Stochastic User Equilibrium Research Articles

Impact evaluation of different network planning concepts on traffic noise

The purpose of this paper is to study the impact of road structure on traffic noise from an urban network planning perspective, to provide solutions to control and prevent traffic noise at source. The process is divided into three parts. Firstly, the stochastic user equilibrium model for traffic flow allocation is improved to be more accurate. Secondly, a global traffic noise simulation method is proposed for the network based on the noise prediction model, and the noise data is visualized. Finally, a noise evaluation system is established to study the traffic noise evolution patterns under different road structures. The results show that with the increase of network density, the traffic noise value of the network decreases. The layout of one-way roads will reduce the regional traffic noise value. The impact of road grade adjustments on traffic noise is positively correlated with the rate of change in road capacity. The study can provide an effective basis for control traffic noise from the network planning stage.

An economic analysis of a multi-modal transportation system with ride-sourcing services and multi-class users

This paper proposes a tractable bi-level model to explore the mode choice of travelers and optimal operation decisions of a public transit operator and a ride-sourcing operator under a multi-modal transportation system. In such a multi-modal system, users may travel by bus, metro, and/or ride-sourcing service. The lower-level network model is utilized to capture the equilibrium mode choices with the consideration of travelers’ heterogeneity in terms of the value of time (VOT), where deterministic user equilibrium (DUE) and stochastic user equilibrium (SUE) are formulated and compared. In the upper-level model, subject to the DUE/SUE, the two operators optimize their operation decisions in the notion that the profit is maximized or the total system cost is minimized. The existence and uniqueness/non-uniqueness of the multi-modal mode choice equilibrium are analyzed. The optimal operation decisions are also compared under different operation regimes. Our results show that SUE model provides a more conservative estimate of the ride-sourcing operator’s profit and total system travel cost compared to DUE. Besides, the total system cost can be reduced while the profit of the ride-sourcing company can be increased under appropriate operation decisions of the public transit operator and the ride-sourcing operator. Sensitivity analysis further indicates that travelers with longer total travel distance tend to use short-distance ride-sourcing services, which suggests that the ride-sourcing operator should dispatch more vehicles to suburbs located in remote areas to enhance service quality.

Cascading failure-based reliability assessment for post-seismic performance of highway bridge network

This paper proposes a novel reliability assessment framework for post-seismic performance of highway bridge network that considers cascading failures caused by traffic flow redistribution. Firstly, the fragility curve of bridge is obtained by probabilistic seismic demand model. Then, we propose the impact factor of path choice probability to characterize the cascading failure of the network. The stochastic user equilibrium assignment of highway bridge network traffic flow is calculated based on the impact factor of path choice probability. To evaluate the network's efficiency and identify the congestion-prone links, the Monte Carlo simulation method is introduced to calculate the probability density curves of different influencing parameters. Finally, the framework proposed in this paper is utilized to analyze the congestion-prone links of the transportation network of some areas of Mianyang City and verify its applicability.

Analysing inequity in land use and transportation models by genetic algorithm for realistically quantified penetration rate of Advanced Driving System Equipped Vehicles

The continued evolutions in automated driving technologies and their rapid testing on common roads make it necessary to evaluate their impacts on land use and transportation models. It is crucial to quantify the number of advanced driving system-equipped vehicles that are going to be part of transportation networks. On the other hand, the intuitive property of these vehicles to create an induced demand can bring both positive and negative effects on the travel equilibrium costs that create inequity. To cater for the gap of realistic quantification of penetration rate and inequity evaluation on the inclusion of such vehicles; this research crafts a detailed and effective methodology. This research formulates a convex minimization problem as a lower-level part of the bi-level optimization model intending to minimize the travel equilibrium cost for all OD pairs. Also, acts as an assignment of demand to the network following the stochastic user equilibrium approach by using the Frank–Wolfe algorithm. Whereas, the upper level of the model maximizes the production of newly generated demand incorporating inequity constraints. A genetic algorithm is used to solve the multi-objective fitness function yielded from the bi-level optimization model by application of the model on a real transportation network of the city of Genoa, Italy.

