An application of combined model for Tehran metropolitan area incorporating captive travel behavior

American Journal of Applied Sciences, Dec, 2008 by Shahriar A. Zargari, Morteza Araghi, Kouros Mohammadian

INTRODUCTION

The four-steps model has been widely used in the metropolitan transportation planning, consisting of: (1) trip generation-to predict the total number of trips per time period (hour or day) that is originated at or destined for each location; (2) trip distribution-to predict the number of trips between pairs of Origins and Destinations (OD); (3) mode choice-to model probability of using private cars, trains, buses, or other modes of travel and (4) traffic assignment-to analyze route choices, which typically assumes user-optimal choices in which all routes used by travelers have equal travel costs and no unused route has a lower cost for each OD pair.

However, the four step modeling framework has several inherent weaknesses. Among others, these include having a trip-based sequential structure with limited behavioral responses that often ignores time of day dimension. Additionally, trip generation step is usually unresponsive to congestion and pricing and consequently unresponsive to most demand management measures. Furthermore, one important shortcoming of the traditional four step approach is the inconsistency among different steps. For example, the OD travel time output from a traffic assignment step may not be the same as the travel time input to the mode choice model. Another problem is the lack of behavioral theory behind the traditional model. (1) These deficiencies have motivated new modeling approaches including emerging activity-based and micro simulation modeling systems that are gaining momentum and are hoped to be moved to practice in the mid- to long-term future. Alternatively, as a short-term practical approach, some researchers have attempted to model the four steps of the framework simultaneously. Modelers then began to ask how to combine these steps into a more consistent method. Because of this irony of history, this literature is widely known today as combined models (2).

The first of such models appeared in the elastic demand traffic assignment problem model of Beckmann et al (3) Evans (1973) extended the formulation to include trip distribution, assuming fixed trip generation and an entropy model for trip distribution (4). Evans proposed a very efficient algorithm in order to solve her combined trip distribution and network assignment model. This technique is related to the Frank-Wolfe algorithm but only constructs a partial linearization of the objective function in finding a search direction.

In 1977 and in order to include mode split, further model was developed by Florian and Nguyen (5). Their model combined trip distribution, mode split (among automobile and bus) and User-Equilibrium (UE) assignment models. They formulated a modified Frank-Wolfe algorithm in order to solve their model. In this model the direction-finding step is a Hitchcock transportation problem that is a linear programming problem distributing flows using fix link costs (6).

Afterwards and Safwat and Magnanti (1988) developed an overall transportation system equilibrium model (STEM), which encompasses all four travel demand components (7). Recently, several attempts have been made to apply combined models to real urban areas (8-10).

The aim of this research is to propose a Combined Trip Distribution and Assignment Model (CTDAM) and apply it to the Tehran area as a metropolis.

Consequently, we consider CTDAM for the simultaneous prediction of trip distribution and trip assignment. The trip distribution was formulated as a standard doubly constrained gravity model. Trip assignment was based on the Wardrop's user optimized principle. The proposed idea of combined model would be reformulated as an Equivalent Minimization Problem (EMP) so that the equilibrium conditions on the network and travel demand functions can be derived as the Karush-Kuhn-Tucker (KKT) conditions of the EMP. When applying the Evans algorithm to the equilibrium problem, the model is expected to be usable in a realistic application and within a reasonable time period for Tehran Metropolitan Area. By the way, comparison study with conventional sequential procedure to assess proposed model is mentioned. Finally we conclude the paper and present some future lines.

MATERIALS AND METHODS

The major components of the proposed combined model include trip distribution and trip assignment. To expound explicitly the basic theories and assumptions that underline the proposed combined model, first each of model components are described separately and then all the components are combined into a single formulation.

Trip distribution: In this study, the trip distribution is concerned with the estimation of the number of trips per unit of time (e.g., morning peak hour) from each origin zone (e.g., place of residence) to each destination zone (e.g., place of work or education) into which an urban area is partitioned. The most commonly used form of trip distribution model is the gravity model. The main purpose of trip distribution modeling is to distribute the total number of trips originating in each zone among all possible destination zones which are available. A number of specifications for the impedance or cost function are possible, but the most common ones used in transport analysis are exponential function (11). The general form of the distribution model is given by: