Emissions minimization on road networks via Generic Second Order Models

Caterina Balzotti; Maya Briani; Benedetto Piccoli; Caterina Balzotti; Maya Briani; Benedetto Piccoli

doi:10.3934/nhm.2023030

Networks and Heterogeneous Media

2023, Volume 18, Issue 2: 694-722. doi: 10.3934/nhm.2023030

Previous Article Next Article

Research article Special Issues

Emissions minimization on road networks via Generic Second Order Models

1.
SISSA Scuola Internazionale Superiore di Studi Avanzati, Trieste, Italy
2.
Istituto per le Applicazioni del Calcolo, Consiglio Nazionale delle Ricerche, Rome, Italy
3.
Department of Mathematical Sciences, Rutgers University, Camden, USA

Received: 22 July 2022 Revised: 19 May 2022 Accepted: 11 January 2023 Published: 22 February 2023

In this paper we consider the problem of estimating emissions due to vehicular traffic on complex networks, and minimizing their effect by regulating traffic at junctions. For the traffic evolution, we consider a Generic Second Order Model, which encompasses the majority of two-equations (i.e., second-order) models available in the literature, and extend it to road networks with merge and diverge junctions. The dynamics on the whole network is determined by selecting a solution to the Riemann Problems at junctions, i.e., the Cauchy problems with constant initial data on each incident road. The latter are solved by assuming the maximization of the flow and assigning a traffic distribution coefficient for outgoing roads of diverges, and a priority rule for incoming roads of merges. A general emission model is considered and its parameters are tuned to the $ {\mathrm{NO_{x}}} $ emission rate. The minimization of emissions is then formulated in terms of the traffic distribution and priority parameters, taking into account travel times. A comparison is provided between roundabouts with optimized parameters and traffic lights, which correspond to time-varying traffic priorities. Our approach can be adapted to manage traffic in complex networks in order to reduce emissions while keeping travel time at acceptable levels.
- Second order traffic models,
- road networks,
- Riemann problem,
- emissions
Citation: Caterina Balzotti, Maya Briani, Benedetto Piccoli. Emissions minimization on road networks via Generic Second Order Models[J]. Networks and Heterogeneous Media, 2023, 18(2): 694-722. doi: 10.3934/nhm.2023030

Related Papers:

Abstract

In this paper we consider the problem of estimating emissions due to vehicular traffic on complex networks, and minimizing their effect by regulating traffic at junctions. For the traffic evolution, we consider a Generic Second Order Model, which encompasses the majority of two-equations (i.e., second-order) models available in the literature, and extend it to road networks with merge and diverge junctions. The dynamics on the whole network is determined by selecting a solution to the Riemann Problems at junctions, i.e., the Cauchy problems with constant initial data on each incident road. The latter are solved by assuming the maximization of the flow and assigning a traffic distribution coefficient for outgoing roads of diverges, and a priority rule for incoming roads of merges. A general emission model is considered and its parameters are tuned to the $ {\mathrm{NO_{x}}} $ emission rate. The minimization of emissions is then formulated in terms of the traffic distribution and priority parameters, taking into account travel times. A comparison is provided between roundabouts with optimized parameters and traffic lights, which correspond to time-varying traffic priorities. Our approach can be adapted to manage traffic in complex networks in order to reduce emissions while keeping travel time at acceptable levels.

