Stochastic Traffic Assignment Model Research Articles

A Reliability-Based Stochastic Traffic Assignment Model for Signalized Traffic Network with Consideration of Link Travel Time Correlations

Traffic assignment model (TAM) is an important research issue of urban traffic design and planning. Most of the existing studies are conducted under deterministic conditions. In reality, the link travel time and waiting time at signalized intersections are stochastic due to many uncertain factors in transportation networks. Under this circumstance, this paper proposes a new travel time reliability-based user equilibrium (TRUE) traffic assignment model with consideration of link travel time correlations and waiting time at signalized intersections in stochastic traffic networks. Under the assumption that link travel times and waiting times at signalized intersections follow normal distributions, the proposed model is transformed into a variational inequality (VI) model. It is rigorously proven that there is at least one solution for the VI problem, and the method of successive average (MSA) is employed to solve the proposed model. The numerical experiments are used to illustrate the applications and effectiveness of the proposed model.

A Revised Logit Model for Stochastic Traffic Assignment With a Relatively Stable Dispersion Parameter

The optimal value of the embedded dispersion parameter in the logit-based stochastic traffic assignment (STA) model significantly impacts predicted network flows. It also varies dramatically for different systems. This prevents its application, especially when real-world network flow data are unavailable for model calibration. To address the problem, this article proposes a revised logit model. Rather than the route travel time in the logit model, it characterizes route utilities by using the relative route travel time defined as the quotient of the estimated route travel time with respect to the mean route travel time for routes between corresponding origin–destination (OD) pairs. The model captures the impacts that the heterogeneous mean route travel time for OD pairs has on travelers’ perception errors. Thus, the dispersion parameter in the revised model is much more stable than that in the original one. <p xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">To reduce the revised model’s computation time, this article also proposes a node-based traffic assignment method that can simultaneously load the demand from all origins to one destination into the network. Calibrated results based on large-scale taxi GPS trajectory data in Nanjing and Beijing, China, show that the optimal values of the dispersion parameters in the revised logit-based STA model for the two networks are very close. The calibrated model can replicate observed traffic flows with high accuracy. Hence, the proposed approach can better assist traffic managers in predicting network flows, particularly when real-world data are not available.

A Random Traffic Assignment Model for Networks Based on Discrete Dynamic Bayesian Algorithms

In this paper, a stochastic traffic assignment model for networks is proposed for the study of discrete dynamic Bayesian algorithms. In this paper, we study a feasible method and theoretical system for implementing traffic engineering in networks based on Bayesian algorithm theory. We study the implementation of traffic assignment engineering in conjunction with the network stochastic model: first, we study the Bayesian algorithm theoretical model of control layer stripping in the network based on the discrete dynamic Bayesian algorithm theory and analyze the resource-sharing mechanism in different queuing rules; second, we study the extraction and evaluation theory of traffic assignment for the global view obtained by the control layer of the network and establish the Bayesian algorithm analysis model based on the traffic assignment; subsequently, the routing of bandwidth guarantee and delay guarantee in the network is studied based on Bayesian algorithm model and Bayesian algorithm network random traffic allocation theory. In this paper, a Bayesian algorithm estimation model based on Bayesian algorithm theory is constructed based on network random observed traffic assignment as input data. The model assumes that the roadway traffic distribution follows the network random principle, and based on this assumption, the likelihood function of the roadway online traffic under the network random condition is derived; the prior distribution of the roadway traffic is derived based on the maximum entropy principle; the posterior distribution of the roadway traffic is solved by combining the likelihood function and the prior distribution. The corresponding algorithm is designed for the model with roadway traffic as input, and the reliability of the algorithm is verified in the arithmetic example.

