Stochastic User Equilibrium Research Articles

Generalized Nested Logit-Based Stochastic User Equilibrium Considering Static Wayfinding Instructions

Generalized Nested Logit-Based Stochastic User Equilibrium Considering Static Wayfinding Instructions

Optimization of the power–transportation coupled power distribution network based on stochastic user equilibrium

With the increasing penetration of electric vehicles (EVs) in road traffic, the spatial and temporal stochasticity of the travel pattern and charging demand of EVs as a mode of transportation and an electrical load have generated different degrees of congestion impacts on both the power grid and the transportation network. Based on this, this paper proposes a power–transportation-coupled distribution network optimization strategy based on stochastic user traffic equilibrium theory. First, a stochastic user equilibrium-mixed traffic flow allocation model that expresses user non-completely rational path selection behavior is established, and the traffic flow equilibrium solution is obtained using an improved method of successive algorithm and mapped to charging loads. Second, a distribution network power flow optimization model under the coupled power–transportation architecture is established to optimize the operation state of the distribution network by combining distributed resources such as energy storage, demand response loads, wind power, photovoltaic, and gas turbines.

Local detouredness: A new phenomenon for modelling route choice and traffic assignment

This study introduces the novel concept of local detouredness, i.e. detours on subsections of a route, as a new phenomenon for understanding and modelling route choice. Traditionally, Stochastic User Equilibrium (SUE) traffic assignment models have been concerned with judging the attractiveness of a route by its total route cost. However, through empirical analysis we show that considering solely the global properties of a route is insufficient. We find that it is important to consider local detouredness both when determining realistic and tractable route choice sets and when determining route choice probabilities. For example, analysis of observed route choice data shows that route usage tends to decay with local detouredness, and that there is an apparent limit on the amount of local detouredness seen as acceptable. No existing models can account for this systematically and consistently, which is the motivation for the new route choice model proposed in this paper: the Bounded Choice Model with Local Detour Threshold (BCM-LDT). The BCM-LDT model incorporates the effect of local detouredness on route choice probability, and has an in-built mechanism that assigns zero probabilities to routes violating a bound on total route costs and/or a threshold on local detouredness. Thereby, the model consistently predicts which routes are used and unused. Moreover, the probability expression is closed-form and continuous. SUE conditions for the BCM-LDT are given, and solution existence is proven. Exploiting the special structure of the problem, a novel solution algorithm is proposed where flow averaging is integrated with a modified branch-and-bound method that iteratively column-generates all routes satisfying local and global bounds. Numerical experiments are conducted on small-scale and large-scale networks, establishing that equilibrated solutions can be found and demonstrating the influence of the BCM-LDT parameters on choice set size and flow allocation.

Exploring the pre-disaster evacuation network design problem under five traffic equilibrium models

This paper explores modeling approaches for the pre-disaster Evacuation Network Design Problem (ENDP) considering different flow equilibrium conditions. We combine this problem with the modeling idea of Continuous Network Design Problem (CNDP), which we call Continuous Evacuation Network Design Problem (CENDP) in this paper. We develop five CENDP models, which are under the consideration of User Equilibrium (UE), Stochastic User Equilibrium (SUE), Boundedly Rational User Equilibrium (BRUE), and Non-equilibrium (NONE), among which we develop two types of models based on BRUE. The modeling is mainly to consider the single objective of optimizing the total evacuation time, and then to provide reasonable road expansion solutions under certain budget constraints and different equilibrium conditions. Our main motivation for developing models is to introduce various types of equilibrium conditions into models and design algorithms to solve these problems while mining for key insights. We design the corresponding five heuristic algorithms to solve models and verify the applicability of the models and algorithms by two test networks (Nguyen-Dupuis network and Sioux-Falls network). We demonstrate whether evacuation flow equilibrium need or not need to be considered in the CENDP, the applicability of different equilibrium conditions, and the correlation between the total evacuation time, the network investment cost, and the network congestion degree. Additionally, we conduct model and algorithm tests on 40 instance networks, dividing them into medium-sized networks (20 instances) and large-sized networks (20 instances). Not only do we further validate the insights obtained from the test networks, but we also expand upon them. Specifically, the main findings of this study are as follows: (1) We demonstrate that considering evacuation flow equilibrium in CENDP is essential to reduce total evacuation time, construction costs, and mitigate congestion. (2) While increased investment in road construction can meet evacuation time requirements, it is crucial to make informed decisions, as investment alone does not directly reduce total evacuation time and congestion. (3) Optimizing road evacuation time is more effective than merely increasing road capacity for reducing total evacuation time and mitigating congestion. (4) From the perspectives of total evacuation time, investment cost, and network congestion degree, the CENDP model considering user equilibrium performs better in medium-sized networks, while the CENDP model considering stochastic user equilibrium performs better in large-sized networks. Conversely, the CENDP model that does not consider flow equilibrium performs the worst across all above three metrics. Based on this, we also provide recommendations on which model to choose for different metrics. In summary, this study not only reveals the importance of different flow equilibrium conditions in evacuation network design but also provides valuable strategic recommendations for practical applications to optimize evacuation effectiveness and resource allocation.

