1. Analytical derivations of merge capacity: a multilane approach Ludovic Leclercq 1,2, Florian Marczak 1, Victor L. Knoop 2, Serge P. Hoogendoorn 2 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 2

3. THE MODELLING FRAMEWORK 3

4. 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

5. 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)

6. Discretionary lane changing (2) Lanes i and j are congested, so – μ(k j )=C j –λ(k j )=λ(k i )=Q max It comes that: 6

7. Capacity formulae for local merging 7 q0q0 C(q0,v0)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

8. 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: q 0, q 12, q 1, q 2

9. NUMERICAL RESULTS 9

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 C 1 and C 2 10

11. Sensitivity to road parameters 11 Length of the insertion area C1C1 C2C2 C1+C2C1+C2 Length of the discretionary lane-changing area C1C1 C2C2 C1+C2C1+C2 Merge ratio C1C1 C2C2 C1+C2C1+C2

12. Sensitivity to vehicle characteristics Car acceleration Truck acceleration Truck proportion Time to perform a discretionary lane-change C1C1 C2C2 C1+C2C1+C2 C1C1 C2C2 C1+C2C1+C2 C1C1 C2C2 C1+C2C1+C2 C1C1 C2C2 C1+C2C1+C2

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

14. EXPERIMENTAL VALIDATION 14

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

16. Extended sketch of the model L 2 DLC =L 1 DLC τ 1 = τ 2 Rough calibration: -FD (per lane): u=115 km/h, w=20 km/h, κ =145 veh/km -a=1.8 m/s 2 ; τ 1 = τ 2 =3 s; -L=160 m ; L 2 DLC =L 1 DLC =100 m

17. Experimental results

18. CONCLUSION 18

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) 19

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.