System Optimal Traffic Assignment Research Articles

Disaggregated spatiotemporal traffic assignment for road reservation service and supply-demand statistical analysis

This paper develops a disaggregated spatiotemporal traffic assignment method with a system-optimal (SO) orientation and analyzes the supply-demand matching degree with four statistical indexes under the background of a road reservation system. Three key issues are addressed. Firstly, the paper illustrates the service process of a road reservation system. It is essential to know how the road reservation system works and the difference between it and other reservation systems. Secondly, a spatiotemporal discretization expression method based on the system-optimal traffic assignment (SOTA) model with predictive origin-destination demand for link travel time is put forward to make the supply space could be reserved, and the demand would not be mutually interfering. Thirdly, the study proposes a reverse feasible spatiotemporal route searching algorithm based on the expected arrival time to individually assign the applicants on the road network. This route searching algorithm does not use the network topology but the spatiotemporal discretized links. The departure time preference was considered in the feasible spatiotemporal route searching algorithm. Moreover, as the real demand distribution of the whole reservation area is not difficult to obtain after a period of updates, it is possible to analyze the supply-demand matching degree of the road network. Thus, four statistical indexes are proposed to assess the state variation of the road network. Simulation results verify the effectiveness and efficiency of the proposed method. The novel reverse feasible routes searching algorithm has a system-optimal trend with inputting the demand individually and an acceptable calculating efficiency. The method proposed by this paper could ensure a reliable road reservation service with accurate demand prediction. Considering the departure time preference would not bring extra burden to the road reservation system but provide more user-friendly service. Through the analysis, the supply-demand matching degree of the road network is significantly influenced by the cohesive capacity connection of the upstream and downstream links. This indicates the network structure and road attributes optimization should be considered in enhancing the road reservation service.

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)).

Dynamic system optimal traffic assignment with atomic users: Convergence and stability

In this study, we analyse the convergence and stability of dynamic system optimal (DSO) traffic assignment with fixed departure times. We first formulate the DSO traffic assignment problem as a strategic game wherein atomic users select routes that minimise their marginal social costs, called a ‘DSO game’. By utilising the fact that the DSO game is a potential game, we prove that a globally optimal state is a stochastically stable state under the logit response dynamics, and the better/best response dynamics converges to a locally optimal state. Furthermore, as an application of DSO assignment, we examine characteristics of the evolutionary implementation scheme of marginal cost pricing. Through theoretical comparison with a fixed pricing scheme, we found the following properties of the evolutionary implementation scheme: (i) the total travel time decreases smoother to an efficient traffic state as congestion externalities are perfectly internalised; (ii) a traffic state would reach a more efficient state as the globally optimal state is stabilised. Numerical experiments also suggest that these properties make the evolutionary scheme robust in the sense that they prevent a traffic state from going to worse traffic states with high total travel times.

Matching and routing for shared autonomous vehicles in congestible network

The dispatch and routing problems of shared autonomous vehicle (DR-SAV) have been widely studied, and one of the key challenges is the modeling complexity and computational burden associated with network congestion. Existing studies on DR-SAV are limited in the sense that traffic congestion and demand–supply interaction, resulting from dispatch and routing decisions, are not fully integrated into the optimization framework. In this work, we explicitly consider the congestion effect of SAV operations in a mixed traffic environment, consisting of SAVs and conventional vehicles (CVs), by proposing a computationally tractable traffic assignment framework for optimal matching and routing of SAV trips, while allowing the sharing of vehicle by up to two trips simultaneously. This problem is formulated as a Stackelberg game where the upper level is inherently a matching and routing problem for SAVs, and the lower level involves a user equilibrium among CVs. Two strategies are proposed to improve the tractability of the proposed problem: (1) a novel convex programming formulation of the joint SAV matching–routing problem based on the system optimal traffic assignment principle, and (2) the invocation of shareability network to facilitate path set generation. Numerical experiments of the proposed method show that the proposed SAV matching and routing scheme could lead to significant reduction in total travel cost.

A Holistic Approach for Optimal Pre-Planning of Multi-Path Standardized Taxiing Routes

Standardized Taxiing Routes (STRs) are defined as published taxiing-in and taxiing-out routes for aircraft between gates and runways, aiming at improving ground movement safety at busy or complex airports. Most of the STRs specify only one path between each O–D (Origin–Destination) pair, which compromises the flexibility of route choice in time-varying traffic scenarios. In this paper, we present a holistic approach of planning and validating Multi-Path Standardized Taxiing Routes (MPSTRs) based on System-Optimal Traffic Assignment (SOTA), by firstly defining the flow-based congestion cost of runway, taxiway, and sectorized apron operation at a macroscopic level. A human-in-the-loop experiment comprised of six operation scenarios follows to investigate the impact of the pre-planned MPSTRs on human controllers’ performance. Results confirm the positive effect of the MPSTRs on taxiing performance without increasing the controllers’ workload, which also implies that the MPSTRs would be a promising approach for balancing safety and efficiency for the STRs-based taxiing operation and dynamic routing optimization without substantial investment.