A Mixed Equilibrium Model and Optimal Path Platooning Method for CAV Platoons in Heterogeneous Traffic Flow

As the emergence of the connected and autonomous vehicles (CAVs), the platooning technology is believed to play a key role in the future intelligent transportation system. However, current studies mainly focus on the beneficial sides of CAV platoons, and less attention is given to their negative effects. This study develops a mixed equilibrium model for CAV platoons and human-driven vehicles (HDVs), which consider both the positive and negative sides of CAV platooning. On the positive side, CAV platoons are assumed to follow user equilibrium (UE) route choice for their information advantages, while HDVs to follow stochastic user equilibrium (SUE). CAV platoons are also presumed to improve the road capacity. On the negative side, the speed of CAV platoons is slower than that of HDVs for safety stakes, which will impede the latter to overtake. The HDVs is split up into overtaking and nonovertaking flows with different speeds. Furthermore, the model is built up as a mixed UE-SUE equilibrium problem and reformulated as a nonlinear complementarity problem. In addition, an optimal path platooning method is proposed to reduce the negative effects, by integrating travel costs of both CAV platoons and HDVs into its objective function. Numerical results show that the introduction of CAV platoons may increase the travel cost at the initial stage, and the proposed method can effectively reduce the platooning disturbance, thus helps promoting the wider applications of CAV platoons.

Impact Evaluation of Network Structure Differentiation on Traffic Noise during Road Network Design

To evaluate the characteristics of traffic noise under different network structures, an evaluation method is established to clarify the mechanism of traffic noise impacted by variational network structures. First, a stochastic user equilibrium (SUE) model considering intersection delays is developed to allocate traffic flows of different network structures, and a flow-based univariate noise prediction model is used to simulate network noise distribution. Secondly, differentiation indexes including the coefficient of inhomogeneity (COI) and the concept of Lane Area Ratio (LAR) are set to quantify the network structure differences. Finally, a structural equation model (SEM) is developed to investigate the influence mechanism of network structure differentiation on traffic noise. The following conclusions are obtained: (1) The impact of network density differentiation on traffic noise is mainly reflected in the changes of road traffic flow and speed. Traffic noise decreases as the network density increases. In this case, when network density increases by 1 km/km2, traffic noise decreases by 1.6 dB. As network density increases, which means a dispensation of traffic flow, traffic noise is diminished by a reduction in traffic flow and speed. (2) The impact of road spatial location differentiation on traffic noise mainly depends on the number of noise sources. Traffic noise increases with the dense distribution of roads. In this case, when the COI increases by 1, the traffic noise increases by 3.0 dB. A higher COI indicates that the region will be exposed to more noise sources, which leads to traffic noise raises. The study can provide an effective basis for traffic noise control at the initial stage of network planning.

Prediction of Traffic Flow considering Electric Vehicle Market Share and Random Charging

This paper mainly studies the multiclass stochastic user equilibrium problem considering the market share of battery electric vehicles (BEVs) and random charging behavior (RCB) in a mixed transport network containing electric vehicles and gasoline vehicles (GVs). In order to analyze the random charging and path choice behaviors of BEV users and extract the differences in travel behaviors between BEV and GV users, an improved logit-based model, multilabel algorithm, and queuing theory are applied. The influencing factors of charging possibility mainly include the initial state of charge (SOC), the SOC at the beginning of charging, and the psychologically acceptable safe SOC threshold arriving at the destination. Diversity choices of user paths and charging locations will result in changes in queuing traffic and differences in queuing time. Conversely, different stations have different queuing dwell times, which will also affect the routing and charging locations for BEVs with RCB. The path-based method of successive averages (MSA) is adopted to solve the model. Through the simulation of the test network Sioux Falls, the equilibrium traffic flow and possible charging flow under different market shares and initial SOC are predicted, and the properties of the model and the feasibility of the algorithm are verified.

Stochastic user equilibrium based spatial-temporal distribution prediction of electric vehicle charging load

As the number of electric vehicles (EVs) connected to the grid increases, the EV electricity demand rises dramatically, affecting the grid’s planning and operation and deepening the coupling of the power and transportation systems. Therefore, accurate spatial–temporal distribution prediction of EV charging load is vital for both power system and coupled power-transportation system studies. This paper proposes a novel method based on stochastic user equilibrium (SUE) for predicting the accurate spatial–temporal distribution of EV charging load synchronized with traffic states. A prediction framework of EV charging load based on SUE and trip chain is proposed, which can effectively reflect the actual behavior of EVs in synchronous traffic states. Then, the extended logit-based SUE and equivalent mathematical model are proposed to obtain more detailed traffic states with intersection turning flows and delays. Meanwhile, the unified reachability and charging models are established to ensure that the trip chain is reachable and the charging characteristics are suitable for different EV types. Finally, the method of the successive averages (MSA) and the Dijkstra-based K-shortest paths algorithms are integrated to solve the proposed framework iteratively with stable convergence. Test results on a realistic traffic network show that the proposed method can effectively reflect the charging and trip characteristics of different EV types while ensuring reachability. And it can also accurately predict the overall and individual EV travel costs and total charging loads in detailed synchronous traffic states. In particular, even in the case of high EV penetration with higher peak-to-valley differences and charging demand, the convergence of the prediction is still stable with even more remarkable prediction effectiveness, especially during peak load hours. Furthermore, the quantitative analysis based on proposed criticality indexes reveals that traffic network failures will affect the network-wide traffic states and EV charging loads with different node-level impact characteristics, which should be considered in joint power-transportation restoration scheduling.

