2013 Session: 451

• Strategies to Decrease the Computational Burden of Path-Based Static Traffic Assignment Algorithms
  Abstract: There are three important stages of path-based algorithms (PBAs) for solving the static user equilibrium traffic assignment problem (STA): finding shortest paths between various origins and destinations based on the present flow conditions to update the path set, updating path flows based on the move direction of the PBA, and updating the link flows and costs. This paper proposes strategies to improve the computational efficiency of these three stages. The first strategy provides a simple method to preclude the through-routing via the zone centroid and helps to avoid unrealistic flow without affecting the flow update process of a PBA. The second strategy seeks to improve the efficiency of the path flow update process by circumventing unnecessary computation. The third strategy proposes faster link flow and link cost update processes along with a link data structure to support it. The computational experiments using two recently developed PBAs validate the effectiveness of these strategies and help to understand their rationale. The strategies are significant from both theoretical and practical perspectives. From a theoretical viewpoint, they help in designing an efficient execution process for PBAs and provide an improved common platform for comparing their performances. For practice, they can reduce the computational cost in finding the solution of the STA without increasing the complexity of the execution of the algorithm.
  Authors: Kumar, Amit; Peeta, Srinivas
  Authors: Kumar, Amit; Peeta, Srinivas
  Year: 2013
  Document Type: Paper
  Subject: Planning and Forecasting
  Session: 451
  Paper Number: 13-0417
• Continuous-Time Dynamic System Optimal for Single-Destination Traffic Networks Considering Queue Spillbacks
  Abstract: Dynamic system optimal (DSO) is a special case of the general dynamic traffic assignment (DTA) and it predicts the optimal traffic states of a network under time-dependent traffic conditions from the perspective of the entire system. In this paper, an optimal control framework is proposed for the continuous-time DSO problem for single-destination traffic networks. Departure time choice is part of the DSO formulation to properly capture the waiting time of vehicles at the origins. The double-queue model is also applied to capture possible queue spillbacks. Solution existence conditions and model properties are discussed. A continuous-time holding-free condition for the DSO model is given. Reformulation schemes of the objective function to achieve desired DSO solutions such as the free-flow and holding-free solutions are proposed. Discretization method is applied and numerical results on a small testing network are shown.
  Authors: Ma, Rui; Ban, Xuegang (Jeff); Pang, Jong-Shi
  Authors: Ma, Rui; Ban, Xuegang (Jeff); Pang, Jong-Shi
  Year: 2013
  Document Type: Paper
  Subject: Planning and Forecasting
  Session: 451
  Paper Number: 13-2752
• Nonholding Back Linear Programming Model for System Optimum Dynamic Traffic Assignment Problem
  Abstract: This paper proposes a non-holding back linear programming (NHBLP) model embedding the cell transmission model (CTM), the basis of which refers to Ziliaskopoulos (2000), to account for the system optimum dynamic traffic assignment problems. The first part of the paper elaborates on the model’s properties which explicitly address most of the limitations from Ziliaskopoulos’s (2000) formulation while preserving the linear nature of the objective function and constraints by introducing the effortless implementable scheme of penalty label for the network. Rigorous proof is presented, complemented with the marginal cost analysis, to show that the optimal solution of the NHBLP formulation completely resolves the unrealistic holding-back issue. The second part of the paper demonstrates the properties of the NHBLP formulation with various test networks. A test network demonstrates the ability to test the route choice behavior in an accident scenario.
  Authors: Zhu, Feng; Ukkusuri, Satish V.
  Authors: Zhu, Feng; Ukkusuri, Satish V.