Multi-objective Eco-Routing Model Development and Evaluation for Battery Electric Vehicles

This paper develops a multi-objective eco-routing algorithm (eco- and travel time-optimum routing) for battery electric vehicles (BEVs) and internal combustion engine vehicles (ICEVs) and investigates the network-wide impacts of the proposed multi-objective Nash optimum (user equilibrium) traffic assignment on a large-scale network. Unlike ICEVs, BEVs are more energy efficient on low-speed arterial trips compared with highway trips. Different energy consumption patterns require different eco-routing strategies for ICEVs and BEVs. This study found that single-objective eco-routing could significantly reduce the energy consumption of BEVs but also significantly increase their average travel time. Consequently, the study developed a multi-objective routing model (eco- and travel time-routing) to improve both energy and travel time measures. The model introduced a link cost function that uses the specification of the value of time and the cost of fuel/energy. The simulation study found that multi-objective routing could reduce BEV energy consumption by 13.5%, 14.2%, 12.9%, and 10.7%, as well as ICEV fuel consumption by 0.1%, 4.3%, 3.4%, and 10.6% for “not congested, “slightly congested,”“moderately congested,” and “highly congested” conditions, respectively. The study also found that multi-objective user equilibrium routing reduced the average vehicle travel time by up to 10.1% compared with the standard user equilibrium traffic assignment for highly congested conditions, producing a solution closer to the system optimum traffic assignment. The results indicate that the proposed multi-objective eco-routing strategy can reduce vehicle fuel/energy consumption effectively with minimum impacts on travel times for both BEVs and ICEVs.

Fuzzy modelling of static system optimum traffic assignment problem having multi origin-destination pair

Traffic congestion is an unpreventable problem to avoid in a transportation network and it has negative effects on traffic accident, time wasting, traffic delay and safety problem. Besides, in transportation networks, drivers do not want to deal with traffic jam while traversing between specified origin-destination pair. Therefore, traffic assignment (TA) is imperative to improve traffic management, transportation safety, time, and cost savings. System Optimum Traffic Assignment Problem (SOTAP) is a kind of TA model which aims to minimize the total system travel time on the network, and satisfies the flow conservation constraints. To model the SOTAP more realistically, the imprecise parameters can be taken as fuzzy. Therefore, in this paper, we focus on converting the conventional SOTAP to a fuzzy quadratic programming problem (QPP) which is named System Optimum Fuzzy Traffic Assignment Problem (SOFTAP). Here, link travel time is expressed with BPR function as generally used in the literature by converting to fuzzy except link-dependent parameters. Thus, the nonlinear objective function of SOFTAP is expressed in terms of fuzzy link flows and fuzzy link travel times. A solution approach from the literature is modified to the reconstructed SOFTAP.

Evaluation of navigation based on system optimal traffic assignment for connected cars

Recently, many cars have become connected to internet. In the near future, almost all cars will be connected cars. Such a connected car will automatically drive according to a navigation system. Conventional car navigation systems are based on User Equilibrium (UE) traffic assignment. However, System Optimal (SO) traffic assignment is better than UE traffic assignment. To realise SO traffic assignment, complete traffic information is required. When connected cars become ubiquitous, all traffic information will be gathered into the cloud. Therefore, a cloud-based navigation system can provide SO-based navigation to connected cars. An SO-based navigation method in which the cloud collects traffic information from connected cars, computes SO traffic assignments, and recommends SO routes to users was recently proposed. In this paper, we evaluate this SO-based navigation method in detail.

Evaluation of navigation based on system optimal traffic assignment for connected cars

Evaluation of navigation based on system optimal traffic assignment for connected cars

System Optimum Fuzzy Traffic Assignment Problem

This paper focuses on converting the system optimum traffic assignment problem (SO-TAP) to system optimum fuzzy traffic assignment problem (SO-FTAP). The SO-TAP aims to minimize the total system travel time on road network between the specified origin and destination points. Link travel time is taken as a linear function of fuzzy link flow; thus each link travel time is constructed as a triangular fuzzy number. The objective function is expressed in terms of link flows and link travel times in a non-linear form while satisfying the flow conservation constraints. The parameters of the problem are path lengths, number of lanes, average speed of a vehicle, vehicle length, clearance, spacing, link capacity and free flow travel time. Considering a road network, the path lengths and number of lanes are taken as crisp numbers. The average speed of a vehicle and vehicle length are imprecise in nature, so these are taken as triangular fuzzy numbers. Since the remaining parameters, that are clearance, spacing, link capacity and free flow travel time are determined by the average speed of a vehicle and vehicle length, they will be triangular fuzzy numbers. Finally, the original SO-TAP is converted to a fuzzy quadratic programming (FQP) problem, and it is solved using an existing approach from literature. A numerical experiment is illustrated.

