In this paper we present a version of the (static) traffic equilibrium problem in which the cost incurred on each path is not simply the sum of the costs on the arcs that constitute that path. We motivate this nonadditive version of the problem by describing several situations in which the classic additivity assumption fails. We describe existence and uniqueness conditions for this problem and we also present convergence theory for a generic algorithm for solving nonadditive problems. INTRODUCTION Paraphrasing Wardrop [33], the (static) traffic equilibrium problem is to find a set of path flows that satisfy certain demand constraints and have the property that the costs on all used paths connecting an origin-destination pair are equal and less than or equal to the cost on all unused paths connecting that pair. In order to prove existence/uniqueness results and develop convergent algorithms, this problem has been formulated as a nonlinear program (NLP) [4], a nonlinear complementarity...

In this paper we present a new algorithm for the approximate solution of the logitbased stochastic user equilibrium problem. The main advantage of this algorithm is that it provides route flows explicitly, of particular interest in the evaluation of route guidance and information systems; in previously proposed methods for the stochastic user equilibrium problem, only link flows are provided. The proposed algorithm alternates between two main phases. In the subproblem phase, profitable routes are generated. In a restricted master problem, a descent method is used to solve the restriction to the original problem to the subset of the total set of routes generated so far. We present and evaluate alternative strategies for generating routes algorithmically, and discuss the possibility of utilizing such strategies for reducing the inherent problem of overlapping route flows in logit-based traffic models. 1 Introduction The traffic assignment problem is fundamental in transportation analysis...

........................................................ xi CHAPTERS 1 INTRODUCTION ...............................................1 1.1 Background ..............................................1 1.2 Problem Statement .........................................5 1.3 Goal and Objectives ........................................9 1.4 Study Area .............................................. 10 1.5 Organization ............................................. 11 2 BACKGROUND AND STATISTICAL TOOLS ....................... 12 2.1 Discrete Choice Models ....................................... 12 2.1.1 Introduction ....................................... 12 2.1.2 Gumbel Distribution ................................. 13 2.1.2.1 Derivation of multinomial logit ................... 16 2.1.2.2 Derivation of binary asymmetrical Gumbel distribution ............................ 19 2.1.2.3 Derivation of multi-asymmetrical Gumbel distribution ............................ 20 2.1.2.4 Method of probability-we...