Link-based system optimum dynamic traffic assignment problems with environmental objectives

Abstract

a b s t r a c tMaintaining air-quality standards has been a priority for transportation planners and policy makers worldwide. However, most existing system optimum dynamic traffic assignment (SO-DTA) models do not accommodate environmental objectives. In this paper, we use the link transmission model (LTM) to develop SO-DTA models that minimize total system emissions (TSE) in single destination networks. We use step functions to approximate cumulative flow curves for individual links, and to decompose link inflow into sub-flows according to time intervals at which they leave the link. The decomposed link inflows are used to estimate link emissions. Dynamic network constraints, non-vehicle holding constraints and link inflow decomposition constraints are considered, and SO-DTA problems with environmental objectives are formulated as mixed integer linear programming (MILP) problems. Any average speed based emission functions can be used for our models. Finally, numerical examples are provided to demonstrate the performance of the proposed models. IntroductionDynamic traffic assignment (DTA) has long been recognized as a key component of network planning and transport policy evaluation, in addition to real-time traffic operation and management (Szeto and Lo, 2006). System-optimum DTA (SO-DTA), a special case of DTA based on a dynamic extension of Wardrop's (1952) second principle, is used to predict a time-dependent traffic state with optimal network performance, and to provide a benchmark for controlling and managing dynamic traffic networks. For example, SO-DTA models are used in road congestion pricing (e.on whether the modeling period is discretized into many time steps. Both categories of model have advantages and disadvantages. Continuous-time models can provide analytical insights (such as the closed form externality analysis), but cannot be efficiently solved due to their complex structure (Nie, 2011). Discrete-time models are usually formulated as mathematical programming problems, such as linear programming (LP) problems (e.g., Ziliaskopoulos, 2000) and mixed integer linear programming (MILP) problems http://dx.Please cite this article in press as: Long, J., et al. Link-based system optimum dynamic traffic assignment problems with environmental objectives. Transport. Res. Part D (2016), http://dx.doi.org/10.1016/j.trd.2016.06.003 (e.g., Lin and Wang, 2004;Pavlis and Recker, 2009), and can thus be more easily solved than continuous-time SO-DTA models. However, this category of models also compromise computational tractability in large-scale network applications due to the presence of numerous decision variables and constraints.There are three major types of objectives in existing SO-DTA models: minimizing total system travel time (TSTT) (e.minimizing both TSTT and TSE for a whole network in an integrated manner (e.g., Aziz and Ukkusuri, 2012;Ma et al., 2015). Most existing SO-DTA models accommodate only network mobility, and are used to meet the first of the above objectives: to minimize the TSTT spent by t...

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