A robust transportation signal control problem accounting for traffic dynamics
TL;DR: A new approach-robust system optimal signal control model is proposed; a supply-side within day operational transportation model where future transportation demand is assumed to be uncertain and a robust dynamic system optimal model with an embedded cell transmission model is formulated.
About: This article is published in Computers & Operations Research.The article was published on 2010-05-01. It has received 84 citations till now. The article focuses on the topics: Traffic generation model & Robust control.
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Book•
01 Jan 1997
TL;DR: This book presents a coherent approach to the analysis of transportation networks based on the concept of network equilibrium and the application of convex programming methods, and indicates promising areas for further research.
Abstract: Transportation Networks. Optimality. Cost Functions. Deterministic User Equilibrium Assignment. Stochastic User Equilibrium Assignment. Trip Table Estimation. Network Reliability. Network Design. Conclusions. References. Index.
584 citations
TL;DR: In this paper, a linear programming formulation for autonomous intersection control (LPAIC) is proposed to account for traffic dynamics within a connected vehicle environment, where a lane based bi-level optimization model is introduced to propagate traffic flows in the network, accounting for dynamic departure time, dynamic route choice, and autonomous intersections control in the context of system optimum network model.
Abstract: This paper develops a novel linear programming formulation for autonomous intersection control (LPAIC) accounting for traffic dynamics within a connected vehicle environment. Firstly, a lane based bi-level optimization model is introduced to propagate traffic flows in the network, accounting for dynamic departure time, dynamic route choice, and autonomous intersection control in the context of system optimum network model. Then the bi-level optimization model is transformed to the linear programming formulation by relaxing the nonlinear constraints with a set of linear inequalities. One special feature of the LPAIC formulation is that the entries of the constraint matrix has only {−1, 0, 1} values. Moreover, it is proved that the constraint matrix is totally unimodular, the optimal solution exists and contains only integer values. It is also shown that the traffic flows from different lanes pass through the conflict points of the intersection safely and there are no holding flows in the solution. Three numerical case studies are conducted to demonstrate the properties and effectiveness of the LPAIC formulation to solve autonomous intersection control.
216 citations
TL;DR: A link based dynamic network loading model is developed to simulate the traffic flow propagation allowing the change of speed limits and the optimal speed limit scheme is obtained by applying the R-Markov Average Reward Technique (R-MART) based reinforcement learning algorithm.
Abstract: This paper proposes a novel dynamic speed limit control model accounting for uncertain traffic demand and supply in a stochastic traffic network. First, a link based dynamic network loading model is developed to simulate the traffic flow propagation allowing the change of speed limits. Shockwave propagation is well defined and captured by checking the difference between the queue forming end and the dissipation end. Second, the dynamic speed limit problem is formulated as a Markov Decision Process (MDP) problem and solved by a real time control mechanism. The speed limit controller is modeled as an intelligent agent interacting with the stochastic network environment stochastic network environment to assign time dependent link based speed limits. Based on different metrics, e.g. total network throughput, delay time, vehicular emissions are optimized in the modeling framework, the optimal speed limit scheme is obtained by applying the R-Markov Average Reward Technique (R-MART) based reinforcement learning algorithm. A case study of the Sioux Falls network is constructed to test the performance of the model. Results show that the total travel time and emissions (in terms of CO) are reduced by around 18% and 20% compared with the base case of non-speed limit control.
82 citations
TL;DR: Different performance metrics from the integrated model are compared with traditional dynamic assignment model and results indicate changes in route choice behavior of the road users when emission objective is integrated to dynamic assignment framework.
Abstract: Maintaining air-quality standards is a major concern for transportation planners and policy makers in the United States. This necessitates considering nontraditional emission objectives in transportation systems modeling. In this research, the authors integrate emission-based objectives into the traditional travel time based dynamic assignment framework. Carbon monoxide (CO) emissions from vehicles are computed as functions of space mean speed (determined from an embedded mesoscopic traffic flow model). Different performance metrics (CO emission, system wide travel time, and speed profiles) from the integrated model are compared with traditional dynamic assignment model (with travel time minimization objective). In addition, results indicate changes in route choice behavior of the road users when emission objective is integrated to dynamic assignment framework.