Using traffic assignment models to assist Bayesian inference for origin–destination matrices

Estimation of traffic volumes between each origin and destination of travel is a standard practice in transport engineering. Commonly the available data constitute traffic counts at various locations on the network, supplemented by a survey-based prior estimate of mean origin–destination traffic volumes. Statistical inference in this type of network tomography problem is known to be challenging. Moreover, the difficulties are increased in practice by the presence of a large number of nuisance parameters corresponding to route choice probabilities, for which we have no direct prior information. Working in a Bayesian framework, we determine these parameters using a stochastic user equilibrium route choice model. We develop an MCMC algorithm for model fitting. This requires repeated computation of stochastic user equilibrium flows, and so we develop a computationally cheap emulator. Our methods are tested on numerical examples based on a section of the road network in the English city of Leicester.

Pre-disaster evacuation network design with uncertain demand and behavioural choices: A bi-criteria generalized cost perspective

Pre-disaster evacuation network design is critical to improving evacuation efficiency and reducing the loss of life and property caused by disasters. However, evacuation network design is complicated by the uncertainty of pre-disaster evacuation demand and the heterogeneity of evacuees’ route choices when faced with a disaster scenario. Therefore, how to design efficient evacuation networks considering these uncertainties has become an important research topic. In this paper, we study the pre-disaster flood evacuation network design problem, define a bi-criteria generalized cost metric based on Evacuation Travel Time (ETT) and Evacuation Network Congestion Degree (ENCD), and develop a model that considers uncertain demand and evacuation behavioural choices to minimize the generalized cost in the evacuation network. For the uncertain behavioural choice, we propose an Expanded Stochastic User Equilibrium (ESUE) model based on the Random Regret Minimization (RRM) principle and Boundedly Rational User Equilibrium (BRUE) conditions to describe it. For the uncertain demand, we design a Distributionally Robust Optimization (DRO) method based on Mean Absolute Deviation (MAD) to deal with this uncertain model. This paper designs an Improved Method of Successive Averages Combined with Genetic Algorithm (IMSA-GA) to solve the model and uses the Nguyen-Dupuis test network to verify the applicability and feasibility of the model and algorithm. In addition, we also conduct an evacuation network design in the Hawkesbury-Nepean region of Australia. The larger the threshold value based on the regret utility ratio, the smaller the generalized cost value, which indicates the behavioural choices of the evacuees have an impact on the evacuation network design, and the generalized cost decreases by 6.12% when the threshold value is increased from 0.1 to 0.9. In addition, the generalized cost value obtained by IMSA-GA will be 0.0025 lower than Improved Method of Successive Averages Combined with Simulated Annealing (IMSA-SA) and 0.0005 lower than Improved Method of Successive Averages Combined with Taboo Search (IMSA-TS). The theoretical contribution of this paper is to find an approach to the uncertain evacuation network design problem, especially to improve the practicality of the model by fully considering evacuation behaviour. The practical contribution is that our findings can provide insights for government authorities to design efficient and reliable evacuation networks that balance evacuation travel time and evacuation network congestion. In the future, if evacuation behavioural choices can be analysed based on actual surveys, the estimation of behavioural parameters based on survey data will be more instructive for the evacuation process.