Forced‐node route guidance system: incorporating both user equilibrium and system optimal benefits

Route guidance systems (RGSs), due to recent advances in technology, are emerging as a low-cost and fast solution to the congestion problem in urban areas. Route guidance with the aim of minimising total travel time (system optimum) causes longer paths, and consequently, more unfairness between individual users. Moreover, more congestion is created when guiding the users to their shortest paths (user equilibrium) to provide fairness among them. Therefore, an RGS that is able to combine these two inconsistent objectives, i.e. minimising total congestion of the network, and travel unfairness between individual travellers, would be of great value. To this end, a forced-node RGS is proposed in this study. The guidance task is delegated to some of the network nodes (e.g. intersections and roundabouts) in a distributed and autonomous way, similar to the routing operation in computer networks. Then, by applying a novel idea in transforming the demand rates, a non-recursive algorithm is proposed and compared with well-known traffic assignment methods; i.e. the classic user equilibrium and system optimal traffic assignment methods. Computational results affirmed the applicability of the forced-node RGS through the incorporation of both system and users’ benefits in different proportions.

A trade-off between average and maximum arc congestion minimization in traffic assignment with user constraints

In system optimal traffic assignment of traffic flows with user constraints the total travel time is minimized on a set of paths with bounded length ensuring a certain level of fairness for users. Minimizing the total travel time may lead to experience large travel times on some arcs. On the other hand, when minimizing the maximum arc travel time, the total travel time cannot be controlled. The increase of arc travel time with respect to arc free-flow travel time is related to the arc congestion that is one of the main issues in road networks. In this paper we propose a new model that is a compromise between minimizing the average arc congestion and the worst arc congestion on the road network. The model is a linear program that minimizes the average arc congestion over a given percentage of the most congested arcs. A heuristic algorithm aimed at reducing the number of paths that are considered for the model is also proposed. A computational study is performed that shows the flexibility of the model and the quality of the heuristic.

Marginal cost pricing for system optimal traffic assignment with recourse under supply-side uncertainty

Transportation networks are often subject to fluctuations in supply-side parameters such as capacity and free-flow travel time due to factors such as incidents, poor weather, and bottlenecks. In such scenarios, assuming that network arcs exist in a finite number of states with different delay functions with different probabilities, a marginal cost pricing scheme that leads to a socially optimal outcome is proposed. The suggested framework makes the behavioral assumption that travelers do not just choose paths but follow routing policies that respond to en route information. Specifically, it is assumed that travelers are fully-rational and that they compute the optimal online shortest path assuming full-reset. However, such policies may involve cycling, which is unrealistic in practice. Hence, a network transformation that helps restrict cycles up to a certain length is devised and the problem is reformulated as a convex optimization problem with symmetric delay functions. The results of numerical tests on the Sioux Falls test network are presented using the Frank–Wolfe algorithm.

Improving regional road network resilience by optimised traffic guidance

ABSTRACTIn this paper, a new approach for improving the traffic performance of regional road networks during the recovery period following a disaster life cycle is presented. Regional road networks are often uncongested and have sparse and long-spanning link densities. Consequently, they are more impacted by natural disasters and thereby by potential road closures that may be imposed afterwards. Information about road closures after disruptive events can be transmitted through roadside information dissemination methods such as variable message signs, Cooperative-Intelligent Transport Systems or highway advisory radio. This paper proposes an optimisation model to find optimal location of roadside guidance devices across a regional road network for improving total travel time (TTT) within the network. To achieve this, firstly, a network design model is formulated using a bi-level framework and implemented to find the optimal locations of roadside guidance devices that lead to reducing the TTT of a disrupted network. Secondly, two methods for solving the formulated problem are presented, an exact solution method called SO-relaxation that cuts the solution space using system optimum traffic assignment. The other method is a hybrid-GA that is a heuristic solution method. Results show that locating guidance devices optimally in a disrupted network leads to a more resilient road network in which the post-disaster TTT of the network during recovery phase is less than when no action is taken. It is also shown that the improvement achieved by roadside guidance is a function of available resources and the road users willingness to obey the guidance provided.

Competitive Traffic Assignment in Road Networks

Abstract Recently in-vehicle route guidance and information systems are rapidly developing. Such systems are expected to reduce congestion in an urban traffic area. This social benefit is believed to be reached by imposing the route choices on the network users that lead to the system optimum traffic assignment. However, guidance service could be offered by different competitive business companies. Then route choices of different mutually independent groups of users may reject traffic assignment from the system optimum state. In this paper, a game theoretic approach is shown to be very efficient to formalize competitive traffic assignment problem with various groups of users in the form of non-cooperative network game with the Nash equilibrium search. The relationships between the Wardrop’s system optimum associated with the traffic assignment problem and the Nash equilibrium associated with the competitive traffic assignment problem are investigated. Moreover, some related aspects of the Nash equilibrium and the Wardrop’s user equilibrium assignments are also discussed.

