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Modeling traffic flow in large-scale networks Guilhem Mariotte & Ludovic Leclercq June 19, 2017 Univ Lyon, ENTPE, IFSTTAR, LICIT SMRT, Grettia, Marne-la-Valle Introduction Macroscopic models Multi-routes Application example

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Modeling traffic flow in large-scale networks

Guilhem Mariotte & Ludovic Leclercq Univ Lyon, ENTPE, IFSTTAR, LICIT June 19, 2017 SMRT, Grettia, Marne-la-Vallée

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Introduction Macroscopic models Multi-routes Application example References

About traffic flow modeling

SMRT – June 19, 2017 – Guilhem Mariotte & Ludovic Leclercq 2

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Introduction Macroscopic models Multi-routes Application example References

Why modeling traffic flow?

Traffjc state estimation Control Urban planning Public transports Gas emissions

photo credits: Lucas Gallone, Hermes Rivera, Markus Spiske – unsplash.com SMRT – June 19, 2017 – Guilhem Mariotte & Ludovic Leclercq 3

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Introduction Macroscopic models Multi-routes Application example References

Brief overview of traffic flow models

Microscopic Macroscopic

(individual vehicle motion) (vehicle fmow and density)

Microscopic

(vehicle level)

Mesoscopic

(link level)

Macroscopic

(network level) Car following (Gipps, IDM, ...) Lane changing Gap acceptance Car following (Newell) LWR LWR CTM

SCALE MODEL DYN.

LTM Vissim

(PTV)

Corsim

(Univ. of Florida)

Aimsum

(TSS)

Movsim

(Kesting, Germ, Budden, Treiber)

Symuvia

(LICIT)

??

SMRT – June 19, 2017 – Guilhem Mariotte & Ludovic Leclercq 4

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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

SMRT – June 19, 2017 – Guilhem Mariotte & Ludovic Leclercq 5

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Introduction Macroscopic models Multi-routes Application example References

Brief overview of traffic flow models

Microscopic Macroscopic

(individual vehicle motion) (vehicle fmow and density)

Microscopic

(vehicle level)

Mesoscopic

(link level)

Macroscopic

(network level) Car following (Gipps, IDM, ...) Lane changing Gap acceptance Car following (Newell) MFD-based Bi-dimensional LWR LWR CTM

SCALE MODEL DYN.

LTM Vissim

(PTV)

Corsim

(Univ. of Florida)

Aimsum

(TSS)

Movsim

(Kesting, Germ, Budden, Treiber)

Symuvia

(LICIT)

SMRT – June 19, 2017 – Guilhem Mariotte & Ludovic Leclercq 6

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Macroscopic MFD-based models

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Split the network into zones or “reservoirs”

Real network

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Split the network into zones or “reservoirs”

Real network Clustering into zones

  • r “reservoirs”

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Split the network into zones or “reservoirs”

Real network Clustering into zones

  • r “reservoirs”

Modeling of flow exchanges between zones

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Flow dynamics in one zone: the single reservoir or bathtub problem

qin(t) qout(t) n(t) n(t) qin(t) qout(t)

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Traffic regimes

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The Macroscopic or Network Fundamental Diagram (MFD or NFD)

Density / number of vehicles Flow of circulating vehicles 1 2 3

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Traffic flow dynamics: two approaches

n(t) P(n) or V(n), L qin(t) qout(t)

single reservoir

P(n) n V(n) = P(n)

n

n

production and speed MFD

dn dt = qin(t) − qout(t) qin(t) : defined by demand qout(t) : ?? → two modeling approaches No spatial extension in a reservoir!! → need to define a trip length

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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): qout(t) = n T = nV L = P L

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t = 0 s L = 50 m n = 3 veh qin qout = 1.05 veh/s

n = 2.5 veh P Prod−MFD 52.7 veh.m/s n = 2.5 veh V Speed−MFD 21.1 m/s

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Trip-based model

(Arnott, 2013)

Explicit formulation of the trip length L: L =

∫ t

t−T(t)

V(n(s))ds ⇐ ⇒ qout(t) = qin(t − T(t)) V(n(t)) V(n(t − T(t)))

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t = 0 s L = 50 m n = 3 veh qin qout = 1.05 veh/s

n = 3 veh P Prod−MFD 60.9 veh.m/s n = 3 veh V Speed−MFD 20.3 m/s

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Accumulation-based (free-flow conditions)

SMRT – June 19, 2017 – Guilhem Mariotte & Ludovic Leclercq 15 1.5 veh/s 0 veh/s

t = 0 s − n = 0 veh

t Nin Nout N−curves 0 veh 0 veh t n Accumulation 0 veh t Travel time n qout Outflow−MFD 0 veh/s

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Trip-based (free-flow conditions)

SMRT – June 19, 2017 – Guilhem Mariotte & Ludovic Leclercq 16 10 20 30 40 50 t = 0 s − n = 0 veh distance traveled D [m] t Nin Nout N−curves 0 veh 0 veh t n Accumulation 0 veh t T Travel time 0 s n V Speed−MFD 25 m/s

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Accumulation-based (congested conditions)

SMRT – June 19, 2017 – Guilhem Mariotte & Ludovic Leclercq 17 1.5 veh/s 0 veh/s

t = 0 s − n = 0 veh

t Nin Nout N−curves 0 veh 0 veh t n Accumulation 0 veh t Travel time n qout Outflow−MFD 0 veh/s

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Trip-based (congested conditions)

SMRT – June 19, 2017 – Guilhem Mariotte & Ludovic Leclercq 18 10 20 30 40 50 t = 0 s − n = 0 veh distance traveled D [m] t Nin Nout N−curves 0 veh 0 veh t n Accumulation 1 veh t T Travel time 0 s n V Speed−MFD 23.4 m/s

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Major differences

Accumulation-based: Trip-based:

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Major differences

Accumulation-based:

  • flow exchange management at the reservoir borders

Trip-based:

  • track of individual vehicles

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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

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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)

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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
  • algorithm complexity depending on the number of reservoirs and the

time step choice (fast)

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)
  • algorithm complexity depending on the number of reservoirs and the

number of vehicles (slower)

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Multi-routes in a reservoir

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Inner dynamics of a reservoir

We may define different travel distances inside the same reservoir, but all users/flows experience the same mean speed → Outflows from each different trips are all inter-dependent!!