Urban network noise control based on road grade optimization considering comprehensive traffic environment benefit

A double-decision optimization model based on the road grade optimization strategy and considered comprehensive traffic environment benefit is proposed to control the traffic noise. The upper-level model maximizes the comprehensive traffic environment benefit, including network noise emission and traffic efficiency. Adjusting the emphasis on noise optimization benefits and traffic efficiency in road network planning through setting weights. The lower-level resolves the question of network traffic flow assignment using a stochastic user-equilibrium model. The increase of traffic environment demand, network noise emissions decrease and travel time rises. In the case, with a low environmental requirement (weighting with 1.1), the sound pressure emission of the network decreases by 9.23% with only a 4.01% increase in travel time. Under the high environmental requirement (weighting with 0.2), the sound pressure decreases by 26.8%, but the travel time rises by as high as 30.9%. The network is optimized towards road grade degradation and is the first to optimize the arterial roads. In addition, it is found that the influence of speed on traffic noise is greater than that of traffic volume through case validation. This method proposing traffic noise optimization strategies at the road network planning level provides technical support for the proactive governance of traffic noise pollution and the improvement of traffic sound environment quality.

A variational inequality formulation for stochastic user equilibrium with a bounded choice set

This study develops a variational inequality (VI) formulation for the stochastic user equilibrium with a bounded choice set, known as the bounded choice model (BCM). A novel mapping is devised to facilitate the development of the VI formulation. The VI formulation offers a new avenue for analysing and solving the BCM. It is shown that all paths in the considered choice set should have an equal mapping at the optimal solution, which resembles the equilibrated travel cost in the user equilibrium (UE). The new formulation has two algorithmic benefits. First, an algorithm that solves a VI problem (i.e., the extragradient method) can outperform the method of successive averages (MSA) in large networks under a UE-type convergent measurement. Second, it is possible to avoid the column reduction procedure when finding the choice set that satisfies the BCM requirement because a projection-type algorithm that solves the VI formulation can assign zero flow to a path. This is more efficient than the MSA, which uses diminishing step sizes to update solutions over iterations, leading to a sublinear rate of convergence and small residual flows on paths that should carry zero flows. Numerical experiments are conducted to demonstrate the properties of the model and compare the performance of different algorithms using the Sioux Falls, Eastern Massachusetts, and Anaheim networks.

System capacity model and algorithm for urban multimodal transport network with transfer

ABSTRACT This paper proposes a method for calculating transport networks capacity in dealing with multimodal transfers. Multimodal networks are represented by a modified ‘supernetwork’, while the passenger’s travels are defined as ‘superpaths’. Within this framework, the relation between the travel demand from O-D matrices and the resulting link flows in the supernetwork is modelled as a relationship matrix to describe urban mobility by using a logit-based stochastic user equilibrium. Based on this relationship matrix, an approximate iteration algorithm (AIA) is developed. Our numerical results show that the AIA performs better than the sensitivity analysis-based algorithm (SAB) and genetic algorithm (GA) regarding the execution-time, and that the capacity of multimodal transport networks can be underestimated if the combined travels are neglected.

Vulnerability analysis of public transit systems from the perspective of the traffic situation

The critical to sustainable urban development that a robust bus transit system is constructed to alleviate urban congestion problems. Unfortunately, disruptions in bus transit systems can lead to dysfunction and threaten sustainable development. This paper proposed a vulnerability analysis model for constructing complementary urban bus networks (UBNs), which considers the actual capacity of the bus network at the speed of transport roads. In addition, the UBNs aimed analysis method is presented from three specific aspects: (a) utilizing the stochastic user equilibrium model and different traffic situations to measure the UBNs of passenger flow distribution according to multi-source data; (b) introducing the node capacity and structural, functional vulnerability analysis model by combining real traffic flows and the complex network theory; (c) analysing the vulnerability characteristics of UBNs cascading failures from different passenger flow distributions and increasing capacity parameters, and comparing with those under different attack methods. Then, the new vulnerability analysis model is applied to the Harbin trunk bus. Considering different attack scenarios, the UBNs show strong vulnerability in the case of high congestion. Compared with other deliberate attacks, the bus network based on the attack mode of the maximum intensity site is more vulnerable at different times. These insights could be used to inform a vulnerability-based spatiotemporal design of bus transit networks.