A Day-to-Day Stochastic Traffic Flow Assignment Model Based on Mixed Regulation

In many cases, the final path selection of travellers’ is not the shortest path, due to the limited computing power and high cost of path search. To solve the problem, this paper proposes a day-to-day (DTD) stochastic traffic flow assignment model that regulates the traffic flow based on the travel time (travel cost) and residual congestion of optional paths. The regulation mechanism is called the mixed regulation. Then, the authored proved the existence, uniqueness and stability of the model solution. The proposed model was verified through simulation on a Nguyen-Dupuis road network. The results show that traffic flows and travel times of all paths reached the equilibrium state, thanks to the DTD mixed regulation for 20~30 days. From the traffic flows and congestion degrees of different sections, it can be seen that our model with mixed regulation diverts the traffic flow to the sections with a low congestion degree, and encourages travellers to drive through the sections with a low traffic flow. In addition, the congestion degrees of the four most congested sections decreased by 5.8%, 4%, 7% and 1.2%, respectively, and the entire road network exhibited a slight downward trend in mean congestion degree. These results prove that our model can uniformize the traffic flow, improve the operation efficiency and alleviate the congestion of the road network. These findings shed new light on the control, guidance and planning of traffic flow in road networks.

Optimal shared mobility planning for electric vehicles in the distribution network

Shared electric vehicle (EV) is an emerging component across interdependent power and transportation networks that affect economic, environmental and societal benefits. Studies on how to collaboratively enable the optimal planning of these interacted networks is less explored. In this work, a joint distribution network expansion planning framework integrated with a shared EV charging station is proposed. One of the objectives is to minimise overall investment cost considering operational waiting cost of shared EV charging service and power loss, while the other aims to maximise the utilisation of charging infrastructures. To overcome the difficulties in solving the multi-objective mixed-integer non-linear problem, Tchebycheff decomposition based evolutionary algorithm is modified to find the Pareto front showing the trade-offs between goals above. Besides, stochastic traffic assignment model is used to obtain traffic distribution and travel demand. The final optimal solution is decided by the fuzzy satisficing method. The performance of the proposed approach is evaluated on a 54-node test system. Sensitivity analysis is performed to assess the impact of key parameters from the perspectives of transportation and distribution network sectors. The numerical results demonstrate the capability and feasibility of the proposed method.

Stochastic Collaborative Planning of Electric Vehicle Charging Stations and Power Distribution System

The increasing prevalence of electric vehicles (EVs) calls for the effective planning of the charging infrastructure. In this study, a multi-objective, multistage collaborative planning model is proposed for the coupled EV charging station infrastructure and power distribution network. The planning model aims to minimize the investment and operation costs of the distribution system while maximize the annually captured traffic flow. The uncertainties of EV charging loads are modeled for three different types of charging stations. The FISK's stochastic traffic assignment model is utilized to model realistic traffic flows. And a new class of volume-delay functions, conical congestion functions, is employed to overcome the shortcomings of the conventional Bureau of Public Roads function. The multi-objective evolutionary algorithm based on decomposition (MOEA/D) algorithm is applied to find the nondominated solutions of the proposed collaborative planning model. Finally, simulations based on a 54-node distribution system are conducted to validate the effectiveness of the proposed method.

Path sets size, model specification, or model estimation: Which one matters most in predicting stochastic user equilibrium traffic flow?

Abstract This study aims to make an objective comparative analysis between the relative significance of three crucial modelling aspects involved in the probabilistic analysis of transport networks. The first question to address is the extent to which the size of generated path sets can affect the prediction of the static flow in the path-based traffic assignment paradigm. The importance of this question arises from the fact that the need to generate a large quantity of paths may be perceived by analysts as a preventative reason as to the application of path-based stochastic traffic assignment (STA) models for large-scale networks. A simulated path generation algorithm, which allows the number of generated paths to be under modeller's control, is applied. Findings show that the size of the generated path sets does not substantially affect the flow prediction outcome in this case study. Further investigations with respect to the relative importance of STA model estimation (or equivalently, parameter calibration) and model specification (or equivalently, error term formulation) are also conducted. A paired combinatorial logit (PCL) assignment model with an origin–destination-specific-parameter, along with a heuristic method of model estimation (calibration), is proposed. The proposed model cannot only accommodate the correlation between path utilities, but also accounts for the fact that travelling between different origin–destination (O–D) pairs can correspond to different levels of stochasticity and choice randomness. Results suggest that the estimation of the stochastic user equilibrium (SUE) models can affect the outcome of the flow prediction far more meaningfully than the complexity of the choice model (i.e., model specification).

