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

2

The modelling Framework

3

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

5

(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:

6

Capacity formulae for local merging

7

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

8

(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

Numerical results

9

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

10

Sensitivity to road parameters

11

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

Comparison with a traffic simulator

ε is the relaxation parameter

Experimental validation

14

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

Experimental results

Conclusion

18

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)

19

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.