Assignment:
A telecommunication network is a set of nodes and directed arcs on which data packets flow. We assume that the flow between each pair of nodes is known and constant over time; please note that the matrix of such flows need not be symmetric, and that packets labeled with a source/destination pair (s, d) are a commodity on their own. Nodes are both source and destination of data packets to and from other nodes, respectively; they can be also used as intermediate nodes for routing, as some pairs of nodes may not be connected directly. Both arcs and nodes are subject to a capacity constraint in terms of packets that they can transport and route over a time frame. Prom an operational point of view, we would like to route all of the traffic, in such a way that no network element (node or arc) is congested. For the sake of simplicity, let us assume that a network element is congested when its traffic load exceeds 90% of its nominal capacity (in practice, congestion is a nonlinear phenomenon). We measure network congestion by the number of network elements whose traffic load exceeds this limit.
• Build a model to minimize network congestion, which has an impact on quality of service.
• Extend the model to include capacity expansion opportunities. For each network element, we may expand capacity either by 25% or by 70%; each expansion level is associated with a fixed cost. Build a MILP model to find a tradeoff between quality of service and network cost.
Provide complete and step by step solution for the question and show calculations and use formulas.