Te its 2017-lesson 17 signal synchronization part 1 v02
Download as PPT, PDF1 like288 views
The document discusses traffic signal synchronization, emphasizing its role in reducing delays at junctions in urban road networks. It outlines ideal synchronization conditions and the mathematical formulation for achieving minimal delays, mentioning challenges in real-world applications. The text also contrasts ideal and real synchronization strategies, highlighting the importance of green bandwidth in optimizing traffic flow.
Te its 2017-lesson 17 signal synchronization part 1 v02
- 1. Prof. Gaetano Fusco gaetano.fusco@uniroma1.it http://w3.uniroma1.it/gaetanofusco Traffic Signal Synchronization Prof. Gaetano Fusco gaetano.fusco@uniroma1.it http://gaetanofusco.site.uniroma1.it/ Academic Year 2015-2016, Spring Semester Course of Traffic Engineering and ITS
- 2. Motivations for synchronization • Delay at junctions is the most relevant component of travel times in urban road networks • Signal synchronization (or signal coordination) sets a relationship among green starts at near junctions. • The goal is to reduce or, if possible, make nil junction delay. • Reduction of delay depends on the distance between junctions, traffic flow patterns and vehicle speed. Traffic Engineering and ITS 05/05/17 Page 2
- 3. Problem Description • The synchronization problem with maximal bandwidth consists in: • Finding the vector of offset θij that minimizes the delays of vehicles traveling along the artery • Given: – The distance between consecutive intersections: li – The signal settings at each intersection: C, gi – The synchronization speed in the two directions, assuming that vehicles travel at that speed along the artery: v1, v2 (or a suitable interval vmin ≤ v ≤ vmax) 05/05/17Traffic Engineering and ITS Page 3
- 4. Ideal synchronization Section One Traffic Engineering and ITS 05/05/17 Page 4
- 5. 05/05/17Traffic Engineering and ITS Page 5 Ideal synchronization
- 6. • Only in one case the node delay can be zero: – All junctions are equally spaced; – No entering or exiting traffic along the artery; – Traffic flow lower than a given value. • Then: – Cycle length and green splits are equal at all junctions. – All vehicles along the artery run at the same speed and form so a uniform and compact platoon. 05/05/17Traffic Engineering and ITS Page 6 Ideal synchronization
- 7. Ideal synchronization • …then: – A vehicle progression along the artery can be found so that vehicles are not delayed at nodes. – At each node, the green must start as the first vehicle of the platoon arrives and must end just after the last vehicle has passed the intersection. 05/05/17Traffic Engineering and ITS Page 7
- 8. A Ideal synchronization C C A 2 3 1 v1 t x r g=b 05/05/17Traffic Engineering and ITS Page 8
- 9. C C θ1,2 = 0,5C θ2,3 = 0,5C x1,2= A x2,3= A 2 3 1 v1 v2 t x t1,2 t2,1 r g=b A Ideal synchronization 05/05/17Traffic Engineering and ITS Page 9
- 10. Mathematical Formulation • The time interval between the green start at near junctions spaced as A, i and j (offset θij) equals the travel time tij: • if v1=v2=v and m=1: • Constraints on speed v and cycle C: vmin ≤ v ≤ vmax Cmin ≤ C ≤ Cmax integer 21 m,mC v A v A tt jiij =+=+ v A CC v A v A tt jiij 2 , =⇒=+=+ 05/05/17Traffic Engineering and ITS Page 10
- 11. Ideal synchronization • The condition Cmin is given by the saturation degree of the most critical junction: Cmin= maxi{Cmin,i} • The condition Cmax is given by the minimum speed: Cmax = 2A/vmin • If Cmin > Cmax the problem has no solution. 05/05/17Traffic Engineering and ITS Page 11
- 12. Ideal synchronization • If Cmin > Cmax the problem has no solution. • High saturation degrees mean high values for Cmin. • The synchronization is possible if Cmax is low, or if the distance A between junctions is short or the synchronization speed v is low. • For example, if: Cmin=70s; v=10m/s, the distance must be: A= vCmin/2 A >350m! 05/05/17Traffic Engineering and ITS Page 12
- 13. Formulation of Maximal Bandwidth Problem Section Two Traffic Engineering and ITS 05/05/17 Page 13
- 14. “Real” synchronization • Ideal synchronization is usually unfeasible because: – Junctions are not equally spaced – Flow is not uniform along the artery – Green splits are not equal. • To solve realistic problems, two different approaches have been proposed, corresponding to two optimization problems: • Minimum delay problem; – non convex • Maximal green bandwidth problem – concave, but different of delay minimization. 05/05/17Traffic Engineering and ITS Page 14
- 15. Green Bandwidth • The green bandwidth is defined as the set of possible trajectories at a constant speed that are uninterrupted along the artery. 05/05/17Traffic Engineering and ITS Page 15
- 16. “Real” Synchronization 0 20 40 60 80 100 120 140 160 180 0 100 200 300 400 500 05/05/17Traffic Engineering and ITS Page 16
- 17. Example of real maximal bandwidth 0 20 40 60 80 100 120 140 160 180 0 100 200 300 400 500 05/05/17Traffic Engineering and ITS Page 17
- 18. Green Bandwidth (2) • The green bandwidth is defined as the set of possible trajectories at a constant speed that are uninterrupted along the artery. • Such possible trajectories are not coincident, in general, with the real trajectories of the vehicles. 05/05/17Traffic Engineering and ITS Page 18
- 19. Green bandwidth and actual platoon progression are different things g=λC r = (1-λ)C b i+1 i l v Bandwidth Delayed vehicles Delayed vehicles Bandwidth 05/05/17Traffic Engineering and ITS Page 19