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System optimal dynamic traffic assignment: Properties and solution procedures in the case of a many-to-one network
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System optimal dynamic traffic assignment: Properties and solution procedures in the case of a many-to-one network
Thanks to its high dimensionality and a usually non-convex constraint set, system optimal dynamic traffic assignment remains one of the most challenging problems in transportation research. This paper identifies two fundamental properties of the problem and uses them to design an efficient solution procedure. The authors first show that the non-convexity of the problem can be circumvented by first solving a relaxed problem and then applying a traffic holding elimination procedure to obtain the solution(s) of the original problem. To efficiently solve the relaxed problem, the authors explore the relationship between the relaxed problems based on different traffic flow models (PQ, SQ, CTM) and a minimal cost flow (MCF) problem for a special space-expansion network. It is shown that all the four problem formulations produce the same minimal system cost and share one common solution which does not involve inside queues in the network. Efficient solution algorithms such as the network simplex method can be applied to solve the MCF problem and identify such an optimal traffic pattern. Numerical examples are also presented to demonstrate the efficiency of the proposed solution procedure.
- Record URL: https://doi.org/10.1016/j.trb.2014.02.002
- Record URL: http://www.sciencedirect.com/science/article/pii/S0191261514000228
- Find a library where document is available. Order URL: http://worldcat.org/issn/01912615
- Abstract reprinted with permission of Elsevier.
- Publication Date: 2014-7
- Media Type: Web
- Features: Figures; References;
- Pagination: pp 1-17
- Transportation Research Part B: Methodological
- Issue Number: 0
- Publisher: Elsevier
- ISSN: 0191-2615
- Serial URL: http://www.sciencedirect.com/science/journal/01912615
Subject/Index Terms
- TRT Terms: Dynamic traffic assignment ; Optimization ; Traffic flow ; Traffic models
- Subject Areas: Highways; Planning and Forecasting; I71: Traffic Theory;
Filing Info
- Accession Number: 01530763
- Record Type: Publication
- Files: TRIS
- Created Date: Jul 24 2014 2:37PM
Discrete-time system optimal dynamic traffic assignment (SO-DTA) with partial control for horizontal queuing networks
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System optimal dynamic traffic assignment: solution structures of the signal control in non-holding-back formulations
- Civil Engineering
Research output : Contribution to journal › Article › Research › peer-review
This paper devises locally optimal traffic Signal Control (SC) settings in a Non-Holding-Back Dynamic Traffic Assignment with SC (NHB DTA-SC) formulation for single destination (i.e. one source to one destination and many sources to one destination) networks. To this end, we apply temporal–spatial dual decomposition method and decompose the NHB DTA-SC problem into intersection cells and non-intersection cells. Then we further decompose the intersection cells into different subproblems, i.e. Occupancy Minimization (OM), Flow Maximization (FM), and SC. To study the optimal SC structures, we examine the Karush–Kuhn–Tucker (KKT) optimality conditions of the decomposed SC subproblem. Finally, we obtain the locally optimal SC structures under different network conditions that include over-saturated, under-saturated, and queue spillback traffic scenarios. We also present several numerical results to verify the optimality structures found by our theoretical derivations.
- cell transmission model
- Dynamic Traffic Assignment
- Lagrangian dual decomposition
- optimal solution structures
- traffic signal control
- vehicle holding-back problem
Access to Document
- 10.1080/21680566.2018.1540950
Other files and links
- Link to publication in Scopus
T1 - System optimal dynamic traffic assignment
T2 - solution structures of the signal control in non-holding-back formulations
AU - Islam, Tarikul
AU - Vu, Hai L.
AU - Panda, Manoj
N2 - This paper devises locally optimal traffic Signal Control (SC) settings in a Non-Holding-Back Dynamic Traffic Assignment with SC (NHB DTA-SC) formulation for single destination (i.e. one source to one destination and many sources to one destination) networks. To this end, we apply temporal–spatial dual decomposition method and decompose the NHB DTA-SC problem into intersection cells and non-intersection cells. Then we further decompose the intersection cells into different subproblems, i.e. Occupancy Minimization (OM), Flow Maximization (FM), and SC. To study the optimal SC structures, we examine the Karush–Kuhn–Tucker (KKT) optimality conditions of the decomposed SC subproblem. Finally, we obtain the locally optimal SC structures under different network conditions that include over-saturated, under-saturated, and queue spillback traffic scenarios. We also present several numerical results to verify the optimality structures found by our theoretical derivations.
AB - This paper devises locally optimal traffic Signal Control (SC) settings in a Non-Holding-Back Dynamic Traffic Assignment with SC (NHB DTA-SC) formulation for single destination (i.e. one source to one destination and many sources to one destination) networks. To this end, we apply temporal–spatial dual decomposition method and decompose the NHB DTA-SC problem into intersection cells and non-intersection cells. Then we further decompose the intersection cells into different subproblems, i.e. Occupancy Minimization (OM), Flow Maximization (FM), and SC. To study the optimal SC structures, we examine the Karush–Kuhn–Tucker (KKT) optimality conditions of the decomposed SC subproblem. Finally, we obtain the locally optimal SC structures under different network conditions that include over-saturated, under-saturated, and queue spillback traffic scenarios. We also present several numerical results to verify the optimality structures found by our theoretical derivations.
