General stochastic user equilibrium traffic assignment problem with link capacity constraints

The stochastic user equilibrium (SUE) traffic assignment model integrates the concepts of random assignment and Wardrop equilibrium, and it makes the assignment results more reasonable. The conventional Logit-based SUE model is explicitly built upon path flow variables, which encumbers its large-scale applications and further theoretical analyses. In this paper, a link-based SUE traffic assignment model with link capacity constraints is developed by using the network equilibrium modeling approach. The solution equivalence and uniqueness of the proposed model are rigorously proved. An efficient solution algorithm is also proposed to obtain the equilibrium solution. Numerical results indicate that the proposed link-based SUE model can reflect the real route choice behavior of travelers more reasonable and also facilitate the algorithmic development and further theoretical analyses.

Turn‐delays in intersections contribute significantly to travel times and thus route choices in urban networks. However, turns are difficult to handle in traffic assignment models due to the asymmetric Jacobian in the cost functions. The paper describes a model where turn delays have been included in the solution algorithm of Stochastic User Equilibrium (SUE) traffic assignment. When the Jacobian is symmetric, SUE minimises the road users' ‘perceived travel resistances’. This is a probit‐model where the links cost‐functions of the links are traffic dependent. Hereby, overlapping routes are handled in a consistent way. However, no theoretical proof of convergence has been given if the Jacobian is asymmetric, although convergence can be shown probable for model data representing realistic road‐networks. However, according to the authors knowledge SUE with intersection delays have not been tested earlier on a full‐scale network. Therefore, an essential part of the paper presents practical tests of convergence. Both geometric delays and delays caused by other turns are considered for each turn. Signalised and non‐signalised intersections are handled in different ways, as are roundabouts. In signalised intersections a separate model handles queues longer than one green‐period. Green‐waves can also be taken into consideration. The model has been tested on a large‐scale network for Copenhagen with good results. To make it possible to establish the comprehensive data, a GIS‐based ‘expert system’ was implemented (see Nielsen, O.A., Frederiksen, R. D. and Simonsen, N. (1997). Using expert system rules to establish data on intersections and turns in road networks. International Transactions in Operational Research, 5, 513–529.

As the last process of traditional four processes management method, traffic assignment plays an important role both in theory and practice. User Equilibrium (UE) traffic assignment is a basic problem in the field of urban traffic equilibrium assignment and many studies focus on it. Ant colony algorithm is a new simulating evolution algorithm which has solved many typical combinatorial optimization problems. This paper tries to solve UE traffic assignment problem with ant colony algorithm and improve the goal function value and the formula of transition probability according to the character of UE traffic assignment. The algorithm may get brush-fire optimum result and stop earlier in large scale problems. To solve this problem, this paper optimizes the formula of trail pheromone increment and use max-min ant system to limit the concentration of path pheromone into a scope. Finally, a numerical example is given to prove the feasibility and validity of this algorithm; the result is also compared with the one gotten by traditional algorithm.

Algorithms for Solving the Probit Path-Based Stochastic User Equilibrium Traffic Assignment Problem with One or More User Classes

A mathematical programming method for sensitivity analysis of the link-capacitated stochastic user equilibrium model is presented in this article. By the sensitivity matrices, the changes in the network flows can be easily obtained, while some links reach the capacity limits. By link-based stochastic user equilibrium model with link capacity constraints, it is possible to formulate an efficient algorithm for the sensitivity analysis. Two numerical examples are provided for demonstrating the correctness and implementability of the method finally. Since the link capacity is one of the constraints of the model, the method presented here can also be used for the basic model with other constraints.

This study proposes a hybrid deep-learning-metaheuristic framework with a bi-level architecture for road network design problems (NDPs). We train a graph neural network (GNN) to approximate the solution of the user equilibrium (UE) traffic assignment problem and use inferences made by the trained model to calculate fitness function evaluations of a genetic algorithm (GA) to approximate solutions for NDPs. Using three test networks, two NDP variants and an exact solver as benchmark, we show that on average, our proposed framework can provide solutions within 1.5 % gap of the best results in less than 0.5 % of the time used by the exact solution procedure. Our framework can be utilized within an expert system for infrastructure planning to determine the best infrastructure planning and management decisions under different scenarios. Given the flexibility of the framework, it can easily be adapted to many other decision problems that can be modeled as bi-level problems on graphs. Moreover, we foreseen interesting future research directions, thus we also put forward a brief research agenda for this topic. The key observation from our research that can shape future research is that the fitness function evaluation time using the inferences made by the GNN model was in the order of milliseconds, which points to an opportunity and a need for novel heuristics that 1) can cope well with noisy fitness function values provided by deep learning models, and 2) can use the significantly enlarged efficiency of the evaluation step to explore the search space effectively (rather than efficiently). This opens a new avenue for a modern class of metaheuristics that are crafted for use with AI-powered predictors.

