Modeling traffic flow in large-scale networks Guilhem Mariotte & Ludovic Leclercq June 19, 2017 Univ Lyon, ENTPE, IFSTTAR, LICIT SMRT, Grettia, Marne-la-Vallée
Introduction Macroscopic models Multi-routes Application example References About traffic flow modeling www.ifs � ar.fr SMRT – June 19, 2017 – Guilhem Mariotte & Ludovic Leclercq 2
Introduction Macroscopic models Multi-routes Application example References Why modeling traffic flow? Urban planning Traffjc state estimation Control Public transports Gas emissions www.ifs � ar.fr photo credits: Lucas Gallone, Hermes Rivera, Markus Spiske – unsplash.com SMRT – June 19, 2017 – Guilhem Mariotte & Ludovic Leclercq 3
Introduction Macroscopic models Multi-routes Application example References Brief overview of traffic flow models Macroscopic SCALE (network level) ?? Mesoscopic (link level) LWR CTM LTM Aimsum (TSS) Microscopic (vehicle level) Car following Movsim LWR Symuvia Vissim (Gipps, IDM, ...) (Kesting, Germ, (LICIT) Car following (PTV) Budden, Treiber) Lane changing (Newell) Corsim Gap acceptance MODEL DYN. (Univ. of Florida) Microscopic Macroscopic (individual vehicle motion) (vehicle fmow and density) www.ifs � ar.fr SMRT – June 19, 2017 – Guilhem Mariotte & Ludovic Leclercq 4
Introduction Macroscopic models Multi-routes Application example References Limitations of these models at the network scale • Computational complexity • Real-time calculations almost impossible • Large and detailed amount of information required (demand patterns, shortest paths, assignment, ...) Road network of Lyon-Villeurbanne: 27,000 links 1700 entries 1700 exits www.ifs � ar.fr SMRT – June 19, 2017 – Guilhem Mariotte & Ludovic Leclercq 5
Introduction Macroscopic models Multi-routes Application example References Brief overview of traffic flow models Macroscopic SCALE (network level) MFD-based Bi-dimensional Mesoscopic (link level) LWR CTM LTM Aimsum (TSS) Microscopic (vehicle level) Car following Movsim LWR Symuvia Vissim (Gipps, IDM, ...) (Kesting, Germ, (LICIT) Car following (PTV) Budden, Treiber) Lane changing (Newell) Corsim Gap acceptance MODEL DYN. (Univ. of Florida) Microscopic Macroscopic (individual vehicle motion) (vehicle fmow and density) www.ifs � ar.fr SMRT – June 19, 2017 – Guilhem Mariotte & Ludovic Leclercq 6
Introduction Macroscopic models Multi-routes Application example References Macroscopic MFD-based models www.ifs � ar.fr SMRT – June 19, 2017 – Guilhem Mariotte & Ludovic Leclercq 7
Introduction Macroscopic models Multi-routes Application example References Split the network into zones or “reservoirs” Real network www.ifs � ar.fr SMRT – June 19, 2017 – Guilhem Mariotte & Ludovic Leclercq 8
Introduction Macroscopic models Multi-routes Application example References Split the network into zones or “reservoirs” Real network Clustering into zones or “reservoirs” www.ifs � ar.fr SMRT – June 19, 2017 – Guilhem Mariotte & Ludovic Leclercq 8
Introduction Macroscopic models Multi-routes Application example References Split the network into zones or “reservoirs” Real network Clustering into zones Modeling of flow or “reservoirs” exchanges between zones www.ifs � ar.fr SMRT – June 19, 2017 – Guilhem Mariotte & Ludovic Leclercq 8
Introduction Macroscopic models Multi-routes Application example References Flow dynamics in one zone: the single reservoir or bathtub problem q in ( t ) n ( t ) q out ( t ) q in ( t ) n ( t ) q out ( t ) www.ifs � ar.fr SMRT – June 19, 2017 – Guilhem Mariotte & Ludovic Leclercq 9
Introduction Macroscopic models Multi-routes Application example References Traffic regimes www.ifs � ar.fr SMRT – June 19, 2017 – Guilhem Mariotte & Ludovic Leclercq 10
Introduction Macroscopic models Multi-routes Application example References The Macroscopic or Network Fundamental Diagram (MFD or NFD) Flow of circulating vehicles 2 3 1 www.ifs � ar.fr Density / number of vehicles SMRT – June 19, 2017 – Guilhem Mariotte & Ludovic Leclercq 11
