Convexity and robustness of dynamic traffic assignment and freeway network control
(2016) In Transportation Research. Part B: Methodological 91. p.446465 Abstract
We study the use of the System Optimum (SO) Dynamic Traffic Assignment (DTA) problem to design optimal traffic flow controls for freeway networks as modeled by the Cell Transmission Model, using variable speed limit, ramp metering, and routing. We consider two optimal control problems: the DTA problem, where turning ratios are part of the control inputs, and the Freeway Network Control (FNC), where turning ratios are instead assigned exogenous parameters. It is known that relaxation of the supply and demand constraints in the cellbased formulations of the DTA problem results in a linear program. However, solutions to the relaxed problem can be infeasible with respect to traffic dynamics. Previous work has shown that such solutions can... (More)
We study the use of the System Optimum (SO) Dynamic Traffic Assignment (DTA) problem to design optimal traffic flow controls for freeway networks as modeled by the Cell Transmission Model, using variable speed limit, ramp metering, and routing. We consider two optimal control problems: the DTA problem, where turning ratios are part of the control inputs, and the Freeway Network Control (FNC), where turning ratios are instead assigned exogenous parameters. It is known that relaxation of the supply and demand constraints in the cellbased formulations of the DTA problem results in a linear program. However, solutions to the relaxed problem can be infeasible with respect to traffic dynamics. Previous work has shown that such solutions can be made feasible by proper choice of ramp metering and variable speed limit control for specific traffic networks. We extend this procedure to arbitrary networks and provide insight into the structure and robustness of the proposed optimal controllers. For a network consisting only of ordinary, merge, and diverge junctions, where the cells have linear demand functions and affine supply functions with identical slopes, and the cost is the total traffic volume, we show, using the Pontryagin maximum principle, that variable speed limits are not needed in order to achieve optimality in the FNC problem, and ramp metering is sufficient. We also prove bounds on perturbation of the controlled system trajectory in terms of perturbations in initial traffic volume and exogenous inflows. These bounds, which leverage monotonicity properties of the controlled trajectory, are shown to be in close agreement with numerical simulation results.
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 author
 Como, Giacomo ^{LU} ; Lovisari, Enrico ^{LU} and Savla, Ketan
 organization
 publishing date
 20160901
 type
 Contribution to journal
 publication status
 published
 subject
 keywords
 Cell transmission model, Convex optimisation, Dynamic network loading, Dynamic network traffic assignment, Optimal control, Robustness analysis
 in
 Transportation Research. Part B: Methodological
 volume
 91
 pages
 20 pages
 publisher
 Elsevier
 external identifiers

 scopus:84975682981
 wos:000381842800023
 ISSN
 01912615
 DOI
 10.1016/j.trb.2016.06.007
 language
 English
 LU publication?
 yes
 id
 5ce94c16495f428b8ced242d3e8f61f0
 date added to LUP
 20160825 19:01:43
 date last changed
 20170811 08:32:57
@article{5ce94c16495f428b8ced242d3e8f61f0, abstract = {<p>We study the use of the System Optimum (SO) Dynamic Traffic Assignment (DTA) problem to design optimal traffic flow controls for freeway networks as modeled by the Cell Transmission Model, using variable speed limit, ramp metering, and routing. We consider two optimal control problems: the DTA problem, where turning ratios are part of the control inputs, and the Freeway Network Control (FNC), where turning ratios are instead assigned exogenous parameters. It is known that relaxation of the supply and demand constraints in the cellbased formulations of the DTA problem results in a linear program. However, solutions to the relaxed problem can be infeasible with respect to traffic dynamics. Previous work has shown that such solutions can be made feasible by proper choice of ramp metering and variable speed limit control for specific traffic networks. We extend this procedure to arbitrary networks and provide insight into the structure and robustness of the proposed optimal controllers. For a network consisting only of ordinary, merge, and diverge junctions, where the cells have linear demand functions and affine supply functions with identical slopes, and the cost is the total traffic volume, we show, using the Pontryagin maximum principle, that variable speed limits are not needed in order to achieve optimality in the FNC problem, and ramp metering is sufficient. We also prove bounds on perturbation of the controlled system trajectory in terms of perturbations in initial traffic volume and exogenous inflows. These bounds, which leverage monotonicity properties of the controlled trajectory, are shown to be in close agreement with numerical simulation results.</p>}, author = {Como, Giacomo and Lovisari, Enrico and Savla, Ketan}, issn = {01912615}, keyword = {Cell transmission model,Convex optimisation,Dynamic network loading,Dynamic network traffic assignment,Optimal control,Robustness analysis}, language = {eng}, month = {09}, pages = {446465}, publisher = {Elsevier}, series = {Transportation Research. Part B: Methodological}, title = {Convexity and robustness of dynamic traffic assignment and freeway network control}, url = {http://dx.doi.org/10.1016/j.trb.2016.06.007}, volume = {91}, year = {2016}, }