Eco-system optimal time-dependent flow assignment in a congested network

Abstract

This research addresses the eco-system optimal dynamic traffic assignment (ESODTA) problem which aims to find system optimal eco-routing or green routing flows that minimize total vehicular emission in a congested network. We propose a generic agent-based ESODTA model and a simplified queueing model (SQM) that is able to clearly distinguish vehicles' speed in free-flow and congested conditions for multi-scale emission analysis, and facilitates analyzing the relationship between link emission and delay. Based on the SQM, an expanded space-time network is constructed to formulate the ESODTA with constant bottleneck discharge capacities. The resulting integer linear model of the ESODTA is solved by a Lagrangian relaxation-based algorithm. For the simulation-based ESODTA, we present the column-generation-based heuristic, which requires link and path marginal emissions in the embedded timedependent least-cost path algorithm and the gradient-projection-based descent direction method. We derive a formula of marginal emission which encompasses the marginal travel time as a special case, and develop an algorithm for evaluating path marginal emissions in a congested network. Numerical experiments are conducted to demonstrate that the proposed algorithm is able to effectively obtain coordinated route flows that minimize the system-wide vehicular emission for large-scale networks. Travel time-based and eco-cost-based traffic assignment modelsFollowing the pioneering work of Merchant and Nemhauser (1978), various approaches have been proposed in the past decades to formulate and solve the travel time-based system optimal dynamic traffic assignment problem in ideal or general networks, such as mathematical programming (e.Shen and Zhang, 2009) and variational inequality (Shen et al., 2007a).As extensions of the user equilibrium and system optimum principles, eco-cost-based, or emission-based, assignment principles have been adopted in a number of STA models. For instance, Benedek and Rilett (1998) presented the emission optimal principle which describes that travellers choose paths so as to minimize the total network emission, rather than total travel time. They also discussed an extension of the user equilibrium principle, the environmental equity principle, in which travellers are assigned in such a way that the amounts of emission on all selected routes are the same. Another line of research was to employ the multi-objective or multi-criterion approaches in traffic assignment models. For example, a multi-criterion system optimum model was proposed by Tzeng and Chen (1993), where the system optimum objective is the sum of total travel time for road users and air pollution for nonusers. Nagurney et al. (1998Nagurney et al. ( , 2002 presented a multi-class user equilibrium traffic assignment model in which each class of users was assumed to select a route with the least weighted sum of travel time, travel cost and emissions. Zhang et al. (2010) developed a system optimal STA model with the objective being the weighted sum of tr...

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