Day-to-Day Dynamic Traffic Flow Assignment Model under Mixed Travel Modes Considering Customized Buses

In recent years, customized buses (CBs), a new form of public travel mode between bus and car, has sprung up in China. Its characteristics include flexible routes, each person having a seat and point-to-point travel have attracted travelers who seek high-quality travel, especially car travelers, alleviating traffic congestion at peak periods and leading to a change in urban travel modes. In addition to providing new travel modes, an exclusive bus lane (EBL) is also an effective means to alleviate traffic congestion. Therefore, this paper establishes link impedance functions under mixed travel modes considering the EBL, including customized buses on different kinds of links, and then presents a day-to-day dynamic traffic flow assignment model based on stochastic user equilibrium (SUE). Some conclusions were summarized by numerical case studies. First, the parameter of travelers’ sensitivity to route travel time affects the speed of traffic flow evolution. When it increases to positive infinity, the final state of the traffic network moves from SUE to deterministic user equilibrium (DUE). Second, the parameter on the degree of dependence of travelers on previous experience can not only influence the value size of actual travel time, but also influence the direction of actual travel time evolution. Third, conventional buses and customized buses have higher transportation efficiency than cars, but if the proportion of conventional bus travelers is too large, the total travel time of all travelers in the traffic network may increase. Fourth, when travel demands increase, the proportion of travelers who choose public transit is required to increase to achieve minimum total travel time. Lastly, from the perspective of the whole traffic network in any case, the EBL is not always beneficial. It is recommended to set EBLs when conventional buses and customized bus flows are heavy, which can be judged based on the model established in this paper.

Dynamic tradable credit scheme for multimodal urban networks

A Tradable Credit Scheme (TCS) is a demand management policy aiming for more sustainable travel behavior. The regulator defines the total credit cap and the credit distribution; it also determines the credit charges for each travel alternative at different times of the day, which modifies the perceived users’ costs. The credit price is determined by trading of credits between travelers. Defining the credit scheme at the urban level and estimating its impacts on user travel decisions and the network congestion dynamics is challenging. We propose a framework wherein travelers change their departure times and choose between solo car driving, Public Transportation (PT), and carpooling to complete their trips under a dynamic TCS, meaning the credit charge is time-dependent. A multimodal macroscopic traffic simulator based on a generalized bathtub model captures the congestion dynamics for the different transport modes. Additionally, we consider different values of time, trip lengths, and desired arrival times for the demand profile.The proposed TCS minimizes the total travel cost, (the sum of all travelers’ travel costs) and the carbon emissions by solving an optimization problem through an iterative method, including an inner loop that updates the users’ choices and credit price under the stochastic user equilibrium principle; and an outer loop that updates the credit charge profile. The methodology is implemented and applied to a realistic test case in Lyon (France). The dynamic TCS profiles result in 36% fewer carbon emissions than static TCS for a total travel cost reduction of 19%. Besides, 94% of the travelers benefit from the TCS as their user costs decrease in the case study. The final results are compared with a more advanced simulation framework, which is too computationally expensive to find the optimal TCS. The proposed TCS is effective with refined traffic dynamics representation.

Market competition oriented air-rail ticket fare optimization

In the business of intermodal passenger transport, fare optimization of intermodal products has significant effects on corporate revenue and passenger travel convenience. This study takes the competitive relationship between high-speed rail (HSR) and airlines as well as carrier connectivity as the starting point, analyzes the advantages and disadvantages of different carriers in the different markets, and researches the optimization of fares. The stochastic user equilibrium model based on elastic demand is used to establish a bi-level programming model for the optimization of fares; the upper and lower models are solved using the particle swarm algorithm and method of successive averages, respectively. The results suggest that airlines are willing to cooperate with the HSR sector and improve the connectivity between aviation and HSR, and a reasonable pricing strategy is more likely to motivate cooperation between aviation and HSR.

