Joaquin De Cea

Transit Assignment for Congested Public Transport Systems: An Equilibrium Model

We propose a new formulation for the assignment problem over congested transit networks. The congestion effects due to insufficient capacity of system elements transit lines are considered to be concentrated at transit stops. Waiting times on access links are therefore dependent on passenger flows. A special formulation of the transit network is used in order to model correctly the congestion effects. Finally, algorithms for solution are analyzed.

Solving network equilibrium problems on multimodal urban transportation networks with multiple user classes

A modelling approach for solving quite general network equilibrium problems (with fixed trip productions and attractions) intrinsic to the urban transport planning process is presented. The framework can consider a variety of demand models and route choice behaviours within the same implementation, including multiple user classes and combined travel modes that interact on the same physical network. The demand choices are assumed to have a hierarchical structure. When trip distribution is variable, a doubly constrained entropy‐maximizing model is considered at the first level of choice and a hierarchical logit model is used for the remaining demand choices (time of departure, travel mode, transfer point for combined modes, etc.). If trip distribution is considered to be exogenous, the demand choices are modelled as a hierarchical logit. One of the main features of the model is that it considers the effects of congestion on the road network as well as congestion and capacity constraints effects in each public transport service network. The problem is formulated mathematically as a variational inequality, with asymmetric cost functions, and solved following the diagonalization procedure. Each iteration of the aforementioned procedure solves an optimization problem using the Evans algorithm. Sufficient conditions for the existence and uniqueness of the solution to the diagonalized problem are obtained. The main results of a simple example (solved with an academic version of the proposed algorithm) are presented to show the consistency of the equilibrium flows and levels of services obtained using the model. Finally, a real scale implementation of the model is briefly described to show the feasibility of its application.

Combined Models with Hierarchical Demand Choices: A Multi-Objective Entropy Optimization Approach

Abstract This article proposes a multi‐objective optimization approach to the formulation of a number of equilibrium problems that typically arise in the transportation planning process. These fall into two classes: combined demand and network equilibrium problems, the latter here called performance‐demand equilibrium problems. The demand formulations are based on entropy maximization while the network equilibrium designs are modelled on Wardrop’s first principle. Both are fully compatible with models based on random utility maximization (multinomial and hierarchical logit). Given the entropy‐maximization aspect of the demand models and the use of symmetric cost functions in the networks, the multi‐objective formulations yield classical single‐objective convex optimization programs. In the past, many such problems have not been obtained deductively, their derivation being based rather on previous knowledge and the modeller’s intuition. Of particular interest, therefore, is the simple deductive method presented here for formulating new problems, one that can accommodate new choices such as departure time and transfer point for combined modes. This novel approach also facilitates a better interpretation of the model parameters. In addition, we suggest a calibration procedure that permits consistent estimation of the proposed model’s parameters.