Modeling Physical and Environmental Side Constraints in Traffic Equilibrium Problem Anthony Chen, 1 Zhong Zhou, 2 and Seungkyu Ryu 1 1 Department of Civil and Environmental Engineering, Utah State University, Logan, Utah, USA 2 Citilabs, Tallahassee, Florida, USA ABSTRACT The traffic equilibrium problem plays an important role in urban transportation planning and management. It predicts vehicular flows on the transportation net- work by assigning travel demands given in terms of an origin-destination trip table to routes in a network according to some behavioral route choice rules. In this paper, we enhance the realism of the traffic equilibrium problem by explicit mod- eling various physical and environment restrictions as side constraints. These side constraints are a useful means for describing queuing and congestion effects, restraining traffic flows to limit the amount of emissions, and modeling different traffic control policies. A generalized side-constrained traffic equilibrium (GSCTE) model is presented and some characterizations of the equilibrium solutions are discussed. The model is formulated as a variational inequality problem and solved by a predictor-corrector decomposition algorithm. Two numerical experiments are conducted to demonstrate some properties of the GSCTE model and the conver- gence properties of the decomposition algorithm. Key Words: decomposition algorithm, emission restriction, physical capacity, side constraints, traffic equilibrium, variational inequality INTRODUCTION According to the well-known Wardrop’s first principle (Wardrop 1952), the traf- fic equilibrium problem is to find a traffic flow pattern such that for each origin-destination (O–D) pair, all used routes have equal and minimal travel cost, while unused ones have equal or higher travel costs. The traditional traffic Received 25 June 2009; accepted 21 April 2010. Address correspondence to Anthony Chen, Department of Civil and Environmental Engin- eering, Utah State University, Logan, UT 84322-4110, USA. E-mail: anthony.chen@usu.edu International Journal of Sustainable Transportation, 5:172–197, 2011 Copyright # Taylor & Francis Group, LLC ISSN: 1556-8318 print=1556-8334 online DOI: 10.1080/15568318.2010.488277 172 Downloaded By: [Chen, Anthony] At: 16:59 7 February 2011