  Year: 2013
  Document Type: Paper
  Subject: Planning and Forecasting
  Session: 451
  Paper Number: 13-3232
• Novel Integer Program Formulation for Dynamic Traffic Assignment Problem
  Abstract: We propose a novel integer program formulation for the vehicle-based dynamic traffic assignment problem with vehicles from multiple origins to multiple destinations in a transportation network. The objective function of the proposed formation is to minimize total travel time of all the vehicles in the network, which adheres to the system optimal principle of the dynamic traffic assignment problems. The underlying constraints explicitly describe realistic traffic dynamics, i.e. queue formation, spillback, and dispersion, as well as link spillover, in light of the Newell’s simplified Kinematic Wave traffic flow model. We also define a set of vehicle driving policy constraints that obey driving rules in real world and support capacity analyses by traffic engineers at merging nodes to maintain fairness and the first-in-first-out principle. This novel formulation provides a way to integrate the dynamic assignment and network loading in a single optimization model that can be solved by an optimization solver. It can be extended to integrate the activity-based demand and dynamic traffic assignment model to incorporate a rich set of travel choice behavior, and provide normative traffic information for route guidance applications and advanced traffic management in the Intelligent Transportation Systems.
  Authors: Zhang, Kuilin; Zhou, Xuesong; Lu, Chung-Cheng
  Authors: Zhang, Kuilin; Zhou, Xuesong; Lu, Chung-Cheng
  Year: 2013
  Document Type: Paper
  Subject: Planning and Forecasting
  Session: 451
  Paper Number: 13-4180
• Solving Multiclass Percentile User Equilibrium Traffic Assignment Problem: Computational Study
  Abstract: The multi-class percentile user equilibrium (MCPUE) problem concerned in this paper assumes that travelers, subject to uncertainty in the transportation network, strive to minimize the reserved travel time (or travel time budget) to ensure their preferred probability of arriving on-time, which identifies their class. An MCPUE, defined as an extension of the Wardrop equilibrium in a probabilistic network, is achieved when no traveler can reduce their reserved travel time by unilaterally changing their routes. This paper studies efficient numerical procedures for computing MCPUE. Specifically, we design a new gradient projection algorithm that avoids path enumeration through a column generation procedure based on a reliable shortest path algorithm. Implementation details of inner iterations, which is critical to the overall efficiency of the algorithms, are also discussed. Comprehensive numerical experiments are conducted to test the computational performance of the proposed algorithm.
  Authors: Wu, Xing; Nie, Yu
  Authors: Wu, Xing; Nie, Yu
  Year: 2013
  Document Type: Paper
  Subject: Planning and Forecasting
  Session: 451
  Paper Number: 13-4100
• Improved Bush-Based Sensitivity Analysis in Network Equilibrium
  Abstract: Calculating equilibrium sensitivity on a bush can be done very efficiently, and serve as the basis for a network contraction procedure which increases the accuracy of subnetwork analysis. This method requires calculating travel time derivatives between two nodes, with respect to the demand between them, assuming that the flow distributes in a way that equilibrium is maintained. In previous research, the author developed two methods for calculating the necessary travel time sensitivities. This paper presents a third method, which is simpler, faster, and just as accurate. The method presented in this paper reformulates the linear system of equations defining these sensitivities as the solution to a convex programming problem, which can be solved by making minor modifications to static user equilibrium algorithms. Numerical experiments on the Austin, TX regional network validate this performance.
  Authors: Boyles, Stephen
  Authors: Boyles, Stephen
  Year: 2013
  Document Type: Paper
  Subject: Planning and Forecasting
  Session: 451
  Paper Number: 13-4519
• Strategic User Equilibrium Assignment Under Trip Variability
  Abstract: One common criticism of traditional traffic network assignment is the lack of observable equilibrium. It is easy to confirm that traffic networks vary continually due to uncertain travel demand, traffic capacity, or individual behaviour. However, in the traditional deterministic user equilibrium assignment, users select paths to minimize their travel time based on a single known demand value. Even with such issues, equilibrium models have persisted in a planning context due to their important mathematical properties (e.g., solution consistency and convergence). What is needed are new network models which directly account for existing variability while still maintaining the beneficial properties of traditional traffic equilibrium models; ideally, new models which better explain variation but are still as comparably simple and practical as existing methods. To address the aforementioned need, this paper examines strategic network assignment models which ensure that users recognize the variations in travel time to their destination and rationally choose routes while considering all possible demand scenarios in a known distribution. The set of chosen routes are then followed regardless of the specific travel demand on any given day. The strategic assignment model therefore produces link flows which will not result in a state of network equilibrium under specific demand realizations. The proposed strategic assignment problem is analytically formulated, and the link proportions and the variance in travel time for the links are analytically derived. Numerical analysis is conducted, and results are compared with two deterministic user equilibrium assignment models, all evaluated with variable demand.
