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

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52 Chapter 4 TORSCHE Scheduling Toolbox for Matlabsubject to:y ≥ 0,M · y ≤ cap,N · y = b,(4.3)where b is a vector of b i , cap is a vector of cap i and a P is a constant vector of apath costs. Each of its elements is defined as a p = ∑ (u,v)∈p a uv. Assignmentf i (u, v) of multi-commodity flow to the edge is given by the vector y and setof paths P.An example of minimum cost multi-commodity flow problem for a realapplication is shown in the Section 5.2.4.4 SummaryThis chapter presents the TORSCHE Scheduling Toolbox for Matlab covering:scheduling on monoprocessor/dedicated processors/parallel processors,open shop/flow shop/job shop scheduling, cyclic scheduling and realtimescheduling. The toolbox already has several real applications. It hasbeen used for the development of a new method for re-configuration of thetasks or a process in an embedded avionics application [Muni 09]. Simulationsin TORSCHE also helped to develop a method optimizing the jitterof tasks in a real-time system [Liu 09]. Recently, TORSCHE has becomea part of a textbook for courses in scheduling “Scheduling: Theory, Algorithms,and Systems” written by M. Pinedo [Pine 08]. The actual versionof the toolbox with documentation and screencasts is freely available athttp://rtime.felk.cvut.cz/scheduling-toolbox/.
Chapter 5Traffic Flow OptimizationThis chapter proposes consecutive steps to find the optimal offset and thesplit of the light controlled intersections in the urban traffic region. Theoptimization takes into account the street length, number of lanes and maximalallowed vehicle speed in consideration to respect the green wave strategycontrol and constant intersection cycle time. The solution of this problem isshown on the urban traffic region in Prague. The problem is formalized andsolved by the TORSCHE.5.1 IntroductionThe light controlled intersections are characterized by several parameters:the number of light phases, phase split, offset time and a list of streets fromwhich the vehicles flow [Gube 08]. The term phase means state of trafficlights on the intersection. The number of phases and the list of streets arepartially given by the urban architecture of the intersection and partiallyby the intersection control strategy (i.e. one-way street, directional roadwaymarking). Both of these parameters are constant. On the other hand, thesplit and offset can be changed dynamically during a day. The split τ vjdefines the time interval of phase j for which the vehicle flow can go throughthe intersection v from one or more streets [Papa 03]. The offset ϕ uv is acertain time delay between phases of two successive intersections u and v.When the offset is zero, all lights in the region turn on and off at the sametime. It is called the synchronized strategy. In the green wave strategy, the53
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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
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 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: 4.3 Implemented Algorithm 51P 2P 1
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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