Link criticality index: Refinement, framework extension, and a case study

The link criticality index (LCI) is a network performance-based measure that assesses criticality of network links based on flow fluctuations during traffic assignment. Unlike other network performance-based methods, LCI does not require link removal or multiple traffic assignments, and can account for topology, redundancy, congestion, and traveler behavior. However, the original LCI is based on a deterministic user equilibrium (UE) framework, which may lead to two issues: (i) a link's criticality index can be affected by origin-destination (O-D) pairs even if their demand is routed away from the link and (ii) identical links can be ranked unequally. In this paper, we suggest a refinement to the functional form of LCI to cater to analysts who prefer to work within the UE framework; and we extend the LCI measure to stochastic user equilibrium (SUE) and SUE with elastic demand (ED). These extensions resolve the issues related to UE-based LCI and add to the behavioral realism of the network model. To demonstrate validity of concept, the resulting LCI measure is applied to assess the criticality of bridges in Winnipeg, Canada. The obtained results are reasonable and consistent with the previous methods based on the full-network scan approach.

Modeling elasticity, similarity, stochasticity, and congestion in a network equilibrium framework using a paired combinatorial weibit choice model

In the traffic assignment problem for predicting traffic flow patterns in a transportation network, it is important to account for route overlap and non-identical perception variance in route choice analysis. In this study, we establish a novel route choice model, named the paired combinatorial weibit (PCW) model, to capture the route overlap and route-specific perception variance. The PCW model retains a closed-form probability solution, which allows the development of an equivalent mathematical programming (MP) formulation for the PCW-based stochastic user equilibrium (PCW-SUE) model. Specifically, we propose two equivalent MP formulations for modeling the fixed demand (FD) and elastic demand (ED), named PCW-SUE-FD and PCW-SUE-ED, respectively. The PCW-SUE-ED model can address the abovementioned two issues in route choice for the FD scheme, but also can consider the effect level-of-service (LOS) in travel choice for the ED scheme. The equivalency and uniqueness of the PCW-SUE-FD and PCW-SUE-ED models are rigorously proved. In addition, a path-based partial linearization algorithm combined with a self-regulated averaging line search strategy is developed to solve the two SUE models. Numerical results are presented to illustrate the features of the PCW-SUE-FD and PCW-SUE-ED models and applicability of the solution algorithm to a real transportation network.

Estimating network flow and travel behavior using day-to-day system-level data: A computational graph approach

To estimate network flow and travel behavior under recurrent traffic conditions, we leverage computational graphs and multi-source system-level data and solve a single-level optimization problem consistent with stochastic user equilibrium under logit assignment (SUELOGIT). Our model learns time-specific O-D matrices and utility functions and network flow parameters such as link flows, path flows, and travel times. To increase the model’s representational capacity for reproducing observed link flows and travel times, the parameters of the link performance functions are assumed link-specific. More importantly, the utility function in the route choice model is enriched with (i) link-specific parameters to capture the effect of unobserved attributes on route choices and (ii) period-specific parameters weighting the observed features in the utility function to capture the heterogeneity of travelers preferences among periods of the day. Experiments on synthetic data show that the parameters of the models can be consistently recovered and that the solution of the model satisfies the SUELOGIT conditions with high accuracy. The estimation procedure is also robust to random noise in both the observed traffic flow and travel time, and it requires very few hyperparameter tuning. Subsequently, the algorithm is deployed at a large scale using real-world multi-source data in Fresno, CA, with hourly data collected during the morning and afternoon peak periods of October 2019. The utility function includes link-specific effects and attributes such as travel time, the standard deviation of travel time, the number of traffic incidents, and socio-demographic information obtained from the US Census. We obtain estimates for the total trips and travelers’ utility function by hour of the day and for the average values of the link performance parameters that are reasonable and informative on the demand and supply characteristics of the transportation network.