A path-based flow formulation for the traffic assignment problem

ABSTRACTIn order to improve cooperation between traffic management and travelers, traffic assignment is the key component to achieve the objectives of both traffic management and route choice decisions for travelers. Traffic assignment can be classified into two models based on the behavioral assumptions governing route choices: User Equilibrium (UE) and System Optimum (SO) traffic assignment. According to UE and SO traffic assignment, travelers usually compete to choose the least cost routes to minimize their own travel costs, while SO traffic assignment requires travelers to work cooperatively to minimize overall cost in the road network. Thus, the paradox of benefits between UE and SO indicates that both are not practical. Thus, a solution technique needs to be proposed to balance UE and SO models, which can compromise both sides and give more feasible traffic assignments. In this paper, Stackelberg game theory is introduced to the traffic assignment problem, which can achieve the trade-off process between traffic management and travelers. Since traditional traffic assignments have low convergence rates, the gradient projection algorithm is proposed to improve efficiency.

A Program for Simultaneous Network Signal Timing Optimization and Traffic Assignment

This study formulates a program for simultaneous traffic signal optimization and system optimal traffic assignment for urban transportation networks with added degree of realism. The formulation presents a new objective function, i.e., weighted trip maximization, and explicit constraints that are specifically designed to address oversaturated conditions. This formulation improves system-wise performance while locally prevents queue spillovers, de-facto reds, and gridlocks. A meta-heuristic algorithm is developed that incorporates microscopic traffic flow models and system optimal traffic assignment in genetic algorithms. This solution technique efficiently optimizes signal timing parameters, at the same time solves system optimal traffic assignment, and accounts for oversaturated conditions and different driver's behaviors. This study also proposes a framework to calculate an upper bound on the value of the objective function by solving the problem while several constraints (i.e., network loading and traffic assignment) are relaxed. An empirical case study for a portion of downtown Springfield, Illinois has been conducted under four demand patterns. Findings indicate that our solution approach can solve the problem effectively. Several managerial insights have also been drawn.

Price of anarchy for reliability-based traffic assignment and network design

This paper proposes reliability-based system-optimal traffic assignment under supply uncertainty based on the concept of the total system travel time budget, and defines the price of anarchy (PoA) for the corresponding user equilibrium (UE) traffic assignment. An analytical formula for a set of the upper bounds of the PoA for the equilibrium assignment to the networks with polynomial link travel time functions is derived. These bounds are proved to be independent of the network topology and demands. The formula for the minimum upper bound is also derived and can be reduced to the upper bound formula for traditional UE traffic assignment as a special case. The PoA for the traditional UE network design problem (NDP) with polynomial link travel time functions is defined, and proved to be bounded by the upper bound of that for traditional UE traffic assignment of the same instance, before any link expansion. The PoA for the reliability-based UE (RUE) NDP with polynomial link travel time functions is also proved to be bounded by the set of upper bounds of that for RUE traffic assignment of the same instance, before any link expansion.

Robust Network Design for Roadway Networks: Unifying Framework and Application

Disturbances in roadway networks due to increases in demand or drops in network capacity can severely degrade the performance of the system. The robustness of a roadway network to such disturbances has been investigated using a variety of methods leading to disparate robust network designs. This paper introduces a unifying framework for understanding and applying different robust network designs based on the context of traffic disturbances and design goals. It presents the objectives, requirements and examples of robust network design with long-term (planning) and shortterm (operation) goals. A sample case study is presented to assess a short-term robust network design using traffic assignment. The preliminary testing results compared to conventional User Equilibrium and System Optimal traffic assignment, demonstrate 20% and 10% travel time savings with demand increase and supply reduction, respectively.

A microeconomic interpretation for the system optimal traffic assignment problem with nonadditive path cost

Using a Bergson–Samuelson welfare function, we outline a microeconomic interpretation of the effects of the non-linearity in the time/cost relationship for travellers in a congested transport network. It is demonstrated that a marginal cost traffic flow assignment following Wardrop's second principle, although it minimizes the total cost of a transport network, may reduce social welfare compared to the market equilibrium assignment based on Wardrop's first principle. A welfare-maximizing assignment model is presented and used to show that if the travellers' utility functions are linear, the assignment that maximizes social welfare will be the same as the assignment that minimizes total network cost, but if users' utility functions are non-linear (reflecting the traditional non-satiation and diminishing marginal utility axioms), the two assignments will be different. It is further shown that the effects of this non-linearity are such that a welfare-maximizing assignment will meet with less user resistance than a minimum total network cost assignment.