Breakdown minimization principle versus Wardrop's equilibria for dynamic traffic assignment and control in traffic and transportation networks: A critical mini-review

We review physical results of applications of the breakdown minimization (BM) principle versus applications of the classical Wardrop's equilibria (Wardrop's user equilibrium (UE) and system optimum (SO)) for dynamic traffic assignment and control in traffic and transportation networks. It is shown that depending on the total network inflow rate there are two different applications of the BM principle: (i) The network throughput maximization approach that maximizes the network throughput ensuring free flow conditions in the network. (ii) The minimization of the network breakdown probability at relatively large network inflow rates. Probabilistic features of the application of the BM principle are studied. We have found that when the application of the BM principle cannot prevent traffic breakdown in the network, nevertheless, a combination of the application of the BM principle with dynamic control of traffic breakdown at network bottlenecks can lead to the dissolution of traffic congestion. We show that applications of the classical Wardrop's equilibria for dynamic traffic assignment deteriorate basically the traffic system in networks.