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

We introduce an optimum principle for a vehicular traffic network with road bottlenecks. 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 in at least 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.