Traffic Assignment Algorithm Research Articles

Graph Neural Networks Model to Generate Transportation Test Networks

Transportation researchers often rely on test networks to evaluate the performance of traffic assignment algorithms, analyze resilience and criticality, study emission productions, investigate transportation economics, and address various other challenges. Existing test networks have limited diversity and might not fully represent the topological features of real-world transportation networks. To address this issue, we proposed a novel approach that leverages real-life road networks extracted from OpenStreetMap to generate synthetic test networks with desired topological properties. We developed a graph neural network model that learns from the extracted networks’ topological patterns and predicts binary adjacency matrices for the generated networks. The proposed model creates synthetic networks resembling real-life networks, demonstrating its effectiveness in generating realistic test networks. The resulting synthetic networks offer a diverse and comprehensive set of test networks for various transportation studies, enabling improved simulations, analyses, and decision making for transportation researchers and practitioners. We have made our source code publicly available for collaboration and further enhancements in the transportation domain.

Evaluating private and system-wide impacts of freight eco-routing

Freight is crucial for economic development, but the trucks hauling this freight significantly contribute towards greenhouse gas emissions, advancing global climate change and criteria pollutant emissions that affect local community health. Hence, this work explores the opportunities and challenges associated with freight eco-routing to mitigate these freight-related externalities in Southern California. To this end, the authors establish the private impacts of a single carrier eco-routing its fleet of freight vehicles with a point-to-point routing tool. Further, the authors investigate network-wide freight eco- routing's system effects with the novel origin-based algorithm for multi-class Traffic Assignment by Paired Alternative Segments (mTAPAS). Overall, the study showcases the potential opportunities with freight eco-routing in reducing transportation-related externalities. However, it also highlights implementation challenges due to a lack of monetary incentives for carriers and regulators to account for these externalities in their decision-making.

A quasi-dynamic air traffic assignment model for mitigating air traffic complexity and congestion for high-density UAM operations

In spite of the significant effects of COVID-19, UAM operations are still expected to grow smoothly and healthily in the near future. If such dense UAM traffic relies on tactical planning to resolve conflicts in a decentralized control scheme, urban airspace could soon be heavily congested and airspace complexity could be overwhelming. In this paper, we propose a Quasi-dynamic Air Traffic Assignment (QATA) model, which aims to allocate traffic flows among air routes in the planning horizon in order to organize UAM traffic flows and reduce air traffic congestion and complexity within a centralized strategic planning scheme while meeting the demand and respecting some criteria. Firstly, UAM traffics are modeled as flows that operate on a 3D two-way UAM route network. Next, the QATA problem is formulated as an optimization problem involving network dynamics to minimize the air traffic complexity evaluated by the linear dynamical system and congestion defined by traffic density and energy consumption. A simulation-based rolling horizon framework is introduced to decompose the QATA problem into several modified static air traffic assignment problems in each time interval. In order to overcome the limitations of conventional dynamic traffic assignment algorithms, a simulated annealing algorithm using parallel computing and a novel neighborhood generation strategy is proposed to efficiently optimize the problem. By applying the model to a pre-designed large-scale UAM route network in Singapore’s urban airspace, Experimental studies demonstrate the performance of the proposed framework and its applicability. Parallel computing can achieve up to three times faster than the original algorithm. The proposed algorithm significantly reduces the value of the objective function by (32.20±0.29)% in 143.47±3.74 seconds at the 95% confidence interval of 100 experiments, far better compared to the representative conventional dynamic traffic assignment algorithms. This study could be useful to assist air traffic control authorities and air navigation service providers in addressing various issues in unmanned traffic management.

Sequential path-equilibration algorithm for highly accurate traffic flow assignment in an urban road network

Nowadays, the issue of traffic flow assignment has become an interdisciplinary topic that concerns multiple research areas and branches of science. This work is focussed on the mathematical and computational aspects of the equilibrium traffic assignment problem in the case when route flows are considered to be decision variables. Firstly, we obtain a fixed-point mapping with the explicit contraction operator, which is proven to equilibrate the journey times on feasible routes between a single origin-destination pair of nodes with the quadratic rate. Remarkable that from mathematical perspectives, the developed operator generalizes most path-equilibration operators already exploited by researchers. Secondly, we use the obtained fixed-point procedure to run the sequential path-equilibration algorithm for traffic flow assignment on well-known test urban road networks with arc-additive travel time functions. Our computational results appear to demonstrate higher accuracy of user-equilibrium traffic assignment solutions than the best ones known to us. In other words, developed within this paper sequential path-equilibration algorithm leads to solutions with less goal function values compared to the best solutions for today, according to our knowledge.