References

[1]	L. J. Alvarez-Vázquez, N. García-Chan, A. Martínez, M. E. Vázquez-Méndez, Numerical simulation of air pollution due to traffic flow in urban networks, J. Comput. Appl. Math., 326 (2017), 44–61. https://doi.org/10.1016/j.cam.2017.05.017 doi: 10.1016/j.cam.2017.05.017
[2]	L. J. Alvarez-Vázquez, N. García-Chan, A. Martínez, M. E. Vázquez-Méndez, Optimal control of urban air pollution related to traffic flow in road networks, Math. Control Relat. F., 8 (2018), 177–193. https://doi.org/10.3934/mcrf.2018008 doi: 10.3934/mcrf.2018008
[3]	C. Appert-Rolland, F. Chevoir, P. Gondret, S. Lassarre, J. P. Lebacque, M. Schreckenberg, Traffic and granular flow '07, Berlin: Springer-Verlag, 2009.
[4]	R. Atkinson, W. P. Carter, Kinetics and mechanisms of the gas-phase reactions of ozone with organic compounds under atmospheric conditions, Chem. Rev., 84 (1984), 437–470. https://doi.org/10.1021/cr00063a002 doi: 10.1021/cr00063a002
[5]	A. Aw, M. Rascle, Resurrection of "Second Order" Models of Traffic Flow, SIAM J. Appl. Math., 60 (2000), 916–944. https://doi.org/10.1137/S0036139997332099 doi: 10.1137/S0036139997332099
[6]	C. Balzotti, Second order traffic flow models on road networks and real data applications, Doctoral Thesis of Sapienza University, Rome, 2021.
[7]	C. Balzotti, M. Briani, B. De Filippo, B. Piccoli, A computational modular approach to evaluate $\mathrm{NO_x}$ emissions and ozone production due to vehicular traffic, Discrete Cont. Dyn.-B, 27 (2022), 3455–3486.
[8]	S. Blandin, D. Work, P. Goatin, B. Piccoli, A. Bayen, A General Phase Transition Model for Vehicular Traffic, SIAM J. Appl. Math., 71 (2011), 107–127. https://doi.org/10.1137/090754467 doi: 10.1137/090754467
[9]	G. M. Coclite, M. Garavello, B. Piccoli, Traffic flow on a road network, SIAM J. Math. Anal., 36 (2005), 1862–1886. https://doi.org/10.1137/S0036141004402683 doi: 10.1137/S0036141004402683
[10]	R. M. Colombo, Hyperbolic Phase Transitions in Traffic Flow, SIAM J. Appl. Math., 63 (2003), 708–721. https://doi.org/10.1137/S0036139901393184 doi: 10.1137/S0036139901393184
[11]	R. M. Colombo, P. Goatin, B. Piccoli, Road networks with phase transitions, J. Hyperbolic Differ. Equ., 7 (2010), 85–106. https://doi.org/10.1142/S0219891610002025 doi: 10.1142/S0219891610002025
[12]	C. F. Daganzo, Requiem for second-order fluid approximations of traffic flow, Transp. Res. B, 29 (1995), 277–286. https://doi.org/10.1016/0191-2615(95)00007-Z doi: 10.1016/0191-2615(95)00007-Z
[13]	M. L. Delle Monache, P. Goatin, B. Piccoli, Priority-based Riemann solver for traffic flow on networks, Commun. Math. Sci., 16 (2018), 185–211. https://doi.org/10.4310/CMS.2018.v16.n1.a9 doi: 10.4310/CMS.2018.v16.n1.a9
[14]	S. Fan, M. Herty, B. Seibold, Comparative model accuracy of a data-fitted generalized Aw-Rascle-Zhang model, Netw. Heterog. Media, 9 (2014), 239–268. https://doi.org/10.3934/nhm.2014.9.239 doi: 10.3934/nhm.2014.9.239
[15]	S. Fan, B. Seibold, Data-fitted first-order traffic models and their second-order generalizations: Comparison by trajectory and sensor data, Transp. Res. Rec., 2391 (2013), 32–43. https://doi.org/10.3141/2391-04 doi: 10.3141/2391-04
[16]	S. Fan, Y. Sun, B. Piccoli, B. Seibold, D. B. Work, A Collapsed Generalized Aw-Rascle-Zhang Model and its Model Accuracy, arXiv: 1702.03624, [Preprint], (2017) [cited 2023 Feb 22]. Available from: https://doi.org/10.48550/arXiv.1702.03624
[17]	M. Garavello, K. Han, B. Piccoli, Models for Vehicular Traffic on Networks, Springfield: American Institute of Mathematical Sciences, 2016.
[18]	M. Garavello, B. Piccoli, Traffic flow on networks, Springfield: American Institute of Mathematical Sciences, 2006.
[19]	M. Garavello, B. Piccoli, Traffic flow on a road network using the Aw-Rascle Model, Commun. Partial. Differ. Equ., 31 (2006), 243–275. https://doi.org/10.1080/03605300500358053 doi: 10.1080/03605300500358053
[20]	M. Garavello, B. Piccoli, Conservation laws on complex networks, Ann. Inst. H. Poincaré Anal. Non Linéaire, 26 (2009), 1925–1951. https://doi.org/10.1016/j.anihpc.2009.04.001 doi: 10.1016/j.anihpc.2009.04.001
