Tunnel effects on road efficiency and travel time explored by a three lane traffic model

Abstract

To ascertain tunnel effects upon road efficiency and travel time of ring road traffic, a mathematical model accounting of three lanes is investigated. The model uses traffic pressure and sound speed in algebraic form, and a single traffic speed to describe the vehicular motions on the three lane instantaneously to simplify mathematical modeling of traffic flow. The ring road with a total length 100km has a tunnel with a length of 8km and a speed limit of 80km/h. The free flow speeds on lane I, II and III are assumed to be 110, 100, and 90km/h. Using the model, a code is elaborated for numerical simulations on the three lane ring road. For validating the model the tunnel length is reset as 1.5km, so that the conformity between the predicted time averaged speed and the recorded speed near the Kobotoke tunnel in Japan can be seen clearly. It is found that the threshold of traffic shock formation near the tunnel can be determined by observing spatiotemporal pattern of traffic flow. When and where traffic shock appears relies on the free flow speed on lane III. Road efficiency and travel time for the ring road traffic are predicted and discussed. The numerical findings in this paper deepen the understanding of tunnel effects.