Stochastic Dynamic Traffic Assignment Research Articles

Route Guidance Model with Limited Overlap on Freeway Network under Traffic Incidents

With the increasing density of the freeway network, frequent traffic incidents on road segments have a significant impact on the operational efficiency of the road network. Therefore, it has become urgent and important to study traffic route guidance strategy on the road network level. The previous traffic route guidance method primarily focused on the congestion on the road segments where incidents occurred, with insufficient attention given to the impact of congestion on the road network level. In this study, a route guidance model with limited overlap is proposed to improve freeway network reliability under traffic incidents. Specifically, in order to explore alternative paths, we conducted a study on the problem of finding k-short paths with limited overlap. The objective is to identify a set of k-paths that are both sufficiently dissimilar and as short as possible. Then, we promptly update the route guidance information using a stochastic dynamic traffic assignment model that aligns with travelers’ path choice psychology. Moreover, we use the reliability of the road network to evaluate the network performance. To illustrate the model, the Jinan freeway network is selected as an experimental study. The effectiveness of this method was validated through SUMO simulations, comparing it with alternative route guidance methods, including Yen’s algorithm, A∗ algorithm, and ant colony algorithm. These results show that the proposed method has proven effective in mitigating traffic congestion arising from incidents and performs well in regard to the reliability of the road network under the impact of incidents.

A Markovian approach for stochastic dynamic traffic assignment

A Markovian approach for stochastic dynamic traffic assignment

A Stochastic Dynamic Traffic Assignment Model for Emergency Evacuations That Considers Background Traffic

In this work, we present a stochastic dynamic traffic assignment model for emergency evacuations that considers background traffic. First, the equilibrium functions of the entry time and path choice are formulated based on the logit model. The constraints of this formulation include the state equation, propagation function, and conservation. The proposed equilibrium functions are formulated as a variational inequality problem, which is solved by the dynamic traffic network demand loading iterative method. Based on a case study in Wenling, China, we verify the proposed model on the basis of iterative evolution, path assignment, and model comparison. In addition, we perform sensitivity analysis of four relevant parameters, namely, the length of the time interval, total number of evacuation vehicles, perception error parameters of the total travel cost, and path travel cost. The results make it evident that the proposed model assists evacuation planners to effectively understand real-time dynamic changes of evacuation vehicles and the influence of background vehicles and to generate optimal emergency plans.

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

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

Model and algorithm of stochastic dynamic traffic assignment based on dynamic rainfall intensity

Frequent occurrence of urban rainy weather, especially rainstorm weather, affects transportation operation and safety, so it is essential that effective intervention measures to recover disordered traffic be adopted and then analyzed for their influence on the dynamic network. Therefore, models and algorithm to show dynamic traffic flow of traffic network in rainy weather are a fundamental need and have drawn great interest from governments and scholars. In this paper, innovative content contains a travel cost function considering rainfall intensity; considering the travel cost function, a dynamic traffic assignment model based on dynamic rainfall intensity is built. Then a corresponding algorithm is designed. Moreover, this study designs three scenarios under rainfall and analyzes the influence of the rainfall on an example network. The results show that rainfall has a significant effect on traffic flow. The finding proved the proposed models and algorithm can express the development trend of path flow rate on a dynamic network under rainfall.

Microscopic Estimation of Road Impedance by Decomposing Traffic Delay into Individual Road Segments: An Analytical Approach

Urban road dynamic impedance calculation is the important basis of dynamic traffic assignment and real-time traffic management and control scheme. The current impedance calculation is mostly based on BPR function, and the BPR function is derived from macroscopic statistical laws, in which the microscopic characteristics of traffic flow are insufficiently described. In order to more accurately express the change laws of traffic impedance at the microscopic level, a stochastic dynamic traffic assignment algorithm based on road impedance function is designed to analyze the time impedance of congested roads under random dynamic traffic assignment under different conditions of road network saturation. Compared with the current model, the comprehensiveness and portability are greatly improved. The results show that the impedance calculation error of this method is less than 10% when the load degree of the road is lower than 0.85, which proves that the method has good precision under unsaturated flow conditions.