A novel flow update policy in solving traffic assignment problems: Successive over relaxation iteration method

This paper presents a novel flow update policy, namely the successive over relaxation (SOR) iteration method, which can be implemented in traffic assignment algorithms. Most existing solution algorithms for the user equilibrium traffic assignment problem (UE-TAP) mainly use two flow update policies: Jacobi and Gauss-Seidel iteration methods. The proposed flow update policy SOR can be a more efficient replacement. Following the path-based gradient projection (GP) algorithm, we developed a new method GP-SOR for the UE-TAP. This study first provides the complete procedure of applying the GP-SOR algorithm to solve the UE-TAP. Subsequently, a few properties of the proposed method are rigorously proven. However, empirical tests of the GP-SOR algorithm demonstrate serious oscillations and poor convergence. To cope with this problem, the Armijo Rule is employed to determine the relaxation factor, which substantially improves the convergence of GP-SOR algorithm. The preliminary numerical examples show that the GP-SOR algorithm has speedier convergence compared with the known alternatives, which is reflected by the evident reduction of the computing time and the number of iterations.

Work Zone Scheduling Problem in the Urban Traffic Networks

Abstract A significant part of highway and street congestion is produced by work zones. Depending on the type of construction and/or rehabilitation activity, street capacity could be significantly decreased, or the street could be completely closed. The work zone generates traffic delays in the street where maintenance is performed. Additionally, the work zone generates additional traffic on the neighboring streets, since many drivers change their routes. There are numerous possible work zone schedules. The total travel time of all network users highly depends on the chosen work zones schedule. Work zones scheduling problem has a natural nested structure that requires to be modeled as a bi-level problem. We considered the bi-level work zones scheduling problem. The objective function in the upper level, which we try to minimize, represents the total travel time of all network users. Relations in the lower level, help us to compute User Equilibrium flows. The proposed solution to the problem is based on the combination of Integer Programming and a heuristic traffic assignment algorithm. The output of the developed model consists of the start time of each work zone. The Sioux Falls benchmark network is used to illustrate the proposed procedures and the achieved performances.

Nonlinear Complementarity Model for Mixed-User Equilibrium Traffic Assignment and Mode Choice of Electric and Gasoline Vehicles

In the early years of 21st century, the ever-increasing volume of greenhouse gases from fossil fuel consumption have made humans seek alternative, non-polluting fuels as an effective strategy to reduce pollution and prevent related environmental issues. Electric vehicles (EVs) are today known as one of the most effective solutions for this purpose. To inform transportation planning and policies pertinent to EVs, models are needed to capture travelers’ behavior for vehicle type and route choice and the impacts on traffic congestion. The present study proposes a mixed complementarity traffic assignment model for the networks involving both EVs and gasoline vehicles so that the demand for each vehicle class depends on the characteristics of the paths and availability of electric charging stations on the paths. To determine the demand of each class, this study applies a logit choice model, which incorporates the effect of ownership and operating costs on demand of each class under different subsidy policies. This paper further investigates the charging behavior of EVs by considering private and public charging facilities in urban areas. To this end, the complementary traffic assignment algorithm has been used to solve the mentioned assignment problem. Besides, we used a label-setting algorithm for solving the constraint shortest path problem. The results of applying the mixed-user equilibrium to Sioux Falls and Chicago sketch networks demonstrate that our proposed algorithm outperforms existing algorithms for both solution time and accuracy across multiple networks.

