Computation of Dynamic Equilibria in Series-Parallel Networks

We consider dynamic equilibria for flows over time under the fluid queuing model. In this model, queues on links of a network take care flow propagation. Flow enters at single source and leaves sink. equilibrium, every infinitesimally small particle reaches sink as early possible given pattern rest flow. Although model has been examined many decades, progress relatively recent. particular, derivatives have characterized thin with resetting, which allows more structural results. Our two main results are based formulation resetting linear complementarity problem its analysis. present constructive proof existence if inflow rate is right-monotone. The complexity computing occurs subproblem in method, still open. settle it class two-terminal, series-parallel networks by giving recursive algorithm that solves all values simultaneously polynomial time.