[21]	M. Garavello, B. Piccoli, Coupling of Lighthill-Whitham-Richards and phase transition models, J. Hyperbolic Differ. Equ., 10 (2013), 577–636. https://doi.org/10.1142/S0219891613500215 doi: 10.1142/S0219891613500215
[22]	N. García-Chan, L. J. Alvarez-Vázquez, A. Martínez, M. E. Vázquez-Méndez, Numerical simulation for evaluating the effect of traffic restrictions on urban air pollution, Progress in Industrial Mathematics at ECMI 2016, Springer International Publishing, 2017,367–373.
[23]	M. Herty, S. Moutari, M. Rascle, Optimization criteria for modelling intersections of vehicular traffic flow, Netw. Heterog. Media, 1 (2006), 275–294. https://doi.org/10.3934/nhm.2006.1.275 doi: 10.3934/nhm.2006.1.275
[24]	M. Herty, M. Rascle, Coupling conditions for a class of second-order models for traffic flow, SIAM J. Math. Anal., 38 (2006), 595–616. https://doi.org/10.1137/05062617X doi: 10.1137/05062617X
[25]	H. Holden, N. H. Risebro, A mathematical model of traffic flow on a network of unidirectional roads, SIAM J. Math. Anal., 26 (1995), 999–1017. https://doi.org/10.1137/S0036141093243289 doi: 10.1137/S0036141093243289
[26]	Y. Huang, C. Lei, C. H. Liu, P. Perez, H. Forehead, S. Kong, J. L. Zhou, A review of strategies for mitigating roadside air pollution in urban street canyons, Environ. Pollut., 280 (2021), 116971. https://doi.org/10.1016/j.envpol.2021.116971 doi: 10.1016/j.envpol.2021.116971
[27]	A. Khelifi, H. Haj-Salem, J. P. Lebacque, L. Nabli, Lagrangian generic second order traffic flow models for node, J. Traffic Transp. Eng., 5 (2018), 14–27. https://doi.org/10.1016/j.jtte.2017.08.001 doi: 10.1016/j.jtte.2017.08.001
[28]	O. Kolb, G. Costeseque, P. Goatin, S. Göttlich, Pareto-optimal coupling conditions for the Aw-Rascle-Zhang traffic flow model at junctions, SIAM J. Appl. Math., 78 (2018), 1981–2002. https://doi.org/10.1137/17M1136900 doi: 10.1137/17M1136900
[29]	J. P. Lebacque, S. Mammar, H. Haj-Salem, Generic second order traffic flow modelling, Transportation and Traffic Theory, Netherlands: Elsevier, 2007,755–776.
[30]	J. P. Lebacque, A two phase extension of the LWR model based on the boundedness of traffic acceleration, Transportation and Traffic Theory in the 21st Century, Bradford: Emerald Group Publishing Limited, 2002.
[31]	M. J. Lighthill, G. B. Whitham, On kinematic waves II. A theory of traffic flow on long crowded roads, Proc. Roy. Soc. A, 229 (1955), 317–345. https://doi.org/10.1098/rspa.1955.0089 doi: 10.1098/rspa.1955.0089
[32]	L. I. Panis, S. Broekx, R. Liu, Modelling instantaneous traffic emission and the influence of traffic speed limits, Sci. Total Environ., 371 (2006), 270–285. https://doi.org/10.1016/j.scitotenv.2006.08.017 doi: 10.1016/j.scitotenv.2006.08.017
[33]	H. J. Payne, Models of freeway traffic and control, Proc. Simulation Council, 1 (1971), 51–61.
[34]	B. Piccoli, K. Han, T. L. Friesz, T. Yao, J. Tang, Second-order models and traffic data from mobile sensors, Transport. Res. C-Emer., 52 (2015), 32–56. https://doi.org/10.1016/j.trc.2014.12.013 doi: 10.1016/j.trc.2014.12.013
[35]	P. I. Richards, Shock Waves on the Highway, Operations Research, 4 (1956), 42–51. https://doi.org/10.1287/opre.4.1.42 doi: 10.1287/opre.4.1.42
[36]	S. Samaranayake, S. Glaser, D. Holstius, J. Monteil, K. Tracton, E. Seto, A. Bayen, Real‐time estimation of pollution emissions and dispersion from highway traffic, Comput-Aided Civ. Inf., 29 (2014), 546–558.
[37]	S. Vardoulakis, B. E. Fisher, K. Pericleous, N. Gonzalez-Flesca, Modelling air quality in street canyons: a review, Atmos. Environ., 37 (2003), 155–182. https://doi.org/10.1016/S1352-2310(02)00857-9 doi: 10.1016/S1352-2310(02)00857-9
[38]	G. B. Whitham, Linear and nonlinear waves, New York: John Wiley and Sons, 1974.
[39]	H. M. Zhang, A non-equilibrium traffic model devoid of gas-like behavior, Transp. Res. B, 36 (2002), 275–290. https://doi.org/10.1016/S0191-2615(00)00050-3 doi: 10.1016/S0191-2615(00)00050-3
[40]	K. Zhang, S. Batterman, Air pollution and health risks due to vehicle traffic, Sci. Total Environ., 450 (2013), 307–316. https://doi.org/10.1016/j.scitotenv.2013.01.074 doi: 10.1016/j.scitotenv.2013.01.074

Reader Comments

Your name:*

Email:*
© 2023 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)