  Authors: Dixit, Vinayak V.; Gardner, Lauren; Waller, S. Travis
  Authors: Dixit, Vinayak V.; Gardner, Lauren; Waller, S. Travis
  Year: 2013
  Document Type: Paper
  Subject: Planning and Forecasting
  Session: 451
  Paper Number: 13-5103
• Assigning User Class Link Flows Uniquely
  Abstract: The standard method for predicting traffic flows on urban road networks, static user-equilibrium traffic assignment, is based on the principle that drivers seek their own least cost routes from their origins to their destinations. This principle corresponds to a user-equilibrium state in which all used routes have equal costs and no unused route has a lower cost for every origin-destination pair. This problem can be formulated as a convex optimization problem with linear constraints, and solved with an iterative algorithm. Although the total flows on links of the urban road network are uniquely determined by this formulation, multi-class link flows, as well as route flows, are not. An additional assumption, called the condition of proportionality, may be imposed to determine these flows uniquely. This condition was the basis for incorporating a post-processing adjustment into two commercial travel forecasting software systems, TransCAD and Visum, as well as designing a new algorithm called TAPAS. Analyses of class link flows from Visum assignments of cars and trucks to the Chicago regional network, with and without the condition of proportionality, are presented. Differences in class link flows with and without the condition of proportionality are analyzed in relation to link attributes. The findings offer insights into the importance of the condition of proportionality in multi-class road traffic assignments at the link level.
  Authors: Xie, Jun; Boyce, David
  Authors: Xie, Jun; Boyce, David
  Year: 2013
  Document Type: Paper
  Subject: Planning and Forecasting
  Session: 451
  Paper Number: 13-1215
  Practice-Ready: Yes
• Assessment of Adherence to the Condition of Proportionality in User Equilibrium Traffic Assignments with Uniquely Determined Route Flows
  Abstract: The standard formulation of static deterministic user equilibrium (UE) traffic assignment problem based on the criterion of Wardrop provides a unique solution in terms of link flows; however, route flows are not determined uniquely. Analyses based on an arbitrary choice among the infinite number of possible route flow solutions could cause inconsistencies or even controversies in applications. In 2010, a computationally efficient algorithm called Traffic Assignment by Paired Alternative Segments (TAPAS) was successfully implemented to identify UE route flows uniquely. So far, no effort has been made to assess adherence to the condition of proportionality in UE traffic assignment with uniquely determined route flows. In this paper, TAPAS was solved to obtain proportional UE route flows for the Chicago regional network in the closest proximity to uniqueness of the solution. Various assessments of adherence to proportionality are performed for a selected pair of alternative segments. The results show that route flows determined by TAPAS correspond closely to exact proportionality. Only minor differences occur between computed and exactly proportional UE route flows. Systematic characteristics of the plots for the two alternative segments show that TAPAS behaves properly according to the condition of proportionality. Insights from these empirical results may help transportation planning professionals to be aware of the magnitude of differences in UE route flows based on proportionality and to be able to differentiate uniqueness from non-uniqueness of route flows in UE traffic assignment. The results may also be useful to software developers in seeking improved adherence to proportionality of route flow solutions.
  Authors: Aungsuyanon, Aroon; Boyce, David; Ran, Bin
  Authors: Aungsuyanon, Aroon; Boyce, David; Ran, Bin
  Year: 2013
  Document Type: Paper
  Subject: Planning and Forecasting
  Session: 451
  Paper Number: 13-1423
  Practice-Ready: Yes
• Risk Assessment of Stability Properties of Dynamic Network Loading
  Abstract: Over the past decades Dynamic Traffic Assignment models are increasingly used for online and offline applications of various urban environments for the successful and efficient deployment of traffic control strategies and the evaluation of traffic management schemes and policies. The stability of the dynamic network loading procedure is crucial for achieving the most accurate representations of traffic phenomena in congested urban networks, where the increase of congestion level often creates problems of discontinuity and system failure especially when the demand levels are temporally unstable and severe. In this paper a stability analysis is proposed in the context of evaluating the properties of the final resulting dynamic network loading solution through the evolution of time. The scope of this analysis is to provide practitioners and researchers a useful tool for the temporal statistical analysis and risk assessment of the dynamic representation of traffic conditions. The methodology of the proposed stability analysis is implemented on two reference networks. The results for the statistical analysis and the evaluation of the stability properties are discussed over an extensive sensitivity analysis of the simulation step to the selected stability measures.
