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Convexity and robustness of dynamic traffic assignment and freeway network control

Como, Giacomo LU ; Lovisari, Enrico LU and Savla, Ketan (2016) In Transportation Research. Part B: Methodological 91. p.446-465
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 cell-based 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 cell-based 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
organization
publishing date
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
0191-2615
DOI
10.1016/j.trb.2016.06.007
language
English
LU publication?
yes
id
5ce94c16-495f-428b-8ced-242d3e8f61f0
date added to LUP
2016-08-25 19:01:43
date last changed
2017-01-01 08:32:37
@article{5ce94c16-495f-428b-8ced-242d3e8f61f0,
  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 cell-based 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         = {0191-2615},
  keyword      = {Cell transmission model,Convex optimisation,Dynamic network loading,Dynamic network traffic assignment,Optimal control,Robustness analysis},
  language     = {eng},
  month        = {09},
  pages        = {446--465},
  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},
}