Assessment of Adherence to the Condition of Proportionality in User Equilibrium Traffic Assignments with Uniquely Determined Route Flows (original) (raw)
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User-equilibrium route flows and the condition of proportionality
Transportation Research Part B: Methodological, 2012
User-equilibrium (UE) static deterministic traffic assignment is a widely accepted model among researchers, and is extensively applied in travel forecasting practice. UE route flows are also quite commonly used in methodological research as well as in practical applications, even though it is well known that route flows are not uniquely determined by the UE conditions. One way to resolve this dilemma is by imposing an additional condition, such as the condition of proportionality.
New Insights and Improvements of Using Paired Alternative Segments for Traffic Assignment
Transportation Research Part B, 2016
The recent literature observes that the development of advanced algorithms for the traffic assignment problem (TAP) heavily relies on the proper use of some specific topological structures. This paper focuses on discussing a particular topological structure named paired alternative segment (PAS), which consists of two path segments sharing the same starting and ending nodes but no other common nodes. We first present two alternative conditions that establish an equivalency relationship between user equilibrium (UE) flows and PAS structures. Starting from the traffic assignment method by paired alternative segments (TAPAS), we then examine the utilization of PASs for TAP and explore some algorithmic and implementation issues, which leads to the birth of an improved TAPAS procedure (termed iTAPAS in this paper). Compared to the original TAPAS, iTAPAS enhances the algorithmic efficiency in two aspects: (1) a more effective PAS identification method is used; (2) each PAS is set as being associated with only one origin in the UE-finding process. Some analytical results based on the new PAS identification method are presented to justify the convergence and efficiency of iTAPAS. A simplified post-process procedure is also presented to achieve the proportionality for iTAPAS. Numerical results obtained from applying the new and original algorithms for several large networks reveal that iTAPAS is nearly two times faster than TAPAS in achieving highly precise link flow solutions while it is practically identical to TAPAS in finding stable path flow solutions that meet consistency and proportionality.
User Equilibrium (UE) method is the most widely used trip assignment method for auto trips. In UE condition, no driver can unilaterally reduce his/her travel time by shifting to another route. That means travel time on each used path between any Origin-Destination (O-D) is the same under this condition. Therefore, UE condition exists naturally in every road network. However, the total system travel time under this condition may not be the minimum. The total system travel time can be found minimum under System Optimum (SO) condition. In this research, UE and SO methods for trip assignment are compared. First, the methodologies are compared; and then link flows and travel times under both conditions are compared. As SO is not a natural process, mechanism to achieve SO is also shown in this paper. Arterial highway network of Sioux Falls, South Dakota consisting of 24 nodes and 76 links with 13 origins and destinations is analyzed for both UE and SO conditions. The network is analyzed by GAMS optimization software. It is found that the system travel time is much less under SO condition than under UE condition.
Equilibrium traffic assignment for large scale transit networks* 1
European journal of operational research, 1988
This paper develops a graph-theoretic framework for large scale transit networks and provides new insight into the equilibrium traffic assignment methodology. Variational inequality formulations for the equilibrium traffic assignment are developed and algorithms for computing equilibrium flows are discussed. A new shortest hyperpaths problem is defined and computational techniques for shortest hyperpaths suggested.
Link- and Path-Based Traffic Assignment Algorithms: Computational and Statistical Study
Transportation Research Record: Journal of the Transportation Research Board, 2002
The computational performance of five algorithms for the traffic assignment problem (TAP) is compared with that of mid- to large-scale randomly generated grid networks. The applied procedures include the Frank-Wolfe, PARTAN, gradient projection, restricted simplicial decomposition, and disaggregate simplicial decomposition algorithms. A statistical analysis is performed to determine the relative importance of various properties (network size, congestion level, solution accuracy, zone-node ratio) of the traffic assignment problem for the five selected algorithms. Regression models, which measure central processing unit time and number of iterations consumed by each algorithm using various factors and their combinations, are derived to provide a quantitative evaluation. Ultimately, the findings of this research will be useful in guiding transportation professionals to choose suitable solution algorithms and to predict the resulting algorithm performance in TAPs.