  Authors: Papatzikou, Eleni; Stathopoulos, Antony
  Authors: Papatzikou, Eleni; Stathopoulos, Antony
  Year: 2013
  Document Type: Paper
  Subject: Planning and Forecasting
  Session: 451
  Paper Number: 13-1476
  Practice-Ready: Yes
• Approximating Time Delays in Solving Continuous-Time Dynamic User Equilibria
  Abstract: We develop an approximation scheme, called ``pseudo-derivative (PD)'' to solving the dynamic user equilibrium (DUE) problem. The PD approximation can convert time-varying, state dependent delays usually involved in DUE to a constant time delay. We study the properties of the proposed PD and the resulting approximate DUE (ADUE) problem after applying the approximation. Some issues of the ADUE, such as the possible violation of the flow conservation at network nodes are also discussed and resolved. It turns out that the original DUE problem can be solved iteratively with an ADUE solved in each iteration. Numerical results are shown on a small testing network and the Sioux Falls network. The results show that the iterative algorithm can converge to some reasonable solution, although a formal convergence proof result is not established in the paper.
  Authors: Ma, Rui; Ban, Xuegang (Jeff); Pang, Jong-Shi; Liu, Henry X.
  Authors: Ma, Rui; Ban, Xuegang (Jeff); Pang, Jong-Shi; Liu, Henry X.
  Year: 2013
  Document Type: Paper
  Subject: Planning and Forecasting
  Session: 451
  Paper Number: 13-2631
  Practice-Ready: Yes
• Does LUCE Outperform OBA? Comparison Study of Two Bush-Based Algorithms for Traffic Assignment Problem
  Abstract: This paper compares two bush-based traffic assignment algorithms, the origin-based algorithm (OBA) and the local user cost equilibrium algorithm (LUCE). The two algorithms are closely related with only one major difference: they solve the decomposed elementary node-based subproblem using different methods. Specifically, LUCE employs a greedy algorithm that is able to solve the subproblem exactly, whereas OBA uses a one-step quasi-Newton method known as gradient projection to solve the subproblem approximately. Therefore, LUCE seems to hold promises to improve OBA because its subproblem solver is presumably faster and more precise. Numerical experiments reported in this paper, however, indicate that LUCE not only provide no obvious computational advantages over OBA, it often fails to converge beyond certain point. The focus of this paper is to find an answer to this counter-intuitive phenomenon. Our analysis suggests that the greedy method used by LUCE require highly accurate estimation of second-order derivatives. When second-order derivatives are subject to large errors, the greedy method can provide consistently sub-optimal descent direction, which it has no mechanism to fix.
