Mixed travel behavior in networks with ATIS and upper bound of efficiency loss

In a transportation network supported by the advanced traveler information systems (ATIS) , the drivers equipped with ATIS are directed by a control center to select their routes so as to minimize the total network travel time, while the unequipped ones make the route choice decisions on the base of minimizing their individual travel times. In this paper, a variational inequality model is presented to formulate the mixed travel behavior associated with both system optimum and user equilibrium, and is derived a general formula for the upper bound of inefficiency loss of the mixed behavior. The upper bounds when all link travel cost functions are polynomial are examined against different ATIS market penetrations. Results show that the upper bound is related to the ATIS market penetration and the corresponding mixed equilibrium flow pattern.