Linear Programming Formulation for Strategic Dynamic Traffic Assignment

Waller, S. Travis; Fajardo, David; Duell, Melissa; Dixit, Vinayak

doi:10.1007/s11067-013-9187-5

Cited by 27 publications

(21 citation statements)

References 30 publications

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“…() and Waller et al. (). The proposed model relaxed the assumption of proportional demand, hence improved the model fidelity.…”

Section: Resultsmentioning

confidence: 98%

“…() and Waller et al. (), which was formulated as

0true trueprefixmin z (false[x false]) = \sum_{n \in N} \int_{0}^{\infty} \int_{0}^{x_{n}} t_{n} ((), yT) G (T) italicdydT

…”

Section: Problem Formulationmentioning

confidence: 99%

“…Dixit et al. () proposed a strategic user equilibrium under trip variability, which was further expanded in the linear programming formulation for DTA, by dividing it into strategic stage and realized demand stage (Waller et al., ); the link flow will therefore fluctuate corresponding to realized demand.…”

Section: Introduction and Backgroundsmentioning

confidence: 99%

See 2 more Smart Citations

A Strategic User Equilibrium for Independently Distributed Origin‐Destination Demands

Wen

Gardner

Dixit

et al. 2017

Computer aided Civil Eng

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This article proposes an extension of the strategic user equilibrium proposed by Waller and colleagues and Dixit and colleagues. The proposed model relaxes the assumption of proportional Origin‐Destination (O‐D) demand, as it accounts for users’ strategic link choice under independently distributed O‐D demands. The convexity of the mathematical formulation is proved when each O‐D demand is assumed to follow a Poisson distribution independently; link flow distributions and users’ strategic link choice are also proved to be unique. Network performance measures are given analytically. A numerical analysis is conducted on the Sioux Falls network. A Monte Carlo method is used to simulate network performance measures, which are then compared to the results computed from the analytical expression. It is illustrated that the model is capable of accounting for demand volatility while maintaining computation efficiency.

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“…() and Waller et al. (). The proposed model relaxed the assumption of proportional demand, hence improved the model fidelity.…”

Section: Resultsmentioning

confidence: 98%

“…() and Waller et al. (), which was formulated as

0true trueprefixmin z (false[x false]) = \sum_{n \in N} \int_{0}^{\infty} \int_{0}^{x_{n}} t_{n} ((), yT) G (T) italicdydT

…”

Section: Problem Formulationmentioning

confidence: 99%

See 1 more Smart Citation

A Strategic User Equilibrium for Independently Distributed Origin‐Destination Demands

Wen

Gardner

Dixit

et al. 2017

Computer aided Civil Eng

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“…The strategic user equilibrium (Dixit et al., ) effectively accounts for the impact of demand uncertainty subject to Wardrop's UE conditions, and under the static user equilibrium, the computation tractability and simplicity are preserved. The model was extended to the dynamic traffic assignment (Waller et al., ), road pricing scheme (Duell et al., ), and independently distributed O–D demands (Wen et al., ).…”

Section: Literature Reviewmentioning

confidence: 99%

Two Methods to Calibrate the Total Travel Demand and Variability for a Regional Traffic Network

Wen

Gardner

Dixit

et al. 2017

Computer aided Civil Eng

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This article proposes a novel methodology that uses the bi‐level programming formulation to calibrate the expected total demand and the corresponding demand variability of traffic networks. In the bi‐level formulation the upper‐level is either a new maximum likelihood estimation method or a least squares method and the lower‐level is the strategic user equilibrium assignment model (StrUE) which accounts for the day‐to‐day demand volatility. The maximum likelihood method proposed in this article has the ability to utilize information from day‐to‐day observed link flows to provide a unique estimation of the total demand distribution, whereas the least squares method is capable of capturing link flow variations. The lower‐level StrUE model can take the total demand distribution as input, and output a set of link flow distributions which can then be compared to the link‐level observations. The mathematical proof demonstrates the convexity of the model, and the sensitivity to the prediction error is analytically derived. Numerical analysis is conducted to illustrate the efficiency and sensitivity of the proposed model. Some possible future research is discussed in the conclusion.

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“…This means that the occupancy of each vehicle is assumed to equal one. Following most of DTA works (e.g., Ran et al, 1993;Wie et al, 2002;Ban et al, 2008;Friesz et al, 2013;Waller et al, 2013), the network is assumed to be empty initially. We note that if the network was not empty initially, the procedures of dynamic network loading and travel time determination were required slight modifications to cater the traffic initially inside the network, and the travel times of flows entering the network were increased if the initial traffic contributed to congestion to the flows and remained unchanged otherwise.…”

Section: Problem Setting and Notationsmentioning

confidence: 99%

An intersection-movement-based stochastic dynamic user optimal route choice model for assessing network performance

Long

Szeto

Huang

et al. 2015

Transportation Research Part B: Methodological

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a b s t r a c tDifferent from traditional methods, this paper formulates the logit-based stochastic dynamic user optimal (SDUO) route choice problem as a fixed point (FP) problem in terms of intersection movement choice probabilities, which contain travelers' route information so that the realistic effects of physical queues can be captured in the formulation when a physical-queue traffic flow model is adopted, and that route enumeration and column generation heuristics can be avoided in the solution procedure when efficient path sets are used. The choice probability can be either destination specific or origin-destination specific, resulting into two formulations. To capture the effect of physical queues in these FP formulations, the link transmission model is modified for the network loading and travel time determination. The self-regulated averaging method (SRAM) was adopted to solve the FP formulations. Numerical examples were developed to illustrate the properties of the problem and the effectiveness of the solution method. The proposed models were further used to evaluate the effect of information quality and road network improvement on the network performance in terms of total system travel time (TSTT) and the cost of total vehicle emissions (CTVE). Numerical results show that providing better information quality, enhancing link outflow capacity, or constructing a new road can lead to poor network performance.

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Linear Programming Formulation for Strategic Dynamic Traffic Assignment

Cited by 27 publications

References 30 publications

A Strategic User Equilibrium for Independently Distributed Origin‐Destination Demands

A Strategic User Equilibrium for Independently Distributed Origin‐Destination Demands

Two Methods to Calibrate the Total Travel Demand and Variability for a Regional Traffic Network

An intersection-movement-based stochastic dynamic user optimal route choice model for assessing network performance

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