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Case of two routes

L1 L2 n2(t) L1 n1(t) L2

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Accumulation-based, two routes, (free-flow)

SMRT – June 19, 2017 – Guilhem Mariotte & Ludovic Leclercq 23 n1 n2

0 veh/s 0 veh/s 0 veh/s 0 veh/s

t = 0 s − n = 0 veh

n1 n2 Accumulation 0 veh 0 veh qin1 qin2 qout1 qout2 In/Outflow 0 veh/s 0 veh/s

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Accumulation-based, two routes, (congestion)

SMRT – June 19, 2017 – Guilhem Mariotte & Ludovic Leclercq 24 n1 n2

0 veh/s 0 veh/s 0 veh/s 0 veh/s

t = 0 s − n = 0 veh

n1 n2 Accumulation 0 veh 0 veh qin1 qin2 qout1 qout2 In/Outflow 0 veh/s 0 veh/s

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Application on a real network

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Application example on the network of Lyon 6

1 2 3 4 5 6 7 8 9 10 11 O1 → O2 → O3 → O4 → O5 → O6 → O 7 → O8 → O 9 → O 1 → O 1 1 → O12 → O 1 3 → O 1 4 → O15 → O 1 6 → O17 → O18 → O19 → O 2 → → D1 → D2 → D3 → D4 → D5 → D6 → D 7 → D8 → D 9 → D10 → D 1 1 → D12 → D13 → D14 → D15 → D16 → D17 → D18

Satellite view of Lyon, France ( c ⃝ Google Maps) SMRT – June 19, 2017 – Guilhem Mariotte & Ludovic Leclercq 26

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Application example on the network of Lyon 6

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Application example on the network of Lyon 6

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R1 R2 R3 R4 R5 R6 R7 R8 R9 R10 R11 t = 0 s Accumulation [veh] Accumulation [-] 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

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Application example on the network of Lyon 6

We can achieve a better distribution of trips among the reservoirs through assignment schemes (Probit here)

1 2 3 4 5 6 7 8 9 10 11 O1 → O2 → O3 → O4 → O5 → O6 → O 7 → O8 → O 9 → O 1 → O 1 1 → O12 → O 1 3 → O 1 4 → O15 → O 1 6 → O17 → O18 → O19 → O 2 → → D1 → D2 → D3 → D4 → D5 → D6 → D 7 → D8 → D 9 → D10 → D 1 1 → D12 → D13 → D14 → D15 → D16 → D17 → D18 1 2 3 4 5 6 7 8 9 10 11 O1 → O2 → O3 → O4 → O5 → O6 → O 7 → O8 → O 9 → O 1 → O 1 1 → O12 → O 1 3 → O 1 4 → O15 → O 1 6 → O17 → O18 → O19 → O 2 → → D1 → D2 → D3 → D4 → D5 → D6 → D 7 → D8 → D 9 → D10 → D 1 1 → D12 → D13 → D14 → D15 → D16 → D17 → D18

3 OD, 3 macro-routes 3 OD, 6 macro-routes

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Application example on the network of Lyon 6

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R1 R2 R3 R4 R5 R6 R7 R8 R9 R10 R11 t = 0 s Accumulation [veh] Accumulation [-] 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

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Current research questions & further work

With real networks and data:

  • MFD definition and estimation
  • Network clustering
  • Trip length definition and estimation

Theoretical issues:

  • Flow merging problems between reservoirs
  • Congestion propagation within multi route frameworks

SMRT – June 19, 2017 – Guilhem Mariotte & Ludovic Leclercq 31

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Acknowledgements

This project has received funding from the European Research Council (ERC) under the European Unions Horizon 2020 research and innovation programme (grant agreement No 646592 – MAGnUM project).

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Thank you for your attention

Guilhem Mariotte & Ludovic Leclercq

  • guilhem.mariotte@ifsttar.fr
  • www.guilhemmariotte.com

Univ Lyon, ENTPE, IFSTTAR, LICIT UMR _T 9401, F-69518, LYON, France

  • Rue Maurice Audin

69518 Vaulx-en-Velin Cedex France

  • +33 (0)4 72 04 77 69

www.entpe.fr | www.ifsttar.fr | www.licit-lyon.eu | magnum.ifsttar.fr SMRT – June 19, 2017 – Guilhem Mariotte & Ludovic Leclercq 33

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References

Arnott, R. (2013). A bathtub model of downtown traffic congestion. Journal of Urban Economics, 76:110–121. Daganzo, C. F. (2007). Urban gridlock: Macroscopic modeling and mitigation approaches. Transportation Research Part B: Methodological, 41(1):49–62. Geroliminis, N. & Daganzo, C. F. (2007). Macroscopic modeling of traffic in cities. In Transportation Research Board 86th Annual Meeting, 07-0413. Washington DC. Little, J. D. C. (1961). A proof for the queuing formula. Operations Research, 9(3):383–387. SMRT – June 19, 2017 – Guilhem Mariotte & Ludovic Leclercq 34