Modeling sustainable traffic assignment policies with emission functions and travel time reliability

Urban transport systems play a crucial role in maintaining sustainability. In this study, we focus on two types of sustainability measures; the gas emission and travel time reliability. We propose several bilevel optimization models that incorporate these sustainability measures. The upper level of the problem represents the decisions of transportation managers that aim at making the transport systems sustainable, whereas the lower level problem represents the decisions of network users that are assumed to choose their routes to minimize their total travel cost. We determine the emission functions in terms of the traffic flow to estimate the accumulated emission amounts in case of congestion. The proposed emission functions are incorporated into the bilevel programming models that consider several policies, namely, the toll pricing and capacity enhancement. In addition to the gas emission, the travel time reliability is considered as the second sustainability criterion. In transportation networks, reliability reflects the ability of the system to respond to the random variations in system variables. We focus on the travel time reliability and quantify it using the conditional value at risk (CVaR) as a risk measure on the alternate functions of the random travel times. Basically, CVaR is used to control the possible large realizations of random travel times. We model the random network parameters by using a set of scenarios and we propose alternate risk-averse stochastic bilevel optimization models under the toll pricing policy. We conduct an extensive computational study with the proposed models on testing networks by using GAMS modeling language.