Hydrogen station allocation under stochastic user-equilibrium network flow

A model to locate hydrogen refueling stations (HRSs) for hydrogen fuel cells vehicles (HFCVs) or hydrogen internal combustion engines vehicles (HICEVs) is proposed in this paper. The model integrated the flow-capturing location allocation (FCLA) model and stochastic user-equilibrium (SUE) status of network flow. An equilibrium algorithm obviating cannibalization was also presented. We compared the effectiveness between node location and link location determined by FCLA between SUE status and non-equilibrium status of the transportation network taking the city of Anaheim in California in America as an example. The results showed that the capture ratios of node-serving and link-serving are different. For the non-equilibrium case, equilibrium case, and hybrid case, the capture ratios of node-serving are 77.72%, 69.51%, and 60.25%, respectively, while the capture ratios of link-serving are 54.37%, 46.34%, and 31.49%, respectively. This means Node-serving performs better than link-serving in terms of capturing flow, either in equilibrium status or non-equilibrium status. The node locations or link locations obtained by the FCLA method in SUE status should be used for locating HRSs because they are consistent with peoples’ route choice behavior and thus can fully capture the expected flow in reality. Practically speaking, link locations are preferable to node locations in locating HRSs because the construction and operation of HRSs on nodes are relatively difficult to implement.

Customer segmentation, pricing, and lead time decisions: A stochastic-user-equilibrium perspective

Multiple price/lead time options are often used as a competitive tool in supply chain operations when customers have heterogeneous price and lead time preferences. We study a two-echelon supply chain network consisting of manufacturers and retailers facing customers that differ in their price- and time-sensitivity. We examine how many price/lead time options should be provided by manufacturers and retailers under decentralized and centralized supply chain management with time-cost tradeoffs. We adopt a stochastic-user-equilibrium (SUE) approach in a supply chain network by incorporating discrete choice theory and using a multinomial logit-based variational inequality to express equilibrium conditions. This is one of the first papers to study time-cost tradeoffs in a supply chain network by introducing an SUE approach. One critical part of our analysis is the establishment of concavity of profit functions, which allows for analytical derivation of the equilibrium strategies. Another critical part of our analysis is the development of SUE conditions in decentralized and centralized supply chain networks. We demonstrate that the variance of heterogeneous customers’ time-sensitivity distribution plays a crucial role in customer segmentations in a time-cost tradeoff supply chain. We find that under SUE conditions, there exists a unique equilibrium in the decentralized and centralized supply chain networks, respectively. We conduct comparative statics analyze to demonstrate the effect of SUE and UE conditions and the influence of decentralized versus centralized supply chain management paradigms. We show how the SUE approach can be applied to supply chain network management with time-cost tradeoffs. Our approach can be extended to other tradeoff decision problems in supply chain network management, especially those in which customers are heterogeneous.

Integrating ride-hailing services with public transport: a stochastic user equilibrium model for multimodal transport systems

Public transport (PT) agencies are increasingly keen on integrating ride-hailing (RH) services with PT to improve overall mobility. Understanding the traffic flow distribution in the integrated system is vital for the policy decision-making and services design of such a system. We propose a stochastic user equilibrium (SUE) model for multimodal transport systems consisting of private car, PT and RH. The travel costs in the SUE model are investigated using a multimodal graph representation to capture the relationship of different travel modes in the integrated system. We apply the proposed model to a toy case and a real-world case. A RH subsidy strategy is compared with the benchmark to demonstrate travellers’ route and mode shifts in the integrated system. Our findings offer insights on subsidising RH services through the proposed model, and provide valuable knowledge on the planning and design of the integrated system.

