Convexity and robustness of dynamic traffic assignment and freeway network control
(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.
(Less)
- author
- Como, Giacomo LU ; Lovisari, Enrico LU and Savla, Ketan
- organization
- publishing date
- 2016-09-01
- 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
- 2024-09-21 21:04:09
@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}}, keywords = {{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}}, doi = {{10.1016/j.trb.2016.06.007}}, volume = {{91}}, year = {{2016}}, }