Throughput Optimality and Overload Behavior of Dynamical Flow Networks Under Monotone Distributed Routing

Como, Giacomo; Lovisari, Enrico; Savla, Ketan

doi:10.1109/tcns.2014.2367361

Cited by 71 publications

(97 citation statements)

References 19 publications

(47 reference statements)

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“…thus {f out l (ρ)} l∈L in v is uniquely defined in (10). Furthermore, by considering the finite set of functions possible for α v (ρ) determined by the minimizing k ∈ L out v in (15), we conclude that f out l (ρ) and thus F l (ρ) is a continuous selection of differentiable functions.…”

Section: E Piecewise Differentiabilitymentioning

confidence: 88%

“…Our work is related to the dynamical flow networks recently proposed in [8], [9] and further studied in [10]. In [8], [9], downstream supply is not considered and therefore the flow exiting a link is equal to the link's demand.…”

Section: Introductionmentioning

confidence: 99%

“…Thus downstream congestion does not affect upstream flow, an unrealistic assumption for traffic modeling. In [10], the authors allow flow to depend on the density of downstream links, but the paper focuses on throughput optimality of a particular class of routing policies that does not accomodate most models of traffic flow, including the proportional-priority, first-in-first-out rule considered in this paper, and limited theoretical results are given for general routing policies. This paper is organized as follows: In Section II, we propose the traffic network model.…”

Section: Introductionmentioning

confidence: 99%

“…In our proposed model, we consider a traffic network composed of road links interconnected at junctions. In keeping with the philosophy of the CTM, the flow of traffic through a junction is determined by the available supply of downstream road space into which vehicles can flow and upstream demand of vehicles wishing to flow into a given link.Our work is related to the dynamical flow networks recently proposed in [8], [9] and further studied in [10]. In [8], [9], downstream supply is not considered and therefore the flow exiting a link is equal to the link's demand.…”

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confidence: 99%

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Dynamical properties of a compartmental model for traffic networks

Coogan

Arcak

2014

2014 American Control Conference

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In this paper, we propose a traffic network flow model particularly suitable for qualitative analysis as a dynamical system. Flows at a junction are determined by downstream supply of capacity (lack of congestion) as well as upstream demand of traffic wishing to flow through the junction. This approach is rooted in the celebrated Cell Transmission Model for freeway traffic flow, and we analyze resulting equilibrium flows and convergence properties. I. INTRODUCTIONCompartmental systems are a broad modeling paradigm to study fluid-like flow of a single substance among interconnected "compartments" [1], [2]. The main contribution of this paper is to propose and analyze a compartmental model of freeway traffic networks that is amenable to analysis as a dynamical system. Existing approaches are often well-suited for simulations or for validation/fitting with empirical data, but the available literature often gives little insight into the network-level, qualitative properties of the dynamics. For example, models such as [3], [4] and the celebrated Cell Transmission Model (CTM) [5], [6] were primarily developed for simulation with few analytical results available. The primary exception is [7] which provides a thorough investigation of the CTM when modeling a stretch of highway with onramp queues but does not consider more general networks.We propose a model that encompasses the CTM and extends the model to general nonlinear supply and demand functions and to more general network topologies. In our proposed model, we consider a traffic network composed of road links interconnected at junctions. In keeping with the philosophy of the CTM, the flow of traffic through a junction is determined by the available supply of downstream road space into which vehicles can flow and upstream demand of vehicles wishing to flow into a given link.Our work is related to the dynamical flow networks recently proposed in [8], [9] and further studied in [10]. In [8], [9], downstream supply is not considered and therefore the flow exiting a link is equal to the link's demand. Thus downstream congestion does not affect upstream flow, an unrealistic assumption for traffic modeling. In [10], the authors allow flow to depend on the density of downstream links, but the paper focuses on throughput optimality of a particular class of routing policies that does not accomodate most models of traffic flow, including the proportional-priority, first-in-first-out rule considered in this paper, and limited theoretical results are given for general routing policies.

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Section: E Piecewise Differentiabilitymentioning

confidence: 88%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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Dynamical properties of a compartmental model for traffic networks

Coogan

Arcak

2014

2014 American Control Conference

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“…In addition, examples show that such a perturbation can be arbitrarily small. Such a behavior arises in multicommodities only, and has no counterpart in single-commodity network, where instead, as shown in [8], well designed routing policies can completely exploit the structure of the network and ensure maximal resilience to perturbations.…”

Section: Introductionmentioning

confidence: 99%

On resilience of multicommodity dynamical flow networks

Nilsson

Como

Lovisari³

2014

53rd IEEE Conference on Decision and Control

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Abstract-Dynamical flow networks with heterogeneous routing are analyzed in terms of stability and resilience to perturbations. Particles flow through the network and, at each junction, decide which downstream link to take on the basis of the local state of the network. Differently from singlecommodity scenarios, particles belong to different classes, or commodities, with different origins and destinations, each reacting differently to the observed state of the network. As such, the commodities compete for the shared resource that is the flow capacity of each link of the network. This implies that, in contrast to the single-commodity case, the resulting dynamical system is not monotone, hence harder to analyze. It is shown that, in an acyclic network, when a feasible globally asymptotically stable aggregate equilibrium exists, then each commodity also admits a unique equilibrium. In addition, a sufficient condition for stability is provided. Finally, it is shown that, differently from the single-commodity case, when this condition is not satisfied, the possible unique equilibrium may be arbitrarily fragile to perturbations of the network.

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