Analytical derivations of merge capacity: a multilane approach
Ludovic Leclercq1,2, Florian Marczak1, Victor L. Knoop2, Serge P. Hoogendoorn2
1 Université de Lyon, IFSTTAR / ENTPE, COSYS, LICIT2 Delft University of Technology
Outline
• Presentation of the analytical framework for multilane freeways
• Numerical results– Sensibility to road parameters– Sensitivity to vehicle characteristics– Comparison with traffic simulation
• Experimental validation
• Conclusion
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Sketch of the merge
4
Mandatory lane-changing
1
Discretianory lane-changing 2
We will put together previous analytical results to fully describe the merge behavior in congestion
Discretionary lane changing (1)
• Lane changing flow ϕ triggers by the positive speed difference between lane i and j
• μ and λ are respectively the supply and the demand derived from the triangular FD
• τ is the time for a lane-changing maneuver to complete
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(Laval and Leclercq, 2008)
Discretionary lane changing (2)
• Lanes i and j are congested, so
– μ(kj)=Cj
– λ(kj)=λ(ki)=Qmax
• It comes that:
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Capacity formulae for local merging
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q0
C(q0,v0)
The effective capacity for a local merge only depends on:-the inserting flow-the initial speed-the FD parameter-the maximal acceleration
(Leclercq et al, 2011), further refined in (Leclercq et al, 2014) presented at ITSC2014, Quingdao, China
Agregating the different components
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(FD)
Capacity formula (1):
Daganzo’s merge model
(FD)
Capacity formula (2):Discretionary lane-changing flow :
(FD)
System of 4 equations with 4 unknowns:q0, q12, q1, q2
Refined capacity formulae for the local merge capacity
• (Leclercq et al, 2014) introduces refined capacity formulae that account for:– The interactions between voids and waves– Heterogeneous merging vehicle characteristics
(mainly a proportion of trucks and different acceleration rates for trucks and cars)
• We use these refined expression for C1 and C2
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Sensitivity to road parameters
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Length of the insertion area
C1
C2
C1+C2
Length of the discretionary lane-changing area
C1
C2
C1+C2
Merge ratio
C1
C2
C1+C2
Sensitivity to vehicle characteristics
Car acceleration Truck acceleration
Truck proportionTime to perform a
discretionary lane-change
C1
C2
C1+C2
C1
C2
C1+C2
C1
C2
C1+C2
C1
C2
C1+C2
Experimental site (M6 – England)
Upstream Downstream
6 days of observations17 periods (20 min) of heavy congestion
Extended sketch of the model
L2DLC=L1
DLC
τ1=τ2Rough calibration:
-FD (per lane): u=115 km/h, w=20 km/h, κ=145 veh/km -a=1.8 m/s2; τ1=τ2=3 s;-L=160 m ; L2
DLC=L1DLC=100 m
Conclusion
• Combining different analytical formulae designed for local problems (local merge, discretionary lane-changing,…) leads to a global analytical model for multilane freeways
• Fast (low computational cost) estimation can be obtained for the total effective capacity and the capacity per lane
• The proposed framework can account for vehicle heterogeneity
• First experimental results are promising
• Of course, this is only an estimate of the mean capacity value for a large time period (20 min). This approach is not able to estimate the short-term evolution of the flow (traffic dynamics)
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Thank you for your attentionThank you for your attention
Leclercq, L., Knoop, V., Marczak, F., Hoogendoorn, S. Capacity Drops at Merges: New Analytical Investigations, Proceedings of the IEEE-ITSC2014 conference, Qingdao, China, October 2014. Leclercq, L., Laval, J.A., Chiabaut, N. Capacity Drops at Merges: an endogenous model, Transportation Research Part B, 45(9), 2011, 1302-1313.
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