Engineering Homework Help

Please help with this three questions. I need answers in 12 hours. Thank you~

Please check the attachment for the notes.

Q1

A network operator would like to design an optical network to connect different cities. The network physical topology is specified in terms of a graph, G(N,E), that has N nodes and E edges where each edge has a capacity, ye, to be determined. The network is to be designed to serve D demands where hd is the volume of demand d. Develop a mixed integer linear programming formulation to determine the capacity of each edge such that the cost of the provisioned network capacity is minimised. Clearly explain each step of the formulation.

Q2

The network operator in Q1 is interested in improving the reliability of its network. Redesign the mixed integer linear programming formulation in Q1 to ensure that the network links can provide enough capacity to route all demands under any possible link failure scenario resulting from a fiber cut. Clearly explain each step of the formulation.

Q3

After operating its network for a period of time,the network operator in Q1 became concerned about the network energy consumption. The network energy consumption can be reduced by putting unused network devices into sleep mode.Propose a routing restriction to the network operator to put more network devices into sleep mode.Redesign the mixed integer linear programming formulation in Q1to represent this routing restriction. Clearly explain each step of the formulation.