KW - cell transmission model
KW - Dynamic Traffic Assignment
KW - Lagrangian dual decomposition
KW - optimal solution structures
KW - traffic signal control
KW - vehicle holding-back problem
UR - http://www.scopus.com/inward/record.url?scp=85057297901&partnerID=8YFLogxK
U2 - 10.1080/21680566.2018.1540950
DO - 10.1080/21680566.2018.1540950
M3 - Article
AN - SCOPUS:85057297901
SN - 2168-0566
JO - Transportmetrica B: Transport Dynamics
JF - Transportmetrica B: Transport Dynamics
IMAGES
VIDEO
COMMENTS
Introduction. Dynamic traffic assignment (DTA) has long been recognized as a key component of network planning and transport policy evaluation, in addition to real-time traffic operation and management (Szeto and Lo, 2006).System-optimum DTA (SO-DTA), a special case of DTA based on a dynamic extension of Wardrop's (1952) second principle, is used to predict a time-dependent traffic state ...
Most current system optimum dynamic traffic assignment (SO-DTA) models do not contain first-in-first-out (FIFO) constraints and are limited to single-destination network applications. ... Based on the properties of the proposed optimization problems, branch-and-bound algorithms are developed to solve SO-DTA problems with FIFO constraints. Two ...
In the present work, we consider a System Optimum Dynamic Traffic Assignment optimization problem on road networks employing time-varying partial traffic flow control. Depending on the network performance, trajectory control between the relative origin and destination nodes is applied to a variable fraction ("compliant") of the demand. Network dynamics is derived by applying a Godunov ...
The Dynamic System Optimum (DSO) traffic assignment problem predicts the optimal time-dependent routing pattern of travellers in a network such that the given time-dependent origin-destination ...
Keywords: Distributed, System Optimal, Dynamic Traffic Assignment, Sub-problem, Decomposition . I. INTRODUCTION Dynamic Traffic Assignment (DTA) is a well-studied research area to determine time-dependent traffic flows minimizing by the cost of the system or individual users in transportation networks. DTA deployment has brought many benefits to a
This study presents a distributed gradient-based approach to solve system optimal dynamic traffic assignment (SODTA) formulated based on the cell transmission model. The algorithm distributes SODTA into local sub-problems, who find optimal values for their decision variables within an intersection. Each sub-problem communicates with its immediate neighbors to reach a consensus on the values of ...
Downloadable (with restrictions)! Thanks to its high dimensionality and a usually non-convex constraint set, system optimal dynamic traffic assignment remains one of the most challenging problems in transportation research. This paper identifies two fundamental properties of the problem and uses them to design an efficient solution procedure.
System optimal dynamic traffic assignment: Properties and solution procedures in the case of a many-to-one network. Thanks to its high dimensionality and a usually non-convex constraint set, system optimal dynamic traffic assignment remains one of the most challenging problems in transportation research.
We consider the System Optimal Dynamic Traffic Assignment problem with Partial Control (SO-DTA-PC) for general networks with horizontal queuing. The goal of which is to optimally control any subset of the networks agents to minimize the total congestion of all agents in the network. We adopt a flow dynamics model that is a Godunov discretization of the Lighthill-Williams-Richards (LWR) partial ...
DOI: 10.1016/J.TRB.2014.02.002 Corpus ID: 154732945; System optimal dynamic traffic assignment: Properties and solution procedures in the case of a many-to-one network @article{Shen2014SystemOD, title={System optimal dynamic traffic assignment: Properties and solution procedures in the case of a many-to-one network}, author={Wei Shen and H. Michael Zhang}, journal={Transportation Research Part ...
ABSTRACT. This paper devises locally optimal traffic Signal Control (SC) settings in a Non-Holding-Back Dynamic Traffic Assignment with SC (NHB DTA-SC) formulation for single destination (i.e. one source to one destination and many sources to one destination) networks. To this end, we apply temporal-spatial dual decomposition method and decompose the NHB DTA-SC problem into intersection ...
Two continuous time formulations of the dynamic traffic assignment problem are considered, one that corresponds to system optimization and the other to a version of user optimization on a single mode network using optimal control theory.
The direction of the traffic flow θ(x,y,t) and the density distribution ρ(x,y,t) are considered as the optimization variables, provided the DSO problem is formulated as an optimization problem. 2.2 Formulation of the dynamic system-optimal model
The cell-transmission model-based single-destination system optimal dynamic traffic assignment problem proposed by Ziliaskopoulos was mostly solved by standard linear programming (LP) methods, e.g., simplex and interior point methods, which produce link-based flows involving vehicle-holding phenomenon.
Because of its non-convex constraints and high dimensionality, system optimal dynamic traffic assignment in a many-to-one network (S-SO-DTA) remains one of the challenging problems in transportation research. ... This paper addresses the system optimum dynamic traffic assignment (SO-DTA) problem with departure time choice on a two-terminal ...
Zheng H (2009) Efficient algorithms for the cell-based single destination system optimal dynamic traffic assignment problem. Ph.D. thesis, University of Arizona, Tucson. Google Scholar; Zheng H, Chiu Y-C (2011) A network flow algorithm for the cell-based single-destination system optimal dynamic traffic assignment problem.
N2 - This paper devises locally optimal traffic Signal Control (SC) settings in a Non-Holding-Back Dynamic Traffic Assignment with SC (NHB DTA-SC) formulation for single destination (i.e. one source to one destination and many sources to one destination) networks.
The challenge of optimal Routing and Spectrum Assignment (RSA) is significant in Elastic Optical Networks. Integrating adaptive modulation formats into the RSA problem - Routing, Modulation Level, and Spectrum Assignment - broadens allocation options and increases complexity. The conventional RSA approach entails predetermining fixed paths and then allocating spectrum within them separately ...
A discrete time model is presented for dynamic traffice assignment with a single destination. Congestion is treated explicitly in the flow equations. The model is a nonlinear and nonconvex mathematical programming problem. A piecewise linear version of the model, with additional assumptions on the objective function, can be solved for a global ...