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

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44 Chapter 4 TORSCHE Scheduling Toolbox for Matlab4.3 Implemented AlgorithmThe biggest part of the toolbox is constituted by scheduling algorithms.There are a large variety of algorithms (see Appendix A) solving both simpleproblems (on a single processor) and practically oriented issues. This sectionshows several of them demonstrated on real applications.4.3.1 List Scheduling AlgorithmList Scheduling (LS) is a basic and popular combinatorial algorithm intendedfor scheduling of set of tasks on a single and parallel processors. In thisalgorithm tasks are fed from a pre-specified list and, whenever a processorbecomes idle, the first available task on the list is scheduled and removedfrom the list. Where the availability of a task means that the task has beenreleased and if there are precedence constraints, all its predecessors havealready been processed [Leun 04]. The algorithm terminates when all tasksfrom the list are scheduled. Its time complexity is O(n). In multiprocessorcase, the processor with minimal time is taken in every iteration of algorithmand the others are relaxed.The fact, which is obvious from the principle of algorithm is that, therearen’t any requirements of knowledge about past or future of content of thelist. Therefore, this algorithm is capable to solve offline as well as onlineno-clairvoyance scheduling problems. There are many strategy algorithmslike the Earliest Starting Time first, the Earliest Completion Time first, theLongest Processing Time first and etc., based on simple ordering of tasks inthe list by various parameters.Algorithm strategy do not guarantee to find optimal solutions for anyinstance of an optimization problem. On condition of appropriate choose ofstrategy it often provide acceptable results with very good time and memorycomplexity.The Earliest Starting Time first (EST) is a strategy in which the tasksare arranged in nondecreasing order of release time r j before the applicationof List Scheduling algorithm. The time complexity of EST is O(n · log(n)).The Earliest Completion Time first (ECT) is a strategy in which the tasksare arranged in nondecreasing order of completion time C j in each iterationof List Scheduling algorithm. The time complexity of ECT is O ( n 2 · log(n) ) .The Longest Processing Time first (LPT) is a strategy in which the
4.3 Implemented Algorithm 45tasks are arranged in non-increasing order of processing time p j before theapplication of List Scheduling algorithm. The time complexity of LPT isO(n · log(n)).The Shortest Processing Time first (SPT) is a strategy in which thetasks are arranged in non-decreasing order of processing time p j before theapplication of List Scheduling algorithm. The time complexity of SPT isO(n · log(n)).List Scheduling is implemented in TORSCHE Scheduling Toolbox byfunction listsch which also allows to user to use any of implemented strategyalgorithms and visualize process of scheduling step by step in text formin MABLAB workspace (see Fig 4.5 for flowchart of function). Moreover,the last version is able to solve scheduling problems on unrelated parallelprocessors. The syntax of listsch function is:TS = listsch(T,problem,processors [,strategy] [,verbose])TS = listsch(T,problem,processors [,option])where:Tis the instance of the Taskset class without schedule,TS is the instance of the Taskset class with schedule,problem is the instance of the Problem class,processors is the number of processors,strategy is the strategy (like LPT, SPT, EST, . . . ),verbose is a level of verbosity,option is the optimization option setting.This subsection concludes by the example. The example solves a problemof manufacturing of a chair by two workers (cabinetmakers). Their goal isto make four legs, seat and backrest of the chair and assembly all of theseparts within minimal time. Material, which is needed to create backrest,will be available in 20 time units and assemblage is divided into two stages(assembly 1/2 and assembly 2/2 ). Fig. 4.6 shows the representation of mentionedproblem by the graph.
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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
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 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 61: 4.2 Tool Architecture and Basic Not
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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