Modeling and Optimization of Traffic Flow in Urban Areas - Czech ...

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22 Chapter 3 General Light Controlled Intersection ModelThe axes show the speeds of transitions T 4 and T 5 . A gray polygon boundsthe area where the possible speed v 4 and v 5 can be placed. This polygonis bounded by v 1 , v 2 and v 3 from one side and by the axes from the otherside. All combinations of the speeds v 4 and v 5 which are in proportion to themaximal speed V 4 and V 5 are located on the line λ. Point A, in Fig. 3.2(a),is where v 4 and v 5 are at a maximum and are located on line λ. The conflictresolution is given by this point A and the speed transitions for T 4 and T 5are v 4 = 30 and v 5 = 10, respectively.Let us consider the modification of speed v 1 from v 1 = 35 to v 1 = 25(see Fig. 3.2(b)). This situation corresponds to point B where v 4 and v 5 areat a maximum and are located closest to line λ. The conflict resolution isgiven by this point and the speed of the transitions T 4 and T 5 is v 4 = 25and v 5 = 15, respectively. Note that the speed is not in proportion to themaximal speed V 4 and V 5 , but it is the maximum firing speed combination.Let us assume v 1 to be equal to 15 (see Fig. 3.2(c)). This situationcorresponds to point C where v 4 and v 5 are at a maximum and are locatedclosest to line λ. The conflict resolution is given by this point and the speedof the transitions T 4 and T 5 is v 4 = 15 and v 5 = 18, respectively. Note thatthere is no actual conflict in this case.We can generalize that the conflict resolution corresponds to the pointlocated on the line segment DE closest to line λ. In the special case whenpoint D is equal to E i.e. |DE| = 0 the transition speed is placed to thispoint, see Fig. 3.2(c) for point C.This geometrical interpretaion of speed computing can be formulated asfollow: consider place P i and the set of transitions Pi◦ having a conflict.The set of transitions Pi◦ indexes is denoted as C i . Variable vi s (t) denotesthe sum of the speeds supplying the place P i at time t. For each transitionT j where j ∈ C i initialize maximum permissible transition speed vjmax (t) asa minimum from the maximal speed V j and separately sum the speed oftransitions which supplied the place from ◦ T j with zero marking. Set thetransition speed v j (t) = 0 and modify it by the iterative Algorithm 3.1.3.2.2 Linear Programming for Conflict ResolutionThis subsection shows how linear programming (LP) can be used for conflictresolution computation. At first, we will use the example in Fig. 3.1 to showhow a conflict resolution can be solved by linear programming at time t. In
3.2 Continuous Petri Net 23v 5V 5vD¸15A105Ev 2V040 10 20 30 v 1 40 50 v 4(a) Proportional resolutionv 5V 5v D3B´E ¸15105v 2V040 10 20 v 1 30 40 50 v 4(b) Resolution close to proportionv 5v 3(c) Resolution close to proportion without the transition T 2 effectV 5C´ D´E¸15105v 2V040 10 v 1 20 30 40 50 v 4Fig. 3.2: Geometrical interpretation of the conflict resolution
Page 1 and 2: Czech Technical University in Pragu
Page 3 and 4: This thesis is dedicated to my wife
Page 5 and 6: Nomenclatureα|β|γ Graham and B̷
Page 7 and 8: NomenclatureviiR 0+ set of non-nega
Page 9 and 10: AbbreviationsCCPN Constant speed Co
Page 11 and 12: Goals and ObjectivesThis thesis wil
Page 13 and 14: ContentsGoals and Objectivesxi1 Int
Page 17 and 18: List of Tables2.1 Traffic data for
Page 19 and 20: Chapter 1IntroductionThe urban traf
Page 21 and 22: 1.1 Related Work 3Traffic stream mo
Page 23 and 24: Chapter 2Simple Light ControledInte
Page 25 and 26: 2.2 Extended Queue Model 72 E( k)AB
Page 27 and 28: 2.2 Extended Queue Model 9E [s]4000
Page 29 and 30: 2.4 Control of The Simple Intersect
Page 37 and 38: Chapter 3General Light ControlledIn
Page 39: 3.2 Continuous Petri Net 21take the
Page 43 and 44: 3.3 Light Controlled Intersection M
Page 49 and 50: 3.4 Performance Evaluation 31-1V[uv
Page 51 and 52: 3.4 Performance Evaluation 33-1V [u
Page 53 and 54: Chapter 4TORSCHE SchedulingToolbox
Page 55 and 56: 4.2 Tool Architecture and Basic Not
Page 63 and 64: 4.3 Implemented Algorithm 45tasks a
Page 65 and 66: 4.3 Implemented Algorithm 47leg 1p=
Page 67 and 68: 4.3 Implemented Algorithm 49unit j
Page 69 and 70: 4.3 Implemented Algorithm 51P 2P 1
Page 71 and 72: Chapter 5Traffic Flow OptimizationT
Page 73 and 74: 5.2 Traffic Region Model 5514 1516
Page 75 and 76: 5.3 Tasks Definition for Intersecti
Page 77 and 78: 5.4 Scheduling with Communication D
Page 79: 5.5 Summary 61Intersection 6T 2,6T
Page 82 and 83: 64 Chapter 6 Conclusionsoptimal und
Page 85 and 86: Appendix ATORSCHE AlgorithmsA.1 Sch
Page 87 and 88: Bibliography[Abou 09] K. Aboudolas,
Page 89 and 90: Bibliography 71[Febb 06] A. D. Febb
Page 91 and 92:
Bibliography 73[Kwak 72]Cybernetics
Page 93:
Bibliography 75[Tolb 01] C. Tolba.
Page 96 and 97:
78 Indexphase, 3offset, 3, 53split,
Page 99 and 100:
List of Author’s PublicationsPape
Page 101:
List of Author’s Publications 83P
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