Incremental equilibrium assignment and applications to traffic network model

AbstractTo find a traffic assignment algorithm that is less complex than the current algorithms in terms of both methodology and implementation, the route‐based incremental equilibrium assignment (IEA) method is proposed. The IEA method iteratively performs incremental assignment and new origin‐destination (O‐D) demand extraction, where the new O‐D demand is obtained by aggregating the traffic flows from the routes whose travel times are greater than the shortest travel time. By extending the IEA method, the incremental stochastic user equilibrium and reliability‐based user equilibrium assignments are proposed to solve the stochastic user equilibrium (SUE) and reliability‐based user equilibrium (RUE) models, respectively. The traffic flow assignment and new O‐D demand extraction are carried out in terms of the route choice probability and the ratio of route flow to O‐D demand in the incremental stochastic user equilibrium assignment method; the redundant traffic flows from the non‐equilibrium routes are extracted. Unlike the IEA method, incremental reliability‐based user equilibrium assignment needs to derive both the mean and variance of the route travel time. The results from numerical experiments demonstrate the essential ideas and convergence performance of the proposed IEA algorithm and illustrate that IEA can be effectively extended to solve the SUE and RUE models.

Proposing a Simulation-Based Dynamic System Optimal Traffic Assignment Algorithm for SUMO: An Approximation of Marginal Travel Time

User equilibrium (UE) and system optimal (SO) are among the essential principles for solving the traffic assignment problem. Many studies have been performed on solving the UE and SO traffic assignment problem; however, the majority of them are either static (which can lead to inaccurate predictions due to long aggregation intervals) or analytical (which is computationally expensive for large-scale networks). Besides, most of the well-known micro/meso traffic simulators, do not provide a SO solution of the traffic assignment problem. To this end, this study proposes a new simulation-based dynamic system optimal (SB-DSO) traffic assignment algorithm for the SUMO simulator, which can be applied on large-scale networks. A new swapping/convergence algorithm, which is based on the logit route choice model, is presented in this study. This swapping algorithm is compared with the Method of Successive Average (MSA) which is very common in the literature. Also, a surrogate model of marginal travel time was implemented in the proposed algorithm, which was tested on real and abstract road networks (both on micro and meso scales). The results indicate that the proposed swapping algorithm has better performance than the classical swapping algorithms (e.g. MSA). Furthermore, a comparison was made between the proposed SB-DSO and the current simulation-based dynamic user equilibrium (SB-DUE) traffic assignment algorithm in SUMO. This proposed algorithm helps researchers to better understand the impacts of vehicles that may follow SO routines in future (e.g., Connected and Autonomous Vehicles (CAVs)).

Complexity optimal air traffic assignment in multi-layer transport network for Urban Air Mobility operations

Large numbers of Urban Air Mobility (UAM) vehicles are expected to operate in urban airspace in the near future, exceeding the capacities of current airspace and Air Traffic Management (ATM) systems. This paper presents an air traffic assignment framework for 3D air transport networks in urban airspace to enable UAM operations at future demand levels. The individual vehicle dynamics are aggregated to describe the overall flow feature in this macroscopic model. Firstly, UAM operations are modeled as flows and structured in a three-dimensional two-way air transport network. Then, a complexity optimal air traffic assignment in urban airspace is formulated as an optimization problem. Based upon the Linear Dynamical System (LDS), a novel complexity metric is defined as objective function, which takes into account dynamic flow structure, congestion, and operational efficiency. A two-phase approach combining Simulated Annealing (SA) and Dafermos’ Algorithm (DA) is introduced to efficiently solve this problem. To validate the proposed model, a case study of an air transport network in Singapore’s urban airspace with two different demands is conducted. Comparative studies are carried out between the proposed algorithm and other widely used traffic assignment algorithms. The results show that the proposed approach is capable of assigning flows in an efficient and effective manner, reducing the complexity of the air transport network significantly. The results also show that optimizing the flow pattern reduces total complexity by 90.44%±0.53% and 92.12%±0.35% with 95% confidence interval, respectively in two scenarios. The framework may be useful for Air Navigation Service Providers (ANSP) in strategic planning for UAM operations and urban airspace design.

