Source-Destination Flow on a Road Network

Garavello, Mauro; Piccoli, Benedetto

doi:10.4310/cms.2005.v3.n3.a1

Cited by 54 publications

(87 citation statements)

References 14 publications

(32 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Let us consider a line I i . We report some results proved in [11]. First we note that the characteristic speed of the density is smaller than the speed of a Π−wave, as follows from the lemma:…”

Section: Estimates On Densitymentioning

confidence: 99%

“…In particular, we define two ways according to which the traffic at a junction is splitted towards the outgoing lines. Let us now comment further the differences with the results of [11]. In such paper, only the routing algorithm (RA1) was considered, together with the first choice of distribution traffic functions (which can be seen as a particular case of the second choice.)…”

mentioning

confidence: 99%

“…The first distribution traffic function has been already analyzed in [11] for road networks using algorithm (RA1), thus we focus on the second one. In particular, we define two ways according to which the traffic at a junction is splitted towards the outgoing lines.…”

mentioning

confidence: 99%

“…A first model for telecommunication networks, similar to that introduced recently for car traffic, has been proposed in [9] where two algorithms for dynamics at nodes were considered and existence of solution to Cauchy Problems was proved. The idea is to follow the approach used in [11] for road networks (see also [6], [8], [10], [13], [15], [16], [17]), introducing sources and destinations in the telecommunication model described in [9] and thus taking care of the paths of the packets inside the network.…”

mentioning

confidence: 99%

See 3 more Smart Citations

A Fluid Dynamic Model for Telecommunication Networks with Sources and Destinations

D’Apice¹,

Manzo²,

Piccoli

2008

SIAM J. Appl. Math.

Self Cite

View full text Add to dashboard Cite

Abstract. This paper proposes a macroscopic fluid dynamic model dealing with the flows of information on a telecommunication network with sources and destinations. The model consists of a conservation law for the packets density and a semilinear equation for traffic distributions functions, i.e. functions describing packets paths.We describe methods to solve Riemann Problems at junctions assigning different traffic distributions functions and two "routing algorithms". Moreover we prove existence of solutions to Cauchy problems for small perturbations of network equilibria.

show abstract

Section: Estimates On Densitymentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

See 2 more Smart Citations

A Fluid Dynamic Model for Telecommunication Networks with Sources and Destinations

D’Apice¹,

Manzo²,

Piccoli

2008

SIAM J. Appl. Math.

Self Cite

View full text Add to dashboard Cite

show abstract

“…A first model for data networks, similar to that used for car traffic, has been proposed in D' Apice et al (2006), where two algorithms for dynamics at nodes were considered and existence of solutions to Cauchy Problems was proved. Then in D' Apice et al (2008), following the approach of Garavello et al (2005) for road networks (see also Coclite et al (2005); Daganzo (1997); Garavello et al (2006); Holden et al (1995); Lighthill et al (1955); Newell (1980); Richards (1956)), sources and destinations have been introduced, thus taking care of the packets paths inside the network.…”

Section: Introductionmentioning

confidence: 99%

Simulation and Optimal Routing of Data Flows Using a Fluid Dynamic Approach

D’Apice¹,

Manzo²,

Piccoli³

2012

Telecommunications Networks - Current Status and Future Trends

Self Cite

View full text Add to dashboard Cite

Comparing comparisons between vehicular traffic states in microscopic and macroscopic first‐order models

Cristiani

Saladino

2018

Math Methods in App Sciences

View full text Add to dashboard Cite

In this paper, we deal with the analysis of the solutions of traffic flow models at multiple scales in both cases of a single road and road networks. We are especially interested in measuring the distance between traffic states (as they result from the mathematical modeling) and investigating whether these distances are somehow preserved passing from the microscopic to the macroscopic scale. By means of both theoretical and numerical investigations, we show that, on a single road, the notion of Wasserstein distance fully catches the human perception of distance independently of the scale, while in the case of networks it partially loses its nice properties. KEYWORDS earth mover's distance, follow-the-leader model, LWR model, many-particle limit, multi-path model, networks, traffic flow, Wasserstein distance INTRODUCTIONIn this paper, we deal with the analysis of the solutions of traffic flow models at multiple scales. More precisely, we are interested in measuring the distance between traffic states (as they result from the mathematical modeling) and investigating whether these distances are somehow preserved passing from the microscopic to the macroscopic scale. We will consider both cases of a single road and road networks.Connections between microscopic (agent-based) and macroscopic (fluid dynamics) traffic flow models are already well established. Aw et al, 1 Greenberg, 2 and Di Francesco et al 3 investigated the many-particle limit in the framework of second-order traffic models, deriving the macroscopic Aw-Rascle-Zhang (ARZ) 4,5 model from a particular second-order microscopic Follow-the-Leader (FtL) 6,7 model. On the other hand, Colombo and Rossi, 8 Rossi, 9 Di Francesco and Rosini, 10 and Di Francesco et al 11 investigated the many-particle limit in the framework of first-order traffic models, deriving the Ligthill-Whitham-Richards (LWR) 12,13 model as the limit of a specific first-order FtL model. Let us also mention the papers by Forcadel et al 14 and Forcadel and Salazar,15 which investigate the many-particle limit exploiting the link between conservation laws and Hamilton-Jacobi equations.Moving to road networks, analogous connections are rarer. This is probably because of the fact that macroscopic traffic models on networks are in general ill-posed, since the conservation of mass is not sufficient alone to characterize a unique solution at junctions. This ambiguity makes more difficult to find the right limit of the microscopic model, which, in turn, can be defined in different ways near the junctions. In this context let us mention the paper by Cristiani and Sahu, 16 which investigates the many-particle limit of a first-order FtL model suitably extended to a road network. The corresponding macroscopic model appears to be the extension of the LWR model on networks introduced by Hilliges and Weidlich 17 and then extensively studied by Briani and Cristiani 18 and Bretti et al. 19 This paper focuses in particular on the comparison of solutions to the equations associated to first-order traffic models....

show abstract

Source-Destination Flow on a Road Network

Cited by 54 publications

References 14 publications

A Fluid Dynamic Model for Telecommunication Networks with Sources and Destinations

A Fluid Dynamic Model for Telecommunication Networks with Sources and Destinations

Simulation and Optimal Routing of Data Flows Using a Fluid Dynamic Approach

Comparing comparisons between vehicular traffic states in microscopic and macroscopic first‐order models

Contact Info

Product

Resources

About