A multi-band approach to arterial traffic signal optimization. Nathan H. Gartner Susan F. Assmann Fernando Lasaga Dennin L. Hou

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1 A mul-an appoach o aeal affc sgnal opmzaon Nahan H. Gane Susan F. Assmann Fenano Lasaga Dennn L. Hou

2 MILP- The asc, symmec, unfom-h anh maxmzaon polem MILP- Exens he asc polem o nclue asymmec anhs n opposng econs, vaale lef-un phase sequence, as ell as ecsons on cycle me lengh an lnk specfc pogesson spees MILP-3 Pesens he ne mul-an, mul-egh appoach, hch also ncopoaes all pevous ecson capales

3 3 Ououn Inefeence vaale Queue cleaance me Ououn anh a Re me Inoun Re me Tme ououn

4 Ououn 3 3, Inenoe offses Tme

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6 Inoun 3 3, Inenoe offses Tme

7 * cycle me m, =,, m s an nege vaale Inanoe offse of nesecon,, m, Tme

8 , Ououn, 0.5 * 0.5 *, 3a Tavel me fom S o S ououn, Tme

9 Inoun,, 0.5 * 0.5 *, 3, Tme

10 ,, m,, 0.5 * 0.5 *, 3a, 0.5 * 0.5 *, 3 Susung 3 no :,, 0.5 * 0.5 * m,

11 If e eplace nesecon y nesecon :, * 0.5 * 0.5,, m, 0.5 * 0.5 *,, m

12 We efne, x x m 0.5 * 0.5 *

13 MILP- sujec o, Max o m,,, Fn m 0.5 * 0.5 * m nege,...,n,,,, 0

14 MILP- The asc, symmec, unfom-h anh maxmzaon polem MILP- Exens he asc polem o nclue asymmec anhs n opposng econs, vaale lef-un phase sequence, as ell as ecsons on cycle me lengh an lnk specfc pogesson spees MILP-3 Pesens he ne mul-an, mul-egh appoach, hch also ncopoaes all pevous ecson capales

15 MILP- Exenson The econal eghng of he o ans Max k, sujec o k f k ououn favoe k f k noun favoe f k alance pogesson k k k

16 Exenson Le oh he common sgnal cycle me C an he lnk specfc pogesson spee v e opmzale vaales C z C z C C, C e g, h, f e g,, h f h loe an uppe lnson cyclelengh f v v e v loe an uppe lmson changen ouounnounspeefeesecon loe an uppe lnson ouounnounspeefeesecon g

17 Dsance eeen Sh an S Pogesson spee Tavel me noun v z v z Sgnal fequency

18 e v f g v v h z e z f z g z h

19 Exenson 3 Deemne he sequence of he lef un phase Lea Lag

20 Ououn lef leas: Inoun lags paen Inoun Ououn L G G L R R R R G G L L G G R L L ououn noun geen me fo hough affc a S me allocae fo ououn noun lef un affc a S common e me n oh econs o pove fo coss see movemen a S

21 Ououn lef lags: Inoun leas paen Inoun Ououn L G G L R R R R G G L L G G R L L ououn noun geen me fo hough affc a S me allocae fo ououn noun lef un affc a S common e me n oh econs o pove fo coss see movemen a S

22 Ououn lef leas: Inoun leas paen 3 Inoun Ououn L L G G R R OR R R G G L L G G R L L ououn noun geen me fo hough affc a S me allocae fo ououn noun lef un affc a S common e me n oh econs o pove fo coss see movemen a S

23 Ououn lef lags: Inoun lags paen Inoun Ououn G G L L R G G OR L L ououn noun geen me fo hough affc a S me allocae fo ououn noun lef un affc a S common e me n oh econs o pove fo coss see movemen a S R R R R G G L L

24 : he me fom he cene of o he nex cene of Tme

25 0.5*[ * L * L ], :0 - vaales Paen L L L L L L 0.5 L L

26 MILP- Fn,, z,,, C C z, Max k, sujec o k k k,,, m o

27 m L L L L z e z f z g z h z e z f z g z h 0,,, z,,, :- 0 vaale, nege m

28 MILP- The asc, symmec, unfom-h anh maxmzaon polem MILP- Exens he asc polem o nclue asymmec anhs n opposng econs, vaale lef-un phase sequence, as ell as ecsons on cycle me lengh an lnk specfc pogesson spees MILP-3 Pesens he ne mul-an, mul-egh appoach, hch also ncopoaes all pevous ecson capales

29 Defne a ffeen anh fo each econal oa secon of he aeal

30 3 Ououn Tme fom gh se of e a S o cenelne of ououn geenan Cenelne of geen an Tme

32 3 Ououn Tme

34 Fo noun Fo noun

35 The ao consan fom MILP- s change o eflec he mul-an suaon Max k, sujec o k f k ououn favoe k f k noun favoe f k alance pogesson k k k k k k

36 MILP-3 Ojecve funcon max B n n a a hee v v s s v p a a s s econal volume on secon, ououn noun sauaon flo on secon, ououn noun p exponenal poe; he values p 0,,, ee use v p

37 To oan an ojecve funcon value ha s conssen h hose use pevously, e nomalze he eghng coeffcens o oan n a n n a n

38 MILP-3 Fn,, z,,,,,,, m o max B n n a a Sujec o k k C C z k

40 m L L L L z e z f z g z h z e z f z g z h 0,,, z,,, :- 0 vaale, nege m

41 Q & A

2 shear strain / L for small angle

2 shear strain / L for small angle Sac quaons F F M al Sess omal sess foce coss-seconal aea eage Shea Sess shea sess shea foce coss-seconal aea llowable Sess Faco of Safe F. S San falue Shea San falue san change n lengh ognal lengh Hooke