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Title:WZ-speed harmonizer: an optimized active traffic and demand management system with speed harmonization for work zones
Author(s):Ramezani, Hani
Director of Research:Benekohal, Rahim F
Doctoral Committee Chair(s):Benekohal, Rahim F
Doctoral Committee Member(s):Work, Daniel B; Ouyang , Yanfeng; Nedich, Angelia
Department / Program:Civil & Environmental Eng
Discipline:Civil Engineering
Degree Granting Institution:University of Illinois at Urbana-Champaign
Subject(s):Speed harmonization, variable speed limit, second order model, large scale optimization, mixed integer nonlinear program
Abstract:Speed harmonization, known as Variable Speed Limit (VSL), is implemented through a number of Changeable Message Signs (CMSs) spaced out over a stretch of highway. The CMSs display advisory speeds that may change over time and space to regulate travel speed and arrival time to a highway bottleneck and consequently reduce congestion impacts. Usually speed harmonization studies determine optimal dynamic advisory speeds to minimize travel time and delay. Delay and travel time can be further minimized if optimal location and number of CMSs are determined as well. Determining dynamic advisory speeds depends on the number and locations of CMSs; thus these variables have to be optimized simultaneously. This study is the first study which simultaneously optimized 1) dynamic advisory speeds, 2) number of CMSs, and 3) location of the CMSs to minimize total travel time and a penalty function for the number of CMSs. This problem is important as it reduces maintenance and installation costs of CMSs and enhances effectiveness of speed harmonization to reduce congestion impacts such as delay. Solving this problem is challenging because it is a large scale Mixed Integer Nonlinear Program (MINLP). Determining traffic speed and extend of queue is critical to develop a speed harmonization scheme to mitigate congestion. Past studies have used first order model or second order model as a constraint in the optimization program to determine speed and extend of queue. This study compared the first order model and the second order model versus field data and showed that the second order model was better in estimating average queue length and maximum queue length. To use the second order mode, it is necessary to calibrate the model parameters, which are relaxation time (τ) and anticipation coefficient (ϑ). This study calibrated the parameters using work zone field data to minimize error in speed and queue length estimates. The calibration is a complex process since there might be many local optimal points returning parameter values that are not physically justifiable. To overcome this issue, this study proposed a new calibration procedure. The methodology detected the behavior of the second order model in the τ- ϑ space and determined a search direction and its boundaries to avoid stopping at local minima. Although the second order model returned acceptable average and maximum queue lengths, it returned slower queue propagation pattern and faster queue dissipation pattern than field data. Thus the two- ϑ model was proposed to more maturely reflect asymmetric queue propagation and dissipation. The modification considered two different anticipation coefficients for queue propagation (ϑ_p) and queue shrinkage (ϑ_s). The two- ϑ model was calibrated using field data and results showed that the ratio of ϑ_s/ϑ_p ranges from 1.86 to 2.6 and both of them are greater than single ϑ. The solutions for the optimization program mainly tackled integrality. One source of integrality is piecewise speed-density models. Previous studies have used single-regime (single piece) models, but these models are not generally sufficient to describe congested conditions. Thus this study included the piecewise models as constraints to enhance accuracy of traffic state prediction in congested conditions. A continuous transformation approach was proposed to eliminate relevant integer variables. The methodology was used to optimize speed harmonization for a 12.5-mile roadway and a 50-min analysis duration where locations of the CMSs were given. For this problem, the methodology eliminated 30,000 binary variables and solved the problem in 23 minutes when the program included roughly 158,000 variables and 186,000 constraints. The results showed that WZSH can reduce delay by 15.7% and maximum queue length by 37.5% compared to the no speed harmonization condition. Another source of integrality is binary variables to determine location and number of CMSs. To solve the problem, three solution methods were proposed: 1) Greedy algorithm, 2) Augmented-Cut and Branch (AC&B) method, and 3) Approximate Decomposition method. The three solution methods were compared using a benchmark problem and results showed that the three methods return very close objective function values (within 1%), but the Approximate Decomposition method requires less computational resources. In particular, the Approximate Decomposition method reduced the number of WZSH solution by factors of 14.1 and 6.6 compared with Greedy Algorithm and AC&B method, respectively.
Issue Date:2016-04-18
Rights Information:Copyright 2016 Hani Ramezani
Date Available in IDEALS:2016-07-07
Date Deposited:2016-05

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