A new network equilibrium flow model: User-equilibrium with quantity adjustment

Travelers’ route choice behaviors affect the distribution of network flow. The paper presents an unconventional equilibrium flow model that extends the well-known non-Walrasian equilibrium theory of economics to the analysis of route choice behavior. With the introduction of path residual capacity as the quantity signal, a quantity adjustment user equilibrium flow model depicts the route choice dynamics based on the maximum path residual capacity, and thus differs from the traditional traffic equilibrium pattern regulated by path travel time. An equivalent nonlinear complementary problem to the proposed model is developed, and further reformulated as an unconstrained mathematical program using a gap function, which permits many efficient solution algorithms. The maximum residual capacity path algorithm and the maximum residual capacity traffic assignment algorithm are developed, and the gradient descent algorithm is used to solve the unconstrained mathematical program. Numerical results show that the proposed model and solution algorithm are feasible and effective. The paper proposes that both price adjustment and quantity adjustment are special cases of the price-quantity adjustment principle, and the equilibrium flow model based on which can capture route choice behaviors that has not been modeled in previous studies.

Parallelization of the B static traffic assignment algorithm

A widely used technique for predicting traffic flows in individual roads of a road traffic network is the user-equilibrium (UE) traffic assignment (TA). This technique assigns trips from origins to destinations in a road traffic network so that all trips use the cheapest path. The cost of the path, which consists of roads (edges), is the sum of the roads costs. These costs increase with increasing flow in these roads. In this paper, we describe the parallelization of the B algorithm – a relatively new TA algorithm with a fast convergence to a solution. Since the nature of the algorithm and the nature of its fast convergence complicate the parallelization itself, we considered and implemented three parallel variants and tested them on real road traffic networks to investigate their convergence, usability, and speed. The parallelization is intended for a shared memory parallel computing environment. The description of the parallelization along with the performed tests is the main contribution of this paper.

Consistent iterative algorithm for stochastic dynamic traffic assignment with a stable route set

AbstractIn stochastic (dynamic) traffic assignment (DTA), route choice (RC) formulations with implicit route set require less memory than their explicit counterparts. To compute turn probabilities, however, a topological ordering of the nodes is needed, which negatively impacts the stability of convergence and consistency of equilibrium. This paper formulates a general framework for the RC module of the efficient stochastic DTA (ESDTA) without topological ordering; we demonstrate how its full fixed route yields smooth and consistent convergence. The theoretical framework requires a series of computational modifications to ensure that numerical errors remain limited and to make the formulation more efficient for use in practice. The resulting ESDTA's computation time to reach equilibrium scales linearly with respect to all relevant complexity dimensions (network size, demand zones, time resolution, and congestion level).

A Study of traffic assignment algorithm in terms of stability and uniqueness

A Study of traffic assignment algorithm in terms of stability and uniqueness

A computationally efficient metric for identification of critical links in large transportation networks

Maintaining safety and resilience in transportation system requires identification of critical components. The existing transportation link criticality metrics typically require multiple traffic assignments to perform a full scan of the network. Link removals create computational burden and can cause network disconnectivity which makes it problematic to run traffic assignment. The authors previously introduced Link Criticality Index (LCI) that identifies the criticality ranking within a single User Equilibrium (UE) traffic assignment using Frank-Wolfe (FW) algorithm. While LCI is shown to provide balanced rankings with respect to connectivity and flow conditions, its computational efficiency diminishes for larger networks due to the need for path enumeration. This paper formulates an adjusted LCI to make it computationally efficient for larger networks. Adjusted LCI utilizes 1) viable routes instead of the complete list of enumerated paths; and, 2) a path-based traffic assignment algorithm (Gradient Projection) to replace FW. The consistency of rankings between original/adjusted LCIs, and other measures from the literature are analyzed and compared for three networks, and through an experimental setup. The proposed method is also applied on a large-scale transportation network, i.e., Chicago network. The results show that both modifications are effective and yield faster results without compromising LCI's advantages.

Column generation for the equilibrium route-flow traffic assignment problem

Today efficient traffic management seems to be impossible without the support of the artificial intelligence systems based on mathematical models of traffic flow assignment since a modern road network is a large-scale system with huge amounts of elements. The present paper is devoted to the route-flow traffic assignment problem, which solution is the most valuable from decision-making perspectives. The paper aims to fill the gap in the relation between the column generation process and the uniqueness of the equilibrium route-flow traffic assignment pattern. The independence of routes is showed to be highly significant when travel time functions are arc-additive. Indeed, on the one hand, the independence of routes is proved to guarantee the uniqueness of the equilibrium route-flow traffic assignment pattern. On the other hand, the independence of routes appears to be crucial for column generation when solving the route-flow traffic assignment problem since the equilibrium travel time is proven to be decreased only by adding independent candidate route. Obtained results contribute to the development of algorithms for route-flow traffic assignment based on travel times equilibration procedure.