Formulation and solution method of bounded path size stochastic user equilibrium models – consistently addressing route overlap and unrealistic routes

Bounded Path Size (BPS) route choice models (Duncan et al, 2021) offer a theoretically consistent and practical approach to dealing with both route overlap and unrealistic routes. It captures correlations between overlapping routes by including correction terms within the probability relations, and has a consistent criterion for assigning zero probabilities to unrealistic routes while eliminating their path size contributions. The present paper establishes Stochastic User Equilibrium (SUE) conditions for BPS models, where the choice sets of realistic routes are equilibrated along with the route flows. Solution existence/uniqueness are addressed. A generic solution algorithm is proposed, where realistic route choice sets are equilibrated from a pre-generated approximated universal set of routes. Numerical experiments on the Sioux Falls and Winnipeg networks show that BPS SUE models can be solved in feasible computation times compared to nonbounded versions, while providing potential for significantly improved robustness to the adopted master route choice set.

Exclusive Bus Lane Allocation Considering Multimodal Traffic Equity Based on Bi-Level Programming

To ensure the equity of exclusive bus lane (EBL) allocation under multimodal traffic conditions, a bi-level programming model is first constructed. The upper-level model is the minimum total system cost considering the Gini coefficient and the lower-level model constructed a stochastic user equilibrium (SUE) model based on logit loading. Secondly, a heuristic algorithm combining an improved genetic algorithm (GA) and a method of the successive average method (MSA) is designed. Finally, the Nguyen and Dupuis networks are used as examples to verify and analyze the effectiveness, superiority and sensitivity of the model and algorithm. The results show that the method can effectively obtain the optimal solution of the upper-level model as 15,004 RMB, the Gini coefficient is 0.31, and the equity is at a relatively reasonable level. Compared with the different allocation schemes, the proposed scheme has a higher bus sharing rate and lower Gini coefficient. At the same time, when the actual demand is twice the basic demand, the bus share rate is the largest, 65%, and the Gini coefficient is the smallest at 0.3. The bus share rate decreases with the increase in the proportion of high time value travelers, which fully verifies the sensitivity of the model to the type of traveler.

Reducing congestion and emissions via roadside unit deployment under mixed traffic flow

It is expected that for a long time the future road traffic will be composed of both regular vehicles (RVs) and connected autonomous vehicles (CAVs). As a vehicle-to-infrastructure technology dedicated to facilitating CAV under the mixed traffic flow, roadside units (RSUs) can also improve the quality of information received by CAVs, thereby influencing the routing behavior of CAV users. This paper explores the possibility of leveraging the RSU deployment to affect the route choices of both CAVs and RVs and the adoption rate of CAVs so as to reduce the network congestion and emissions. To this end, we first establish a logit-based stochastic user equilibrium model to capture drivers’ route choice and vehicle type choice behaviors provided the RSU deployment plan is given. Particularly, CAV users’ perception error can be reduced by higher CAV penetration and denser RSUs deployed on the road due to the improved information quality. With the established equilibrium model, the RSU deployment problem is then formulated as a mathematical program with equilibrium constraints. An active-set algorithm is presented to solve the deployment problem efficiently. Numerical results suggest that an optimal RSU deployment plan can effectively drive the system towards one with lower network delay and emissions.

Stochastic ridesharing equilibrium problem with compensation optimization

In the urban traffic system with ridesharing programs, we develop a generalized stochastic user equilibrium model to formulate travelers’ mode and route choice behavior. To suit more general scenarios, the proposed model takes into consideration travelers’ heterogeneity in terms of car ownership and value of time, and travelers’ limited perceived information based on the stochastic user equilibrium principle instead of Wardrop’s user equilibrium principle. The proposed model is formulated as variational inequalities and an equivalent nonlinear mixed complementarity problem due to the inseparable and asymmetric travel cost functions. Furthermore, we address the decision-making problem of ridesharing compensation from the perspective of traffic managers and policy-makers who want to minimize the total travel cost and vehicular air pollution emissions simultaneously. A bi-objective optimization model and two single-objective optimization models are proposed to formulate this decision-making problem, in which travelers’ mode and route choice behavior has been respected. As a mathematical problem with complementarity constraints, the bi-objective optimization model is solved by an improved Non-Dominated Sorting Genetic Algorithm II to generate a set of Pareto-optimal solutions for policy-makers and allow them to choose desired solutions. Finally, several numerical experiments based on two different scales of networks are conducted to demonstrate the properties of the problem and the performance of the proposed model and algorithm. The results show that rational pricing of ridesharing compensation can indeed mitigate urban traffic congestion and pollution emissions simultaneously. Moreover, by integrating travelers’ choice behavior based on the stochastic user equilibrium principle instead of the user equilibrium principle in the ridesharing compensation optimization model, this study derives a series of more effective decision-making strategies for ridesharing compensation.