Stochastic Dynamic Traffic Assignment Model under Emergent Incidents

Urban emergent incidents affect transportation operation and result in the rapid spread of traffic congestion in network, so it's necessary to analyze the dynamic changes of traffic flow distribution under emergent incidents. Therefore, model and algorithm for the dynamic traffic assignment problem under emergent incidents have been highly concerned by government and scholars. This paper proposes a stochastic dynamic traffic assignment (SDTA) model based user optimum considering the loss of node capacity and change of network structure under traffic and environment emergencies. The Nested Logit model is used to describe the departure time and path choice. Then, the variational inequality formulation is proposed and discrete dynamic network loading algorithm is designed and validated by a numerical example. The results show that the model and algorithm can be used to express the development trend of actual dynamic network under emergency.

Evaluation of Incident Management Impacts Using Stochastic Dynamic Traffic Assignment

In this paper, a dynamic traffic assignment (DTA) formulation with probabilistic capacity constraints is suggested in order to incorporate accident-induced random capacity reductions into evaluation of incident management strategies. For this purpose, a cell transmission model (CTM) based system optimal dynamic traffic assignment (SODTA) formulation is used as the underlying network model. Hypothetical scenarios are devised in which the potential incident management (IM) strategies are assumed to reduce either the average or the variation of the incident duration. For each case, a small scale Monte Carlo simulation is also performed and compared with the analytic results of the stochastic DTA model. It was shown that the stochastic DTA model not only provides the changes in total system travel time within the reliability measure, but it also provides the analytical results which requires significantly less computational burden. The model also incorporates the impacts of rerouting which is not possible with a queuing theory based analysis on a single link. The results also show that rather than reducing the average duration, comparable delay reductions can be achieved by reducing the variance while keeping the average accident duration unchanged. Hence, IM strategies, solely targeting average duration may be deemed not to be successful, yet, they may be an effective policy to reduce delay. Overall, the proposed model provides a computationally efficient network-wide analysis of incident induced delay without ignoring the highly stochastic nature of roadway incidents.

Reliable Shortest Path Problems in Stochastic Time-Dependent Networks

This study investigates the time-dependent reliable shortest path problem (TD-RSPP), which is commonly encountered in congested urban road networks. Two variants of TD-RSPP are considered in this study. The first variant is to determine the earliest arrival time and associated reliable shortest path for a given departure time, referred to as the “forward” TD-RSPP. The second problem is to determine the latest departure time and associated reliable shortest path for a given preferred arrival time, referred as the “backward” TD-RSPP. It is shown in this article that TD-RSPP is not reversible. The backward TD-RSPP cannot be solved by the algorithms designed for the forward problem using the reverse search from destination to origin. In this study, two efficient solution algorithms are proposed to solve the forward and backward TD-RSPP exactly and the optimality of proposed algorithms is rigorously proved. The proposed solution algorithms have potential applications in both advanced traveler information systems and stochastic dynamic traffic assignment models.

A Cell-Based Model for Multi-class Doubly Stochastic Dynamic Traffic Assignment

This article proposes a cell-based multi-class dynamic traffic assignment problem that considers the random evolution of traffic states. Travelers are assumed to select routes based on perceived effective travel time, where effective travel time is the sum of mean travel time and safety margin. The proposed problem is formulated as a fixed point problem, which includes a Monte-Carlo-based stochastic cell transmission model to capture the effect of physical queues and the random evolution of traffic states during flow propagation. The fixed point problem is solved by the self-regulated averaging method. The results illustrate the properties of the problem and the effectiveness of the solution method. The key findings include the following: (1) Reducing perception errors on traffic conditions may not be able to reduce the uncertainty of estimating system performance, (2) Using the self-regulated averaging method can give a much faster rate of convergence in most test cases compared with using the method of successive averages, (3) The combination of the values of the step size parameters highly affects the speed of convergence, (4) A higher demand, a better information quality, or a higher degree of the risk aversion of drivers can lead to a higher computation time, (5) More driver classes do not necessarily result in a longer computation time, and (6) Computation time can be significantly reduced by using small sample sizes in the early stage of solution processes.