Convergence behavior for traffic assignment characterization metrics

Traffic assignment is used for infrastructure planning, based on metrics like total system travel time (TSTT), vehicle-miles traveled (VMT) and link or path flows. Algorithms for traffic assignment converge to an equilibrium solution over multiple iterations, but these metrics converge at different rates. Current guidance indicates that freeway link flows stabilize at a relative gap of roughly . This study generalizes this guidance by testing additional networks and metrics, in more experimental settings. Our results reveal that aggregate metrics (VMT and TSTT) stabilize earlier (relative gap ) than link flows (relative gap ), which in turn stabilize slightly before the set of most likely used paths and flows on these paths (relative gap ). These results are stable across the TAPAS and Algorithm B methods for solving assignment. Our results also show strong linear correlations between alternative gap measures, allowing for the translation of stabilization results across other gap definitions as well.

Research on Traffic Assignment Model and Algorithm Based on Cumulative Prospect Theory under Uncertain Factors

Current traffic assignment theories and methods are studied. To address the limitations of existing models and algorithms in solving the traffic assignment problems under uncertain supply and demand, a traffic assignment model based on the cumulative prospect theory is proposed. Firstly, the problem of uncertain supply and demand of the traffic network is described, and an improved traffic impedance function of road sections is proposed. Then, the reference point of generalized cost and the reference point of the dynamic section risk are set up, and the comprehensive cumulative prospect value function considering the preference coefficient of the reference point is given. A traffic assignment model based on the cumulative prospect theory is constructed, and an isolation niche genetic simulated annealing algorithm is designed to solve the model. Finally, with the highway traffic network in the Sichuan-Tibet region as an example, the process of network traffic equilibrium based on the cumulative prospect theory under the fixed and changing network structure is studied respectively, and parameter sensitivity and algorithm comparison are analyzed. The results show that the proposed traffic assignment model based on the cumulative prospect theory provides a good idea for solving the traffic assignment problem under uncertain supply and demand, and is of theoretical significance and application value.

Traffic Flow Estimation Based on Toll Ticket Data Considering Multitype Vehicle Impact

Traffic flow estimation (TFE) plays an important role in transportation systems, especially in relation to the detection, planning, and management of traffic for expressway systems. However, traditional approaches to TFE using roadside detectors usually have low-coverage and high-cost problems. This paper proposes a toll ticket data (TTD)–based approach to TFE for filling the gaps in existing approaches and also considers multitype vehicles’ impact on traffic flow for more accurate TFE results. First, route choice models are constructed to capture travel characteristics of mult-type vehicles and acquire route traffic flow from TTD. Then, a simulation-based dynamic traffic assignment (DTA) algorithm is developed to obtain traffic flow regarding vehicle type, time, and location, with the consideration of multitype vehicles’ impact by using a tollbooth conversion factor (TCF) and point-of-queue model (PQM). The proposed approach is evaluated empirically using data relating to the Shandong Expressway Toll System in China. The results confirm that it performs effectively. This research could contribute to future TFE and provide references for dynamic, delicate traffic management in an economical and reliable way.

A faster path-based algorithm with Barzilai-Borwein step size for solving stochastic traffic equilibrium models

Step size determination (also known as line search) is an important component in effective algorithmic development for solving the traffic assignment problem. In this paper, we explore a novel step size determination scheme, the Barzilai-Borwein (BB) step size, and adapt it for solving the stochastic user equilibrium (SUE) problem. The BB step size is a special step size determination scheme incorporated into the gradient method to enhance its computational efficiency. It is motivated by the Newton-type methods, but it does not need to explicitly compute the second-order derivative. We apply the BB step size in a path-based traffic assignment algorithm to solve two well-known SUE models: the multinomial logit (MNL) and cross-nested logit (CNL) SUE models. Numerical experiments are conducted on two real transportation networks to demonstrate the computational efficiency and robustness of the BB step size. The results show that the BB step size outperforms the current step size strategies, i.e., the Armijo rule and the self-regulated averaging scheme.