80 citations
Cites background or methods from "A robust transportation signal cont..."
...Venigalla et al. (1999) applied a multiple-user-class assignment formulation to compute emission (Traffic Assignment Program for Emission Studies [TAPES]). Further, Nagurney (2001), Yin and Lawphongpanich (2006), and Benedek and Rilett (1998) considered environmental objectives within assignment framework....
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...The advantage of CTM is that it represents queue spillover and shockwave propagation in traffic networks (Szeto and Sumalee, 2011; Sun et al., 2006; Ziliaskopoulos, 2000; Beard and Ziliaskopoulos, 2006; Ukkusuri et al., 2010; Lin, 2011)....
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...Ukkusuri et al. (2010) and Lin and Wang (2004) in their research approximated the total number of stops in the network and incorporate that in the objective function (signal optimization)....
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...Venigalla et al. (1999) applied a multiple-user-class assignment formulation to compute emission (Traffic Assignment Program for Emission Studies [TAPES])....
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TL;DR: The aim of the presented research is to elaborate a traffic-responsive optimal signal split algorithm taking uncertainty into account taking into account the traffic control objective to minimize the weighted link queue lengths within an urban network area.
Abstract: The aim of the presented research is to elaborate a traffic-responsive optimal signal split algorithm taking uncertainty into account. The traffic control objective is to minimize the weighted link queue lengths within an urban network area. The control problem is formulated in a centralized rolling-horizon fashion in which unknown but bounded demand and queue uncertainty influences the prediction. An efficient constrained minimax optimization is suggested to obtain the green time combination, which minimizes the objective function when worst case uncertainty appears. As an illustrative example, a simulation study is carried out to demonstrate the effectiveness and computational feasibility of the robust predictive approach. By using real-world traffic data and microscopic traffic simulator, the proposed robust signal split algorithm is analyzed and compared with well-tuned fixed-time signal timing and to nominal predictive solutions under different traffic conditions.
73 citations
Cites background from "A robust transportation signal cont..."
...Note that condition (8) is also necessary to assure the feasibility of the proposed robust optimization for oversaturated traffic network (see Section IV)....
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References
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Book•
01 Jan 1976TL;DR: In this article, a confused decision maker, who wishes to make a reasonable and responsible choice among alternatives, can systematically probe his true feelings in order to make those critically important, vexing trade-offs between incommensurable objectives.
Abstract: Many of the complex problems faced by decision makers involve multiple conflicting objectives. This book describes how a confused decision maker, who wishes to make a reasonable and responsible choice among alternatives, can systematically probe his true feelings in order to make those critically important, vexing trade-offs between incommensurable objectives. The theory is illustrated by many real concrete examples taken from a host of disciplinary settings. The standard approach in decision theory or decision analysis specifies a simplified single objective like monetary return to maximise. By generalising from the single objective case to the multiple objective case, this book considerably widens the range of applicability of decision analysis.
8,895 citations
27 Jun 2011
TL;DR: This textbook provides a first course in stochastic programming suitable for students with a basic knowledge of linear programming, elementary analysis, and probability to help students develop an intuition on how to model uncertainty into mathematical problems.