Vulnerability of road network based on generalised travel time

In this paper the vulnerability of a transportation network is defined from the perspective of the sensitivity of the transportation system against external disturbances. The generalised travel time is defined as the weighting of both the ratio of actual travel time to free travel time and the unreliability of the travel time. The reciprocal of generalised travel time taken as the utility function, the impact of external disturbances on the transportation system can be quantified. Meanwhile, the vulnerability model is established using the change rate of the utility index. The stochastic user equilibrium traffic assignment model is formulated on the assumption of minimisation of travel cost. Finally, the real road network of the city of Harbin in China is taken as an example to illustrate the applicability and efficiency of the proposed model. This approach can be used as a decision-supporting tool for identifying critical infrastructures in transportation management and planning.

Algorithm research for capacity-constrained stochastic traffic assignment model

The paper presents incremental load algorithm and successive equilibrium algorithm to solve the stochastic capacity-constrained traffic assignment model on the base of combining the Fisk's logit assignment optimal theory and Wardrop's optimisation principals. A system optimal quantitative indicator based on minimum O-D average cost principal is developed to evaluate the traffic flow assignment result. The simulation results for a small traffic network show that more reasonable traffic assignment is achieved when using more batches and optimal batch ratios with incremental load algorithm, while, the overall result is superior utilising successive equilibrium algorithm.

Stochastic Traffic Assignment Model Based on Travel Time Reliability

Considering the un-deterministic transportation networks, the paper proposes the change of the route choice decisions under the stochastic transportation networks. The route choice behavior is described as a choice for a time shortest route which is subject to a time-reliability level. The paper also considered this new route choice behavior in the stochastic user equilibrium model, and proposed stochastic user equilibrium model based on the optimized reliability travel time route choice behavior in the stochastic networks. The equivalence and uniqueness of the solution of the model are demonstrated. Numerical results of a small network show that the proposed model can reflect the real traveler’s route choice behavior in stochastic transportation networks.

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.

A Reliability-Based Stochastic Traffic Assignment Model for Network with Multiple User Classes under Uncertainty in Demand

This paper presents a novel reliability-based stochastic user equilibrium traffic assignment model in view of the day-to-day demand fluctuations for multi-class transportation networks. In the model, each class of travelers has a different safety margin for on-time arrival in response to the stochastic travel times raised from demand variations. Travelers' perception errors on travel time are also considered in the model. This model is formulated as an equivalent variational inequality problem, which is solved by the proposed heuristic solution algorithm. Numerical examples are presented to illustrate the applications of the proposed model and the efficiency of solution algorithm.

Network pricing optimization in multi-user and multimodal context with elastic demand

Network Pricing Optimization (NPO) is formulated first as a Network Design Problem (NDP) where the design variables are tolls, the objective function is the Social Surplus and the equilibrium constraint is any current multi-user multimodal stochastic traffic assignment model with elastic demand up to trip generation and asymmetric arc cost function Jacobian. NPO is then formulated also as an Efficient Allocation Problem (EAP), where an optimal flow pattern, the System Optimum (SO), is sought and tolls are consistently determined. Necessary and sufficient conditions for the solutions to both problems are stated, showing the validity of the marginal pricing principle in the context considered.