This study presents a comprehensive comparative analysis of the effect of route set size on stochastic user equilibrium (SUE) traffic assignment, focusing on both logit-based (Multinomial Logit (MNL) and Path Size Logit (PSL)) and weibit-based models (Multinomial Weibit (MNW) and Path Size Weibit (PSW)). The primary objective is to investigate the influence of route set size on traffic patterns and determine the minimum requisite number of routes for flow stabilization within the SUE framework. The analysis, conducted on the Winnipeg network using a customized Self-Regulated Averaging (SRA) scheme, yields three key findings. First, all models successfully converged, but the weibit-based models (MNW and PSW) converged faster than the logit-based models. Second, an analysis of perceived total travel time demonstrated that the majority of efficiency gains from route inclusion diminish after a threshold of approximately maximum 30 routes to 40 routes per O-D pair, indicating this number is sufficient for achieving stable SUE results in both model families. Third, the weibit-based model was found to be more sensitive to route overlap effects, continuing to adjust flow patterns up to maximum 45 routes per O-D pair, and exhibiting a greater tendency to allocate flow to less overlapping outer roads. This highlights the superior capability of the weibit formulation, which accounts for heterogeneous perception variance, to achieve a more behaviorally realistic equilibrium compared to the logit models.

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.

Most solution methods for the traffic assignment problem can be categorized as either link-based or route-based. Only a few attempts have followed the intermediate, origin-base dapproach. This paper describes the main concepts of a new, origin-based method for the static user equilibrium traffic assignment problem. Computational efficiency in time and memory makes this method suitable for large-scale networks of practical interest. Experimental results show that the new method is especially efficient in finding highly accurate solutions.KeywordsOrigin-based traffic assignmentuser equilibriumnetwork optimization

An improved parallel block coordinate descent (iPBCD) algorithm for solving the user equilibrium traffic assignment problem is proposed. The iPBCD algorithm is developed based on the parallel block coordinate descent algorithm (PBCD). The hybrid flow update policy is investigated to enhance the robustness and performance of the PBCD algorithm. Two update order rules, namely a cyclic rule and a greedy rule are compared for block indices. Then, the block size is optimized using a sensitivity analysis test. Finally, five index-grouping rules are tested for comparative purposes. Numerical experiments indicate that index-grouping rules have a significant influence on convergence: the information-based drop-out rule performs better in terms of convergence and efficiency.

The ongoing quest for transportation electrification with the massive proliferation of EV charging stations (EVCSs) will deepen the interaction and require the further coordination of coupled power and transportation networks (PTN). The individually-owned EVCSs located in an urban transportation network (UTN) will compete using price signals to maximize their respective payoffs. In this paper, a multi-agent deep reinforcement learning (MA-DRL) method is proposed to model the pricing game in UTN and determine the optimal charging prices for a single EVCS. The EVCS charging demand is first analyzed using a modified user equilibrium traffic assignment problem (UE-TAP) with elastic traveling demands and different charging prices. The price competition problem is then formulated as a game with incomplete information in which the market environment is complex due to nonlinear traffic assignments. Thus, the MA-DRL approach is proposed to learn the charging pricing strategies of multiple EVCSs and approximate the Nash Equilibrium (NE) of the pricing game using the incomplete information. The proposed solution will determine the optimal pricing strategies for an EVCS in UTN. The case studies on a 24-node Sioux-Falls network, and the real-world Xi'an and Hangzhou cities are conducted to verify the effectiveness and scalability of the proposed approach.

Strategies to Enhance the Performance of Path‐Based Static Traffic Assignment Algorithms

This paper first analyzes link and route travel time distributions in a degradable road network by assuming a uniform distribution on the capacity of each link. It is postulated that travelers, by acquiring route travel time variability from past experiences, make route decisions based on a travel time budget, which is the summation of the mean route travel time and the safety margin of the travel time. This paper then formulates a novel travel time budget-based stochastic user equilibrium traffic assignment model with multiple user classes and elastic demand as a variational inequality problem. Finally, a numerical example of a small road network is presented to illustrate the properties of the proposed model.

A new approach to solving dynamic user equilibrium traffic assignment problem

User-equilibrium (UE) traffic assignment is widely used in travel forecasting models. Analyses of assignment results often require detailed information about route flows. For a given UE model, total link flows are uniquely determined, but there can be many route flow solutions. Our goal is to evaluate the potential disagreement between different route flow solutions for the same UE model. We considered a case study of a UE model for the Chicago region. We examined 1,000 different UE route flow solutions. Out of 127,248 routes used by UE solutions, 53,134 have alternatives. For 51,748 routes (97%) the flow is completely undetermined, meaning that it is zero in one UE solution and equal to the total origin-destination (O-D) flow in another UE solution. Significant differences were also found in the distribution of users of a given link among O-D pairs (“select link analysis”). We conclude that in analyses that require route flows, it is important to make a proper choice of a specific route flow solution, such as the maximum entropy user equilibrium route flow solution.