On the well-posedness of deterministic queuing networks with feedback control
(2021) In Transportation Research. Part B: Methodological 150. p.323-335- Abstract
We study the well-posedness of a class of dynamical flow network systems describing the dynamical mass balance among a finite number of cells exchanging flow of traffic between themselves and with the external environment. Dynamical systems in the considered class are described as differential inclusions whereby the routing matrix is constant and the outflow from each cell in the network is limited by a control that is a Lipschitz continuous function of the state of the network. This framework finds application in particular within traffic signal control, whereby it is common that an empty queue can be allowed to have more outflow than vehicles in the queue. While models for this scenario have previously been presented for open-loop... (More)
We study the well-posedness of a class of dynamical flow network systems describing the dynamical mass balance among a finite number of cells exchanging flow of traffic between themselves and with the external environment. Dynamical systems in the considered class are described as differential inclusions whereby the routing matrix is constant and the outflow from each cell in the network is limited by a control that is a Lipschitz continuous function of the state of the network. This framework finds application in particular within traffic signal control, whereby it is common that an empty queue can be allowed to have more outflow than vehicles in the queue. While models for this scenario have previously been presented for open-loop outflow controls, our result ensures the existence and uniqueness of solutions for the network flow dynamics in the case Lipschitz continuous feedback controllers.
(Less)
- author
- Como, Giacomo LU and Nilsson, Gustav
- organization
- publishing date
- 2021-08-01
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Feedback control, Queuing networks, Reflection principle, Transportation networks, Well-posedness
- in
- Transportation Research. Part B: Methodological
- volume
- 150
- pages
- 13 pages
- publisher
- Elsevier
- external identifiers
-
- scopus:85109212614
- ISSN
- 0191-2615
- DOI
- 10.1016/j.trb.2021.06.010
- language
- English
- LU publication?
- yes
- additional info
- Funding Information: This research was carried on within the framework of the MIUR-funded Progetto di Eccellenza of the Dipartimento di Scienze Matematiche G.L. Lagrange , CUP: E11G18000350001 , and was partly supported by the Compagnia di San Paolo, Italy and the Swedish Research Council.
- id
- a0b5075b-71c7-441e-8181-cc8785d90dd4
- date added to LUP
- 2021-08-18 09:48:51
- date last changed
- 2022-05-05 02:58:02
@article{a0b5075b-71c7-441e-8181-cc8785d90dd4,
abstract = {{<p>We study the well-posedness of a class of dynamical flow network systems describing the dynamical mass balance among a finite number of cells exchanging flow of traffic between themselves and with the external environment. Dynamical systems in the considered class are described as differential inclusions whereby the routing matrix is constant and the outflow from each cell in the network is limited by a control that is a Lipschitz continuous function of the state of the network. This framework finds application in particular within traffic signal control, whereby it is common that an empty queue can be allowed to have more outflow than vehicles in the queue. While models for this scenario have previously been presented for open-loop outflow controls, our result ensures the existence and uniqueness of solutions for the network flow dynamics in the case Lipschitz continuous feedback controllers.</p>}},
author = {{Como, Giacomo and Nilsson, Gustav}},
issn = {{0191-2615}},
keywords = {{Feedback control; Queuing networks; Reflection principle; Transportation networks; Well-posedness}},
language = {{eng}},
month = {{08}},
pages = {{323--335}},
publisher = {{Elsevier}},
series = {{Transportation Research. Part B: Methodological}},
title = {{On the well-posedness of deterministic queuing networks with feedback control}},
url = {{http://dx.doi.org/10.1016/j.trb.2021.06.010}},
doi = {{10.1016/j.trb.2021.06.010}},
volume = {{150}},
year = {{2021}},
}