THE EPSILON-EQUILIBRIUM IN TRANSPORTATION NETWORKS

The principle of traffic equilibrium (Wardrop, 1952) demands that the trip makers have enough knowledge of transportation networks, which ne eds to be attained by accumulating experiences for a long time. Becaus e of the complexity of traffic situation in the networks, the route ch oice decisions for trip makers are, however, not always optimal object ively. As a consequence, it is impossible to strictly attain Wardrop e quilibrium. In this paper, a new concept of equilibrium, epsilon-equil ibrium is proposed under the realistic assumption, i.e., the fuzzy roa d information and random route choices. epsilon-equilibrium in the net work is discussed by adopting fuzzy set theory, mixed stochaistic Game s and Brouwer fixed point theorem in topological space. The conclusion is that there is epsilon-equilibrium in the real transportant network and this epsilon-equilibrium has some deviations from the strict Ward rop equilibrium. The notion of epsilon-equilibrium extends the traditi onal notion of network equilibrium. It shows that traffic flow in the network converges to a region rather than to the points.