Analytical derivations of merge capacity: a multilane approach

1. 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, LICIT 2 Delft University of Technology

2. 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

3. The modelling Framework

4. Sketch of the merge Discretianory lane-changing 2 1 Mandatory lane-changing We will put together previous analytical results to fully describe the merge behavior in congestion

5. Discretionary lane changing (1) • Lane changing flow ϕ triggers by the positive speed difference between lane i and j • μ andλ are respectively the supply and the demand derived from the triangular FD • τ is the time for a lane-changing maneuver to complete (Laval and Leclercq, 2008)

6. Discretionary lane changing (2) • Lanes i and j are congested, so • μ(kj)=Cj • λ(kj)=λ(ki)=Qmax • It comes that:

7. Capacity formulae for local merging C(q0,v0) q0 • 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

8. Agregating the different components Capacity formula (1): Daganzo’s merge model Capacity formula (2): (FD) (FD) Discretionary lane-changing flow : (FD) System of 4 equations with 4 unknowns: q0, q12, q1, q2

9. Numericalresults

10. 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

11. Sensitivity to road parameters C1+C2 C1+C2 C2 C2 C1 C1 Length of the discretionary lane-changing area Length of the insertion area C1+C2 C2 C1 Merge ratio

12. Sensitivity to vehicle characteristics C1+C2 C1+C2 C2 C2 C1 C1 Truck acceleration Car acceleration C1+C2 C1+C2 C2 C2 C1 C1 Time to perform adiscretionary lane-change Truck proportion

13. Comparison with a traffic simulator ε is the relaxation parameter

14. Experimental validation

15. Experimental site (M6 – England) Downstream Upstream 6 days of observations 17 periods (20 min) of heavy congestion

16. Extended sketch of the model L2DLC=L1DLC τ1=τ2 • Rough 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 ; L2DLC=L1DLC=100 m

17. Experimental results

18. Conclusion

19. 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)

20. Thank 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.