A New Vision of Optimal Equilibrium in Traffic Network: Maximum of Satisfaction Equilibria

We consider the Braess Paradox, a well-known phenomenon: adding a new route to a traffic network may not improve efficiency of the whole network; to the contrary, it increases total travel time. The reason of that paradox happens is that under User Equilibrium assignment (UE), commuters route their traffic absolutely selfishly, which meanwhile contributes to an increase in travel time for other network users. So traffic planners who want to implement an optimal assignment of global network to that sum of total latency is minimized, which is System Optimization (SO). The objective of SO is to maximize the benefit of whole network, but it is absence of attention to consider loss of part of road users in the optimal situation, which leads to the difficulty of reaching SO. Therefore, this paper regards first the loss of road users as opportunity cost to explore a new optimal equilibrium, named Maximum of Satisfaction Equilibria (MSE). We build a traffic network equilibrium model involved in opportunity cost and loss aversion and use a simple two-node network with a linear function of its congestion. The conclusion shows that 1) the sum of total travel time is similar to 4/5 in MSE in best situation, which is more than the quantity in SO (3/4) and less than that in UE (1); 2) a new way to explain why SO is hard to reach; and 3) it is not really good to provide the most accurate information about the actual state of the system to traffic users.