Network equilibrium models arise in applied contexts as varied as urban transportation, energy distribution, spatially separated economic markets, electrical networks, and water resource planning.In this paper, we propose and study an equilibrium model for one of these applications, namely for predicting traffic flow on a congested transportation network. The model is quite similar to those that arise in most contexts of network equilibria, though, and the methods that we use are applicable in these other settings as well.
Transit assignment is an important problem in the literature of transportation. Almost all competitive algorithms in this area are strategy based. For uncongested transit networks, the problem may be formulated into an optimization problem for which good solution algorithms exist. A variational inequality formulation of the problem with several solution methods is also presented in the literature for congested networks. This paper is devoted to solving a transit assignment problem based on complementarity formulation using path flows. The solution algorithm exploits the three concepts of decomposition, path generation, and linearization. The procedure has been applied on a large-scale realcase transit network under fixed travel times as well as flow-dependent dwell times. Computational experiments show rapid convergence of the algorithm. Moreover, for the limited experiments performed, the computational time for the flow-dependent problem is only about twice that of the case for the fixed travel times, without an appreciable excess memory requirement.
The transit assignment process applied as part of the development of the Tehran transportation model is described. The process includes development of various models for dwell time as a function of transit volume. Dwell time is the time a transit vehicle spends at a stop to allow passengers to alight and board. This method was implemented by using EMME/2 transportation planning software. The calculation of dwell time is necessary in modeling transit assignment because an accurate estimation of dwell time will lead to more precise transit assignment results. The area analyzed in the model comprises various transportation analysis zones in the city of Tehran. The model output was shown to be statistically significant. Calculations were found to be valid when compared with observed data.Population growth on one hand and physical limitations of resources and constraints on the other hand have hindered further expansion of road network systems of cities around the world. As a result, cities are focusing on improving their public transit systems. This requires more accurate modeling to better replicate the systems. An important element of any transit system is dwell time, the time a transit vehicle spends at a stop to allow passengers to alight and board. An accurate estimation of dwell time can improve the reliability of transit assignment. Also, by generating accurate results for dwell time, an analyst can improve the transit system by reducing delay. Estimation of dwell time, however, historically has received little attention in transit modeling. This study focuses on a new approach to simulate dwell time at stops. The method used is applicable in studies in which transit assignment is part of the modeling process and allows forecasting dwell time at stops in the transit network.The proposed method was developed and tested in Tehran, the capital of Iran, as part of a comprehensive transportation plan. Through this comprehensive study, the first multimodal transportation model was developed, along with many submodels. The major challenges were that most elements of the model had to be developed from scratch, coupled with the large scale of the study area and lack of suitable data. Also, the model had to be compatible with local needs. Tehran has a population of 7 million spanning an area of more than 600 km 2 . The model area includes peripheral cities as well (1). EMME/2 transportation planning computer software was used in developing the model. Both the automobile and transit network systems were coded into EMME/2. This model has been used to evaluate alternative transportation plans.The transit assignment model option in EMME/2 is based on the concept of optimal strategy. An optimal strategy (2) is composed of the transit routes that minimize the expected auxiliary transit, wait, and in-vehicle time for any transit trip from an origin to a destination. Auxiliary transit is referred to as a mode of transportation used for access or egress from the transit lines or for transfers from one line to another. Travel tim...
This article studies the problem of locating fuel stations to minimize the extra cost spent in refueling detours, which belongs to a class of discretionary service facility location problems. Unlike many studies of similar problems in the literature, the proposed model considers capacity constraints and compares different ways to incorporate them in the formulation. Note that ignoring the capacity constraint results in nonoptimal and unrealistic solutions. The proposed models are solved using both an off‐the‐shelf solver (CPLEX) and a specialized meta‐heuristic method (Simulated Annealing) developed in this study. The solution methods are tested and compared in two case studies; a test benchmark network and a large‐scale network. An effort to overcome the memory limitation of CPLEX through more compact formulation was partially successful: it results in a model that is less tightly bounded by its linear relaxation and hence is much more difficult to solve. In contrast, the Simulated Annealing algorithm scales better and is able to consistently yield high‐quality solutions with a reasonable amount of computation time.
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