The Internet, Evolutionary Variational Inequalities, and the Time-Dependent Braess Paradox

In this paper, we develop an evolutionary variational inequality model of the Internet with multiple classes of traffic and demonstrate its utility through the formulation and solution of a time-dependent Braess paradox. The model can handle time-dependent changes in demand as a consequence of developing news stories, following, for example, natural disasters or catastrophes or major media events. The model can also capture the time-varying demand for Internet resources during a regular weekday with its more regular rhythm of work and breaks. In addition, the model includes time-varying capacities on the route flows due to, for example, government interventions or network-type failures.