A stochastic transit assignment model considering differences in passengers utility functions

The paper presents a framework for public traffic assignment that builds on the probit-based model of Sheffi and Powell [Sheffi, Y., Powell, W.B., 1981. A comparison of stochastic and deterministic traffic assignment over congested networks. Transportation Res. B. 15 (1), 53–64; Sheffi, Y., Powell, W.B., 1982. An algorithm, for the equilibrium assignment problem with random link Times. Networks 12 (2), 191–207.]. Hereby, the problems with overlapping routes that occur in many public transport models can be avoided. The probit-based model with modifications similar to the principles in Nielsen [Nielsen, O.A., 1996. Do stochastic traffic assignment models consider differences in road users utility functions? Twentyfourth European Transport Forum (PTRC Annual Meeting). London, UK, Seminar M.] is used as a starting point. This makes it possible to describe passengers’ different preferences towards different sub-modes and against transfers. This also considers dependencies of choices through chains of sub-modes. The simulation of perceived travel times is extended to describe differences in the distribution of travel- and waiting times for different sub-modes. Parallel lines are frequency aggregated in order to handle waiting times appropriately. Initial tests on a full-scale case show that the methodology can describe route choices in public transport very well. This is both due to the model’s ability to describe overlapping routes and due to the many different coefficients, error components and distributions that make it possible to calibrate the model. In practice, the many parameters might also be the main weakness, since this complicates the calibration. At the end of the paper, proposals to coefficients are presented based on a Danish SP-analysis. This demonstrated the applicability of the method.

Estimation of Link Flow Variance by Stochastic Traffic Assignment

A stochastic traffic assignment model for estimating the variance of the link flow is proposed. The covariance matrix of the link flows can be obtained by the proposed solution algorithm together with the estimated link flows. In the proposed model, the perceived and measured path cost errors are assumed to be distributed Gumbel and Normal respectively. The commonality factor recently proposed for overcoming the Independence of Irrelevant Alternatives’(IIA) problems in the route choice logit model is also incorporated in the proposed model. Numerical example on one of the Hong Kong expressway corridors is used for illustrating the application of the model.

A Combined Algorithm for Solving and Calibrating the Stochastic Traffic Assignment Model

This paper studies Fisk's stochastic user equilibrium (SUE) assignment model in which travellers are assumed not to have perfect knowledge of the traffic system. It is shown that the stochastic properties of this model completely depend on the calibration parameter. After giving the searching method of an 'efficient paths' set, a modified combined algorithm for solving and calibrating Fisk's stochastic traffic assignment model is developed. In this algorithm, the path enumeration is achieved automatically in the preliminary phase and renewed in the iterative processes, and the number of alternative paths generated can be controlled by a predetermined function. Two numerical examples are presented to illustrate the model's properties and the algorithm's efficiencies.

A Combined Algorithm for Solving and Calibrating the Stochastic Traffic Assignment Model

A Combined Algorithm for Solving and Calibrating the Stochastic Traffic Assignment Model

A Combined Algorithm for Solving and Calibrating the Stochastic Traffic Assignment Model

A Combined Algorithm for Solving and Calibrating the Stochastic Traffic Assignment Model

Large Population Approximations of a General Stochastic Traffic Assignment Model

Recent interest in stochastic traffic assignment models has been motivated by a need to determine the stationary probability distribution of a network's traffic volumes and by the possibility of using time-series of traffic counts to fit and test travel demand models. Because of the way traffic volumes are generated as the sum of path flows from different origin-destination pairs, and because of the nonlinear nature of the process relating traffic conditions to traveler route selection, most plausible assignment models tend to be intractable. In this paper, we first pose a general stochastic assignment model that includes as special cases most models which have appeared in the literature, and then verify that the probability distributions of an equivalent Markovian model converge to a stationary distribution. We next verify that as the number of individual travelers becomes large, the general model can be approximated by the sum of a nonlinear deterministic process and a time-varying linear Gaussian process. The stationary distribution of this approximation is readily characterized, and the approximation also provides a means for employing linear system methods to estimate model parameters from a set of observed traffic counts. For the case where the route choice probabilities are given by the multinomial logit function, computationally feasible procedures for implementing the approximate model exist.

Algorithms for solving fisk's stochastic traffic assignment model

In this, the logit-based stochastic traffic assignment model is explored. Two new improved algorithms are presented for solving this type of stochastic assignment problem. The major improvement achieved in these algorithms is that the step length in each iteration of the search process is optimized instead of using fixed step lengths as in the existing method of successive averages (MSA).