Reinforcement learning of route choice considering traveler’s preference

ABSTRACT Travelers always perform some preference during the decision-making process. The preference will affect the decision results and can be improved by continuously learning. In order to understand the influence of individual preference on travel behavior choice , two individual preferences, including indifference preference and compulsive preference are considered in the paper. Two updating mechanisms of compulsive preference are proposed to obtain the choosing probability of all alternatives. Reinforcement learning models are established integrating the gain stimulating and loss stimulating considering expected utility. Nguyen Dupuis network is adopted for numerical simulation to study the updating process. Simulation results denote that the equilibrium state is much more efficient when preference learning mechanism is considered comparing with the traditional stochastic user equilibrium model, and can decrease the total travel time greatly, which can be applied for urban traffic management. Personalized traffic guidance is the effective solution to traffic congestion in the future

Impact of customer portrait information superiority on competitive pricing of EV fast-charging stations

The rapid development of electric vehicles (EVs) has increased the demand for public fast-charging stations (FCSs). Multiple self-interested charging service operators (CSOs) in an urban transportation network compete with each other through pricing signals to maximize their respective profits, where the information about customer demands and heterogeneous preferences work as important decision criteria. With the prevailing data transaction, the information superiority differences between CSOs may significantly affect the competitive pattern in the charging market. In this study, a Nash-Stackelberg-Nash game framework is established to investigate the strategic pricing of CSOs under different information distribution scenarios. The customer response pattern, namely, the routing and charging choices of EV drivers to pricing signals, is described via a computationally efficient extended stochastic user equilibrium model comprehensively considering heterogeneous customer preferences and decision stochasticity. Then, aiming at different data forms, both parameter-driven and sample-driven CSO pricing models are proposed. The pricing models are reformulated as a tractable single-level mixed-integer linear program, and the game equilibrium is solved alternately via Gauss-Seidel iteration. Numerical simulations are conducted to analyze the impact of single CSO information superiority and double CSO information distribution on CSO profitability and customer experience in both data forms. The influences of endogenous factors like CSO data amount and processing ability, as well as exogenous scenario parameters like customer preference distribution and perception error distribution, are discussed.

A Systematic Approach for the Calibration of Route Choice Models Based on Stochastic User Equilibrium

Different from the traditional deterministic user equilibrium (DUE) model based on fixed travel time, the stochastic user equilibrium (SUE) model is established by assuming the perceived route travel time as a random variable. It plays an important role in traffic assignment, wherein the setting of route choice parameters decides system performance. This article studies parameter calibration of widely used SUE models including the multinomial logit (MNL), length-based C-logit (LCL), and congestion-based C-logit (CCL) models. We establish a bilevel model in which the upper level is designed to minimize the error between the real and model-based traffic flow patterns, whereas the lower level copes with the SUE traffic assignment. A series of innovative methods are built to solve this bilevel model. Considering the nonlinear calibration problem in the upper level, a Bayesian optimization method is used. For the SUE traffic assignment in the lower level, dedicated algorithms are proposed, which combine a partial linearization algorithm and a feasible direction method. Furthermore, two revised solution methods are provided: a Barzilai–Borwein (BB) step-size method and a parallel framework. Finally, the proposed model and corresponding solution approach are validated based on a case study of Yuyao, China. Solutions show that the CCL SUE model has the highest precision while requiring the longest computation time. LCL takes only 11.7% of the computation time of CCL when reaching an acceptable precision.

An Evolutionary Game of Perception-Based Stochastic User-Equilibrium in a Parallel Network

In recent years, advanced information communication technology (such as beyond 5G and 6G) will enable convenient end-to-end communication. This would allow collections of individual preferences as predictions of travellers’ perceptions, and thus support data analysis and traffic control in a dynamic circumstance. Therefore, analysis of nonlinearly modelled perceptions and perception-based user equilibrium are the necessary problem we encounter. This research explores the existence characteristics of perception-based stochastic user equilibrium (P-SUE), a type of stochastic user equilibrium where travelers make route choices according to their perceptive traffic circumstances instead of actual ones. A nonlinear perception model with stochasticity is developed and the traffic arrivals are approximately transformed from Poisson-distributed to Normal-distributed. From a static perspective, we develop a P-SUE model with a heterogeneous traveler community and discuss the interaction among travelers’ attitude, grouping and static perception-based stochastic user equilibrium (P-SSUE). After embedding a day-to-day learning process into the P-SSUE model, we further explore evolutionary dynamics of the equilibrium. Several scenarios are provided to investigate effects and sensitivity of traveler-related and road-related factors. It is found that learning produces perturbation and makes the existence condition of P-SSUE more complicated; the convergence processes of P-SSUEs are significantly shortened as the learning rate increases to higher than 0.1.