On Endogenously Distinguishing Inactive Paths in Stochastic User Equilibrium: A Convex Programming Approach with a Truncated Path Choice Model

On Endogenously Distinguishing Inactive Paths in Stochastic User Equilibrium: A Convex Programming Approach with a Truncated Path Choice Model

Stochastic Traffic assignment with Electric Vehicles: a convex optimization approach

Electric vehicles and charging stations are increasing worldwide to reduce emissions at the city level. In order to analyze traffic flows and quantify the demand for energy recharge, it is necessary to model users’ choices considering different kinds of traffic flows. In this paper, attention is focused on the formalization of the joint traffic and energy demand assignment conditions over a traffic network in presence of electric vehicles (EVs). Specifically, the so-called stochastic user equilibrium (SUE) conditions are used to define the steady state behaviour of a generic traffic network in which some arcs are equipped with EV charging stations. A convex optimization problem is defined and solved, which is equivalent to the solution of the nonlinear and nonconvex set of SUE conditions under a multinomial Logit user's choice function. A real case study, related to a touristic area in the Liguria Region (from Genova airport to Portofino), is considered.

Effects of congestion charging and subsidy policy on vehicle flow and revenue with user heterogeneity.

Traffic congestion is a major issue in urban traffic networks. Both congestion charging and subsidy policy can solve traffic congestion to some extent, but which one is better? Based on this, this paper constructs a typical transit network consisting of three travel tools in four common travel modes. Travelers' values of time affect their choice of transportation in the congestion network, thus a stochastic user equilibrium model is established by considering travelers' heterogenous values of time to evaluate the effects of different combinations of congestion charging and subsidy policies on vehicle flow and revenue. Numerical results indicate that the effectiveness of congestion charging and subsidy policy in alleviating traffic congestion depends on the object of charging or subsidizing. Congestion charging for private cars can reduce traffic flow and alleviate traffic congestion, but charging for ridesharing cars does not reduce traffic flow and may even cause traffic congestion. Subsidizing public buses does not reduce traffic flow, but it can ease congestion by coordinating traffic flow on both edges of the dual-modal transport. The combination of no subsidy for public buses and charging for both private cars and ridesharing cars can obtain the greatest revenue, but it does not alleviate traffic congestion. Although the combination of charging for private cars and subsidizing public buses does not bring the most benefits, it can reduce traffic flow, and its revenue is also considerable. This study can provide quantitative decision support for the government to ease traffic congestion and improve government revenue.

Environmental sustainability or equity in welfare? Analysing passenger flows of a mass rapid transit system with heterogeneous demand

Comfort could be one of the major factors influencing demand for public transit systems across income groups. Those in the high-income group, typically car owners, value comfort more than those in the traditionally captive low-income group. This paper examines the heterogenous effect of crowding on mode choice and the subsequent demand for mass rapid transit (MRT) system across income groups using stated-preference data collected from Dhaka, Bangladesh. The crowding variable was incorporated into mixed logit models as a Bureau of Public Roads (BPR)-type function, establishing non-linear sensitivity of different income groups to the effect of crowding on mode choice. We then estimate equilibrium passenger flows for different income groups for multiple scenarios based on varying levels of fares and capacity under the stochastic user equilibrium (SUE) condition. The consumer surplus, revenue, and total surplus associated with each scenario were calculated. The findings show that fares that maximize social welfare are not equitable as they result in very low MRT demand among the low-income group. Meanwhile, higher fares result in greater demand for MRT among the high-income group, improved social welfare, and less total car use. These results highlight the trade-off between an equitable public transport system and environmental sustainability.

Time-dependent pricing strategies for metro lines considering peak avoidance behaviour of commuters

With growing concerns about travel demand management practices in overcrowded metro systems, it is considered that time-dependent pricing strategies are effective for dealing with the crowding occurring during peak commuting hours. In this study, a bi-level optimisation framework is used to consider the peak avoidance behaviour of commuters in the development of time-dependent pricing strategies. The behavioural sensitivity of commuters to pricing factors is investigated in terms of departure time and mode shift decisions based on a stated preference survey conducted in Beijing, China. The proposed bi-level programming model comprises a multi-objective optimisation model at the upper level and a nested logit-based stochastic user equilibrium model at the lower level. Based on an empirical case study of the Batong line in Beijing metro, nine optimal time-dependent pricing strategies are tailored by representative decision preferences, yielding up to 13.97% decrease in the peak ridership during rush hours.