Evaluation of VMS-Based Traffic Information Using Multiclass Dynamic Traffic Assignment Model: Experience in Kolkata

The effect of on-road variable message sign (VMS)-based traffic information on mixed traffic stream is evaluated using a multiclass and stochastic dynamic traffic assignment model. Two types of traffic information are considered which differ in terms of the content displayed on VMS board: one, the instantaneous travel time alone (TI-I) and the other instantaneous travel time along with its variation level (TI-II). The work is demonstrated with reference to a case study in Kolkata Metro City. The analysis of study corridors in a dynamic paradigm indicates that VMS-based traffic information can be instrumental for temporal and spatial management of congestion at corridor level. The influence of VMS is found to be more predominant at higher traffic volume levels. The benefit gained under TI-II is estimated marginally higher than that of TI-I which encourages further investigation on VMS displaying multiple items as traffic information.

Evacuation Network Modeling via Dynamic Traffic Assignment with Probabilistic Demand and Capacity Constraints

Two major sources of uncertainty in evacuation modeling are randomness in evacuation demand and roadway capacity. This paper takes these two sources of uncertainty into account in proposing an analytical system-optimal dynamic traffic assignment model with probabilistic demand and capacity constraints. The problem is modeled on the basis of two stochastic modeling approaches considering the problem's constraints, namely, individual chance constraints and joint chance constraints. The probability distributions of random demands and capacities are assumed to be discrete. A solution method customized for stochastic programming models with random discrete right-hand sides is used. The differences in reliability between the two models are discussed with the help of a numerical example. Although use of the proposed stochastic dynamic traffic assignment is not confined to evacuation modeling, it provides an important probabilistic modeling and analysis framework for evacuation modeling in which the demand and capacity uncertainties are vital. Overall, the proposed model enables evacuation planners to obtain results that can be interpreted through well-understood reliability measures instead of deterministic point estimates of the highly stochastic evacuation process.

Multimodal, multiclass stochastic dynamic traffic assignment for evaluating information provision strategies

AbstractA multimodal, multiclass stochastic dynamic traffic assignment model was developed to evaluate pre‐trip and enroute travel information provision strategies. Three different information strategies were examined: user optimum [UO], system optimum [SO] and mixed optimum [MO]. These information provision strategies were analyzed based on the levels of traffic congestion and market penetration rate for the information equipment. Only two modes, bus and car, were used for evaluating and calculating the modal split ratio. Several scenarios were analyzed using day‐to‐day and within day dynamic models. From the results analyzed, it was found that when a traffic manager provides information for drivers using the UO strategy and drivers follow the provided information absolutely, the total travel time may increases over the case with no information. Such worsening occurs when drivers switch their routes and face traffic congestion on the alternative route. This phenomenon is the 'Braess Paradox'.

A chance-constrained based stochastic dynamic traffic assignment model: Analysis, formulation and solution algorithms

This paper is concerned with the system optimum-dynamic traffic assignment (SO-DTA) problem when the time-dependent demands are random variables with known probability distributions. The model is a stochastic extension of a deterministic linear programming formulation for SO-DTA introduced by Ziliaskopoulos (Ziliaskopoulos, A.K., 2000. A linear programming model for the single destination system optimum dynamic traffic assignment problem, Transportation Science, 34, 1–12). The proposed formulation is chance-constrained based and we demonstrate that it provides a robust SO solution with a user specified level of reliability. The model provides numerous insights and can be a useful tool in producing robust control and management strategies that account for uncertainty in applications where SO-DTA is relevant (e.g. evacuation modeling, computing alternate routes around freeway incidents and establishing lower bounds on network performance).