  Authors: Xie, Jun; Nie, Yu; Yang, Xiaoguang
  Authors: Xie, Jun; Nie, Yu; Yang, Xiaoguang
  Year: 2013
  Document Type: Paper
  Subject: Planning and Forecasting
  Session: 451
  Paper Number: 13-5174
  Practice-Ready: Yes
• Assigning User Class Link Flows Uniquely
  Authors: Boyce, David
  Authors: Boyce, David
  Year: 2013
  Document Type: Presentation
  Subject: Planning and Forecasting
  Session: 451
  Paper Number: 13-1215
• Assessment of Adherence to the Condition of Proportionality in User Equilibrium Traffic Assignments with Uniquely Determined Route Flows
  Authors: Aungsuyanon, Aroon
  Authors: Aungsuyanon, Aroon
  Year: 2013
  Document Type: Presentation
  Subject: Planning and Forecasting
  Session: 451
  Paper Number: 13-1423
• Strategies to Decrease the Computational Burden of Path-Based Static Traffic Assignment Algorithms
  Authors: Kumar, Amit
  Authors: Kumar, Amit
  Year: 2013
  Document Type: Presentation
  Subject: Planning and Forecasting
  Session: 451
  Paper Number: 13-0417
• Assessment of Adherence to the Condition of Proportionality in User Equilibrium Traffic Assignments with Uniquely Determined Route Flows
  Authors: Boyce, David
  Authors: Boyce, David
  Year: 2013
  Document Type: Presentation
  Subject: Planning and Forecasting
  Session: 451
  Paper Number: 13-1423
• Risk Assessment of Stability Properties of Dynamic Network Loading
  Authors: Papatzikou, Eleni
  Authors: Papatzikou, Eleni
  Year: 2013
  Document Type: Presentation
  Subject: Planning and Forecasting
  Session: 451
  Paper Number: 13-1476
• Approximating Time Delays in Solving Continuous-Time Dynamic User Equilibria
  Authors: Ma, Rui
  Authors: Ma, Rui
  Year: 2013
  Document Type: Presentation
  Subject: Planning and Forecasting
  Session: 451
  Paper Number: 13-2631
• Nonholding Back Linear Programming Model for System Optimum Dynamic Traffic Assignment Problem
  Authors: Zhu, Feng
  Authors: Zhu, Feng
  Year: 2013
  Document Type: Presentation
  Subject: Planning and Forecasting
  Session: 451
  Paper Number: 13-3232
• Continuous-Time Dynamic System Optimal for Single-Destination Traffic Networks Considering Queue Spillbacks
  Authors: Ma, Rui
  Authors: Ma, Rui
  Year: 2013
  Document Type: Presentation
  Subject: Planning and Forecasting
  Session: 451
  Paper Number: 13-2752
• Solving Multiclass Percentile User Equilibrium Traffic Assignment Problem: Computational Study
  Authors: Wu, Xing
  Authors: Wu, Xing
  Year: 2013
  Document Type: Presentation
  Subject: Planning and Forecasting
  Session: 451
  Paper Number: 13-4100
• Novel Integer Program Formulation for Dynamic Traffic Assignment Problem
  Authors: Zhang, Kuilin
  Authors: Zhang, Kuilin
  Year: 2013
  Document Type: Presentation
  Subject: Planning and Forecasting
  Session: 451
  Paper Number: 13-4180
• Improved Bush-Based Sensitivity Analysis in Network Equilibrium
  Authors: Boyles, Stephen
  Authors: Boyles, Stephen
  Year: 2013
  Document Type: Presentation
  Subject: Planning and Forecasting
  Session: 451
  Paper Number: 13-4519
• Does LUCE Outperform OBA? Comparison Study of Two Bush-Based Algorithms for Traffic Assignment Problem
  Authors: Nie, Yu
  Authors: Nie, Yu
  Year: 2013
  Document Type: Presentation
  Subject: Planning and Forecasting
  Session: 451
  Paper Number: 13-5174
• Class of Flow-Splitting Models for Day-to-Day Traffic Assignment
  Abstract:

  The splitting rate model recently proposed by Smith and Mounce is a traffic evolution model established on a link-node network representation, which overcomes the unrealism in traditional path-based models, and provides the ease of implementing control strategies at nodes. While Smith's model offers a new regime for modeling traffic evolution, it contains an ad-hoc step of flow adjustment, for the purpose of maintaining the flow conservation. The additional adjustment in Smith's approach results in difficulties in analyzing system's properties. This paper proposes a general formulation for a class of flow splitting models, which endogenously preserves the flow conservation. The modeling framework provides the ease for constructing various day-to-day traffic assignment models, and serves as a bridge connecting the splitting rate model with the link-based model. A numerical example demonstrates the implementation of the proposed modeling framework, as well as its convergence to user equilibrium.

  Authors: He, Xiaozheng; Liu, Henry X.
  Authors: He, Xiaozheng; Liu, Henry X.
  Year: 2013
  Document Type: Paper
  Subject: Planning and Forecasting
  Session: 451
  Paper Number: 13-5236