge set of the graph illustrated in Figure Q3. ii. Explain what is meant by the phrase "degree of a vertex in a graph". Support your answer by identifying the degree of the vertex labelled a in Figure Q3. (b) If the probability that any intermediate node has failed is 0.05, and the inter- mediate nodes fail independently of each other, what is the probability that the message gets delivered? Does this meet the specified service requirements? (c) Intermediate node failure is dependent on ambient temperature, where the prob- ability of failure is 0.05 if temperatures are below 25 degrees Celsius, and 0.25 if temperatures are at or above 25 degrees Celsius. What is the maximum proba- bility p of temperature being above 25 degrees Celsius that will allow us to meet the service requirement? Explain your reasoning. 4 marks 2 marks 6 marks 8 marks A b d B Figure Q3: Network to allow message passing between A and B Q3. The message passing network illustrated in Figure Q3 consists of five intermediate nodes, and communication links between those nodes. A message can be successfully passed between A and B if there is a path between them along which all intermediate nodes are functional. To meet service requirements, the network should be designed such that the probability of a message being delivered from A to B exceeds 95%. (a) i. Use set notation to describe the vertex set and the edge set of the graph illustrated in Figure Q3. ii. Explain what is meant by the phrase "degree of a vertex in a graph". Support your answer by identifying the degree of the vertex labelled a in Figure Q3. (b) If the probability that any intermediate node has failed is 0.05, and the inter- mediate nodes fail independently of each other, what is the probability that the message gets delivered? Does this meet the specified service requirements? (c) Intermediate node failure is dependent on ambient temperature, where the prob- ability of failure is 0.05 if temperatures are below 25 degrees Celsius, and 0.25 if temperatures are at or above 25 degrees Celsius. What is the maximum proba- bility p of temperature being above 25 degrees Celsius that will allow us to meet the service requirement? Explain your reasoning. 4 marks 2 marks 6 marks 8 marks