Stochastic quasi-gradient algorithm for the off-line stochastic dynamic traffic assignment problem

This paper proposes a stochastic quasi-gradient (SQG) based algorithm to solve the off-line stochastic dynamic traffic assignment (DTA) problem that explicitly incorporates randomness in O–D demand, as part of a hybrid DTA deployment framework for real-time operations. The problem is formulated as a stochastic programming DTA model with multiple user classes. Due to the complexities introduced by real-time traffic dynamics and system characteristics, well-behaved properties cannot be guaranteed for the resulting formulation and analytical functional forms that adequately capture traffic realism typically do not exist for the associated objective functions. Hence, a simulation-based SQG method that is applicable for a generalized differentiable (locally Lipschitz) non-convex objective function and non-convex constraint set is proposed to solve the problem. Simulation is used to estimate quasi-gradients that are stochastic to incorporate demand randomness. The solution approach is a generalization of the deterministic DTA solution methodology; under it, deterministic DTA models are special cases. Of practical significance, it provides a robust solution for the field deployment of DTA, or an initial solution for hybrid real-time strategies. The solution algorithm searches a larger feasible domain of the solution space, leading to a potentially more robust and computationally more efficient solution than its deterministic counterparts. These advantages are highlighted through simulation experiments.

Formulation and Solution Algorithm for Fuzzy Dynamic Traffic Assignment Model

An issue that is always important in the development of traffic assignment models is how travelers' perceptions of travel time should be modeled. Because travelers rarely have perfect knowledge of the road network or of the travel conditions, they choose routes on the basis of their perceived travel times. Traditionally, travelers' perceived travel times are treated as random variables, leading to the stochastic traffic assignment problem. However, uncertain factors are also observed in the subjective recognition of travel times by travelers, and these can be illustrated as fuzzy variables. Therefore, a fuzzy dynamic traffic assignment model that takes into account the imprecision and the uncertainties in the route choice process is proposed. By modeling the expressions of perceived travel times as fuzzy variables, this model makes possible the description of a traveler's process of choosing a route that is more accurate and realistic than those from its deterministic or stochastic counter parts. The fuzzy perceived link travel time and fuzzy perceived path travel time are defined, and a fuzzy shortest path algorithm is used to find the group of fuzzy shortest paths and to assign traffic to each of them by using the so-called C-logit method. The results of the proposed model are also compared with those from the stochastic dynamic traffic assignment model, and it is demonstrated that the impact of advanced traveler information systems on the traveler's route choice process can be readily incorporated into the proposed model.

Robustness of the off-line a priori stochastic dynamic traffic assignment solution for on-line operations

This paper focuses on the off-line stochastic dynamic traffic assignment (DTA) problem as part of a hybrid framework that combines off-line and on-line strategies to solve the on-line DTA problem. The primary concept involves the explicit recognition of stochasticity in O–D demand and/or network supply conditions to determine a robust off-line a priori solution that serves as the initial solution on-line. This strategy ensures that the computationally intensive components, which exploit historical data, are executed off-line while circumventing the need for very accurate on-line O–D demand forecast models. Thereby, efficient on-line reactive strategies could be used to address unfolding traffic conditions. The paper investigates the robustness of the off-line a priori DTA solution under plausible on-line situations. The results illustrate the superiority of the a priori solution over the currently used mean O–D demand-based solution for on-line route guidance applications.

A Priori Stochastic Dynamic Traffic Assignment for On-Line Operations Under Information Systems

Existing dynamic traffic assignment (DTA) formulations predominantly assume the time-dependent origin-destination (O-D) trip matrix to be known a priori for the planning horizon or require robust a priori O-D predictions. Such assumptions are unduly optimistic for general networks in an on-line operational framework. Also, the associated solution approaches are computationally intensive in a centralized architecture. To address these key on-line issues, a stochastic DTA approach is proposed in which O-D desires are explicitly recognized as random variables. To ensure that the associated solution methodology is feasible for on-line implementation, a combination of on-line and off-line strategies is proposed. In this paper, an a priori optimization strategy is used to address the off-line problem. Experimental results indicate that the off-line solution serves as an effective and robust initial on-line solution.