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

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58 Chapter 5 Traffic Flow OptimizationAlgorithm 5.1 Processing time computation1. Create tasks T uv , with temporary processing time p ′ uv = ∑ ψi=1 f i(u, v).>> T56 = task(’T(5,6)’, 0.0069)Task "T(5,6)"Processing time: 0.0069Release time: 0>> T26 = task(’T(2,6)’, 0.0222);>> T96 = task(’T(9,6)’,0.0079);2. Group the tasks into a taskset and add precedence constrains.>> prec6 = [0 1 1; 0 0 0; 0 0 0];>> TS6 = taskset([T56 T26 T96],prec6);Set of 3 tasksThere are precedence constraints3. Compute a length of critical path CP v by the asap (as soon as possible)function.>> TS6.asap;>> asapStart = asap(TS6,’asap’);>> CP6 = max(asapStart + TS6.ProcTime)CP6 =0.02914. From the length of the critical path and cycle time C we obtain processingtime p uv as a linear proportion of flow: p uv = p ′ uv · C/CP v .>> C = 90;>> TS6.ProcTime = TS6.ProcTime * C / CP6;5. We can display intersection phases by the plot function, see toFig. 5.4(b).>> TS6.asap;>> plot(TS6,’asap’,1,’prec’,0)
5.4 Scheduling with Communication Delay 595.4 Scheduling with Communication DelayThe intersection phase offset and split is computed for the green wave strategy.The green wave strategy, specified by the engineering skills, extends thetasks precedence constraints by the relationships between successive intersectiontasks. The precedence constraints must be in the out-tree form. Eachof those relationships defines the offset ϕ uv as a time, which a vehicle needsto pass from intersection u to intersection v. The ϕ uv is given by the streetlength a uv and vehicle speed W uv as ϕ uv = a uv /W uv (see Table 5.3).The split can be found by an algorithm for scheduling with a communicationdelay [Chre 95]. The scheduling with communication delay problemextends the precedence constraints in the classical scheduling by the communicationdelay between dependent tasks assigned to distinct processors.In our case the communication delay is equal to the offset ϕ uv . Let D bea matrix of communication delays, where the elements are ϕ uv in the casethat the offset between intersections u and v is considered, zero otherwise.We can classify our instances as tasks with precedence constraints in an outtreeform, communication delays, unlimited number of processors and noduplication of tasks. In Graham and B̷lażewicz notation it can be denoted asP ∞ |out-tree, c jk |C max . This problem can be solved in O(n) by the allgorithmpresented in [Chre 89] which is implemented in the TORSCHE toolbox (seeChapter 4) as a function chretienne.Fig. 5.3 shows the problem solution for three intersections (6, 7 and 8).First, the taskset object TSall with eight tasks corresponding to the intersectioncontrol is defined. The tasks and precedence constraints among themare shown in Fig. 5.4(a). The precedence constraints given by the green-wavestrategy are drawn as solid lines. Consequently, matrix D and the notation ofthe problem prob is defined. Finally, the scheduling problem is solved by thealgorithm chretienne and the resulting Gantt chart is shown in Fig. 5.4(b).The figure shows the tasks for the three considered intersections includingthe processing time p uv , split τ vj and offset ϕ uv . The split is given by theprocessing time of the scheduled tasks. The tasks are periodically repeatedwith a cycle time C.
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Czech Technical University in Pragu
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This thesis is dedicated to my wife
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Nomenclatureα|β|γ Graham and B̷
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NomenclatureviiR 0+ set of non-nega
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AbbreviationsCCPN Constant speed Co
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Goals and ObjectivesThis thesis wil
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ContentsGoals and Objectivesxi1 Int
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List of Tables2.1 Traffic data for
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Chapter 1IntroductionThe urban traf
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1.1 Related Work 3Traffic stream mo
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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 and 40: 3.2 Continuous Petri Net 21take the
Page 41 and 42: 3.2 Continuous Petri Net 23v 5V 5vD
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: 5.3 Tasks Definition for Intersecti
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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