Equilibrium traffic assignment for large scale transit networks
European Journal of Operational Research, 1988
This paper develops a graph-theoretic framework for large scale transit networks and provides new insight into the equilibrium traffic assignment methodology. Variational inequality formulations for the equilibrium traffic assignment are developed and algorithms for computing equilibrium flows are discussed. A new shortest hyperpaths problem is defined and computational techniques for shortest hyperpaths suggested.
The formulation of the static user equilibrium traffic assignment problem (UETAP) under some simplifying assumptions has a unique solution in terms of link flows but not in terms of path flows. Large variations are possible in the path flows obtained using different UETAP solution algorithms. Many transportation planning and management applications entail the need for path flows. This raises the issue of generating a meaningful path flow solution in practice. Past studies have sought to determine a single path flow solution using the maximum entropy concept. This study proposes an alternate approach to determine a single path flow solution that represents the entropy weighted average of the UETAP path flow solution space. It has the minimum expected Euclidean distance from all other path flow solution vectors of the UETAP. The mathematical model of the proposed entropy weighted average method is derived and its solution stability is proved. The model is easy to interpret and generalizes the proportionality condition of Bar-Gera and Boyce (1999). Results of numerical experiments using networks of different sizes suggest that the path flow solutions for the UETAP using the proposed method are about identical to those obtained using the maximum entropy approach. The entropy weighted average method requires low computational effort and is easier to implement, and can therefore serve as a potential alternative to the maximum entropy approach in practice.
A computational study of traffic assignment algorithms
Traffic congestion is an issue in most cities worldwide. One way to model and analyse the effect of congestion and other factors on route choice behaviour and to predict the impact of traffic management projects and transport policies is traffic assignment (TA). The most commonly used TA model is known as user equilibrium (UE), which is based on the assumption that all drivers want to minimise their travel time or generalised cost. As a result, an equilibrium is achieved when no one has an incentive to switch to another route. Although the conventional mathematical model of TA belongs to the convex optimisation domain and, hence, is relatively easy to solve, efficient algorithms are required in order to be able to solve TA in a reasonable amount of time for realistic transport networks. This motivates researchers to propose numerous methods and algorithms to solve this problem in the literature. However, there is no comprehensive empirical study that compares the performance of different approaches on benchmark instances. In this study, our objective is to fill this gap. We provide a literature review of the most promising methods. We classify algorithms according to the way the solution is represented, namely, link-based (solution is represented by link flows), path-based (solution is represented by path flows) and origin-based (solution is represented by link flows corresponding to each origin), and implement the most representative algorithms in each group. We perform numerical tests on benchmark instances of various sizes, compare the algorithms and analyse the impact of their main components on their running time. We also study the convergence behaviour of the methods with respect to different levels of solution accuracy.
ARRBTRAFIC: program user manual - equilibrium traffic assignment for fixed demands
1979
This manual is a revised edition of ATM no 4 (IRRD no 229983). The report provides detailed documentation and examples of input and output for a family of four equilibrium traffic assignment programs. ARRBTRAFIC/CDC CYBER (1) is useful for an accurate prediction of traffic flows according to the first wardrop equilibrium assignment principle (user cost minimisation). ARRB/TRANPLAN includes subroutines to interface with other travel demand programs to form a comprehensive planning system for generation, distribution and assignment. ARRBTRAFIC/NOVA-840 is suited to educational and research purposes and offers more options than the other versions. ARRBTRAFIC/CDC-CYBER (2) runs considerably faster and it uses the recent Dial - Klingman - Glover shortest path algortithm. An optional direct calculation method is included for combining two consecutive solutions, but may produce less accurate results when this option is selected. A generalised piece- wise speed- flow relationship is also pr...