Optimum principle for a vehicular traffic network: Minimum probability of congestion

We discuss an optimum principle for a vehicular traffic network with road bottlenecks introduced by the author recently [B.S. Kerner, J. Phys. A: Math. Theor. 44, 092001 (2011)]. This network breakdown minimization (BM) principle states that the network optimum is reached, when link flow rates are assigned in the network in such a way that the probability for spontaneous occurrence of traffic breakdown at one of the network bottlenecks during a given observation time reaches the minimum possible value. Based on numerical simulations with a stochastic three-phase traffic flow model, we show that in comparison to the well-known Wardrop's principles the application of the BM principle permits considerably greater network inflow rates at which no traffic breakdown occurs and, therefore, free flow remains in the whole network.