Optimum Principle For Calculating The Minimum Probability Of Congestion

Abstract

This paper discusses an optimum principle for traffic and transportation networks with road bottlenecks introduced by the author recently [B.S. Kerner, J. Phys. A: Math. Theor. 44, 092001 (2011)]. This network breakdown minimisation (BM) principle states that the network optimum is reached, when dynamic traffic optimisation is performed 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; this is equivalent to the maximization of the probability that traffic breakdown occurs at none of the network bottlenecks. 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.