Abstract: The aim of stochastic programming is to find optimal decisions in problems which involve uncertain data. This field is currently developing rapidly with contributions from many disciplines including operations research, mathematics, and probability. At the same time, it is now being applied in a wide variety of subjects ranging from agriculture to financial planning and from industrial engineering to computer networks. This textbook provides a first course in stochastic programming suitable for students with a basic knowledge of linear programming, elementary analysis, and probability. The authors aim to present a broad overview of the main themes and methods of the subject. Its prime goal is to help students develop an intuition on how to model uncertainty into mathematical problems, what uncertainty changes bring to the decision process, and what techniques help to manage uncertainty in solving the problems.In this extensively updated new edition there is more material on methods and examples including several new approaches for discrete variables, new results on risk measures in modeling and Monte Carlo sampling methods, a new chapter on relationships to other methods including approximate dynamic programming, robust optimization and online methods.The book is highly illustrated with chapter summaries and many examples and exercises. Students, researchers and practitioners in operations research and the optimization area will find it particularly of interest. Review of First Edition:"The discussion on modeling issues, the large number of examples used to illustrate the material, and the breadth of the coverage make'Introduction to Stochastic Programming' an ideal textbook for the area." (Interfaces, 1998)
5,398 citations
"A robust transportation signal cont..." refers background in this paper
...A compact formulation of a general stochastic linear programming is given in [13,7]....
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Journal Article•
TL;DR: In this paper, a functional relationship between flow and concentration for traffic on crowded arterial roads has been postulated for some time, and has experimental backing, from which a theory of the propagation of changes in traffic distribution along these roads may be deduced.
Abstract: This paper uses the method of kinematic waves, developed in part I, but may be read independently. A functional relationship between flow and concentration for traffic on crowded arterial roads has been postulated for some time, and has experimental backing (§2). From this a theory of the propagation of changes in traffic distribution along these roads may be deduced (§§2, 3). The theory is applied (§4) to the problem of estimating how a ‘hump’, or region of increased concentration, will move along a crowded main road. It is suggested that it will move slightly slower than the mean vehicle speed, and that vehicles passing through it will have to reduce speed rather suddenly (at a ‘shock wave’) on entering it, but can increase speed again only very gradually as they leave it. The hump gradually spreads out along the road, and the time scale of this process is estimated. The behaviour of such a hump on entering a bottleneck, which is too narrow to admit the increased flow, is studied (§5), and methods are obtained for estimating the extent and duration of the resulting hold-up. The theory is applicable principally to traffic behaviour over a long stretch of road, but the paper concludes (§6) with a discussion of its relevance to problems of flow near junctions, including a discussion of the starting flow at a controlled junction. In the introductory sections 1 and 2, we have included some elementary material on the quantitative study of traffic flow for the benefit of scientific readers unfamiliar with the subject.
3,983 citations
TL;DR: In this article, a simple theory of traffic flow is developed by replacing individual vehicles with a continuous fluid density and applying an empirical relation between speed and density, which is a simple graph-shearing process for following the development of traffic waves.
Abstract: A simple theory of traffic flow is developed by replacing individual vehicles with a continuous “fluid” density and applying an empirical relation between speed and density. Characteristic features of the resulting theory are a simple “graph-shearing” process for following the development of traffic waves in time and the frequent appearance of shock waves. The effect of a traffic signal on traffic streams is studied and found to exhibit a threshold effect wherein the disturbances are minor for light traffic but suddenly build to large values when a critical density is exceeded.
3,475 citations
TL;DR: In this paper, the authors propose an approach that attempts to make this trade-off more attractive by flexibly adjusting the level of conservatism of the robust solutions in terms of probabilistic bounds of constraint violations.
Abstract: A robust approach to solving linear optimization problems with uncertain data was proposed in the early 1970s and has recently been extensively studied and extended. Under this approach, we are willing to accept a suboptimal solution for the nominal values of the data in order to ensure that the solution remains feasible and near optimal when the data changes. A concern with such an approach is that it might be too conservative. In this paper, we propose an approach that attempts to make this trade-off more attractive; that is, we investigate ways to decrease what we call the price of robustness. In particular, we flexibly adjust the level of conservatism of the robust solutions in terms of probabilistic bounds of constraint violations. An attractive aspect of our method is that the new robust formulation is also a linear optimization problem. Thus we naturally extend our methods to discrete optimization problems in a tractable way. We report numerical results for a portfolio optimization problem, a knapsack problem, and a problem from the Net Lib library.
3,364 citations