Introduction Macroscopic models Multi-routes Application example References Traffic flow dynamics: two approaches V ( n ) = P ( n ) P ( n ) n P ( n ) or V ( n ) , L q in ( t ) q out ( t ) n ( t ) n n single reservoir production and speed MFD dn dt = q in ( t ) − q out ( t ) q in ( t ) : defined by demand q out ( t ) : ?? → two modeling approaches No spatial extension in a reservoir!! www.ifs � ar.fr → need to define a trip length SMRT – June 19, 2017 – Guilhem Mariotte & Ludovic Leclercq 12
Introduction Macroscopic models Multi-routes Application example References Accumulation-based model (Daganzo, 2007, Geroliminis & Daganzo, 2007) Use the principle of the queuing formula of Little (1961): q out ( t ) = n T = nV L = P L t = 0 s L = 50 m q in q out = 1.05 veh/s n = 3 veh Speed−MFD Prod−MFD 52.7 veh.m/s 21.1 m/s P V n = 2.5 veh n = 2.5 veh www.ifs � ar.fr SMRT – June 19, 2017 – Guilhem Mariotte & Ludovic Leclercq 13
Introduction Macroscopic models Multi-routes Application example References Trip-based model (Arnott, 2013) Explicit formulation of the trip length L : ∫ t V ( n ( t )) L = V ( n ( s )) ds q out ( t ) = q in ( t − T ( t )) ⇐ ⇒ V ( n ( t − T ( t ))) t − T ( t ) t = 0 s L = 50 m q in q out = 1.05 veh/s n = 3 veh Speed−MFD Prod−MFD 60.9 veh.m/s P 20.3 m/s V n = 3 veh n = 3 veh www.ifs � ar.fr SMRT – June 19, 2017 – Guilhem Mariotte & Ludovic Leclercq 14
Introduction Macroscopic models Multi-routes Application example References Accumulation-based (free-flow conditions) N−curves N in t = 0 s − n = 0 veh 0 veh 0 veh N out t Accumulation 1.5 veh/s n 0 veh t 0 Travel time t 0 veh/s Outflow−MFD 0 veh/s q out n www.ifs � ar.fr SMRT – June 19, 2017 – Guilhem Mariotte & Ludovic Leclercq 15
Introduction Macroscopic models Multi-routes Application example References Trip-based (free-flow conditions) t = 0 s − n = 0 veh N−curves N in 0 veh 0 veh N out t Accumulation n 0 veh t Travel time T 0 s t Speed−MFD 25 m/s V n 0 10 20 30 40 50 distance traveled D [m] www.ifs � ar.fr SMRT – June 19, 2017 – Guilhem Mariotte & Ludovic Leclercq 16
Introduction Macroscopic models Multi-routes Application example References Accumulation-based (congested conditions) N−curves N in t = 0 s − n = 0 veh 0 veh 0 veh N out t Accumulation 1.5 veh/s n 0 veh t 0 Travel time t 0 veh/s Outflow−MFD 0 veh/s q out n www.ifs � ar.fr SMRT – June 19, 2017 – Guilhem Mariotte & Ludovic Leclercq 17
Introduction Macroscopic models Multi-routes Application example References Trip-based (congested conditions) t = 0 s − n = 0 veh N−curves N in 0 veh 0 veh N out t Accumulation n 1 veh t Travel time 0 s T t Speed−MFD 23.4 m/s V n 0 10 20 30 40 50 distance traveled D [m] www.ifs � ar.fr SMRT – June 19, 2017 – Guilhem Mariotte & Ludovic Leclercq 18
Introduction Macroscopic models Multi-routes Application example References Major differences Accumulation-based: Trip-based: www.ifs � ar.fr SMRT – June 19, 2017 – Guilhem Mariotte & Ludovic Leclercq 19
Introduction Macroscopic models Multi-routes Application example References Major differences Accumulation-based: • flow exchange management at the reservoir borders Trip-based: • track of individual vehicles www.ifs � ar.fr SMRT – June 19, 2017 – Guilhem Mariotte & Ludovic Leclercq 19
Introduction Macroscopic models Multi-routes Application example References Major differences Accumulation-based: • flow exchange management at the reservoir borders • outflow demand explicitly defined by the formula of Little (1961) Trip-based: • track of individual vehicles • outflow demand implicitly defined: result of the vehicles traveling at the reservoir mean speed www.ifs � ar.fr SMRT – June 19, 2017 – Guilhem Mariotte & Ludovic Leclercq 19
Introduction Macroscopic models Multi-routes Application example References Major differences Accumulation-based: • flow exchange management at the reservoir borders • outflow demand explicitly defined by the formula of Little (1961) • smooth and continuous evolution of flow Trip-based: • track of individual vehicles • outflow demand implicitly defined: result of the vehicles traveling at the reservoir mean speed • irregular and discontinuous representation of flow (stochasticity) www.ifs � ar.fr SMRT – June 19, 2017 – Guilhem Mariotte & Ludovic Leclercq 19
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