Algorithm for network topology design Algorithm for network topology design ... 1.To design an algorithm

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  • Czech Technical University in Prague Faculty of Electrical Engineering

    Department of Control Engineering

    Algorithm for network topology design

    Doctoral Thesis

    Tomáš Fencl

    Prague, March 2011

    Ph.D. Programme: Electrical Engineering and Information Technology Branch of study: Control Engineering and Robotics

    Supervisor: Doc. Ing. Jan Bı́lek CSc.

  • Copyright by

    Tomáš Fencl 2011

  • Acknowledgements In the first place, I would like to thank my advisor Jan Bı́lek for his support and patience when not everything was going well and for his human quality. I would like to thank also Pavel Burget for his support and help. My big thanks belong to my family and friends who supported me in every possible way during those years and make me smiled when I needed it. I would like to thank to those all who I met during this time and allowed to me see things from different points of view and help to recognize what is really important. My thanks belong also to my colleagues for friendly atmosphere. I want to say thanks also to all people who have read all papers and works before its submitting and advised me how to improve it. My thanks belongs to all anonymous reviewers for their comments that allows to improve this work.

    This works has been co-financed by the Grant Agency of the Czech Republic, project number 102/08/1429 “Safety and Security of Networked Embedded System Applications” and by the Czech Ministry of Education, Youth, and Sports as Eu- Sophos project No.2C06010 This work was supported by the Ministry of Education of the Czech Republic under project 1M0567.

    Czech Technical University in Prague Tomáš Fencl March 2011

  • Nomenclature

    C Matrix of the acquisition costs; ci,j describes the costs that is necessary to pay for the connection of the nodes i and j

    CF Matrix of the costs for the fibre cable CM Matrix of the costs for the metallic cable capi Capacity of the communication link Cost Costs of the designed network as well as the fitness function D Matrix of the maximal permitted delays (a worst-case scenario) Depth Depth of a node in the tree topology Depthmax Maximal permitted depth of the tree topology er Number of links connected to the nodes that should be removed F Matrix of data-flows, fi,j - size if the data-flow between nodes i and j j Number of data-flows in the network core K Array describing the number and kind of communication ports, kfi - the

    number of communication ports of node i that can be connected to the fibre cable, kmi - the number of communication ports of node i that can be connected to the metallic cable,

    kdis Number of nodes that are disconnected from the main node (root node) kcyc Number of cycles in the network k Number of nodes at which the number of communication ports is

    smaller than a number of available communication ports kD Number of data-flows that have bigger delay than it is the maximal per-

    mitted delay kF Number of independent paths l Length of the chromosome of the logical topology M Matrix of the fault-tolerance. mi,j - describes the number of the inde-

    pendent communication paths between nodes i and j m Number of communication links in the core Np Number of iterations of the genetic algorithm for the design of the phys-

    ical topology Nch Number of chromosomes of the genetic algorithm for the design of a

    physical topology NLch Number of chromosomes of the genetic algorithm for the design of a

    logical topology P Matrix describes the designed network, pi,j describes the connection of

    the nodes i, j; 0-there is no connection, 1-there is a connection created by the metallic cable, 2 -there is a connection created by the fibre cable

  • v

    Packlen Length of data packets Pen Penalty function r Flag of the fault-tolerance; 1-network is not fault-tolerant at the de-

    manded level, 0-network is fault-tolerant Red List of the nodes to be removed∑ ce+ Costs of all edges that were added to the original topology∑ ce− Costs that is necessary to pay for the removal of the communication

    links from the original network u u = 1 if the network described by the chromosome is already in the

    accumulator of the unsuitable topologies; u = 0 if the chromosome is not in the accumulator of unsuitable topologies

  • Algorithm for network topology design Ing. Tomáš Fencl

    Czech Technical University in Prague, 2011 Thesis Advisor: Doc. Ing. Jan Bı́lek CSc.

    The application of the distributed control systems became a standard solution in the area of industrial control systems. The ability of the industrial control system is not only dependent on the ability of every part of the control system but also on their ability to communicate among them. The operation of the control system can be very limited if a part of the control system does not receive the demanded data or receives data too late. Unfortunately, the design of the suitable network topology is often omitted and the limitation of the network topology can cause the limited functionality of the control system.

    The existing algorithms for the network topology design do not offer a design of the network with demanded attributes. These algorithms often do not apply some of the real life limitations such as the limited number of communication ports, fault- tolerance of the network or limitation caused by the environment in which the network will be used. Moreover, some algorithms are not able to ensure some ability that should be fulfilled (Algorithms are not able to ensure the design of the fault-tolerant network even if they offer it). Therefore, a novel algorithm for the design of the network topology is proposed in the thesis.

    The algorithm is able to design the network with the different levels of fault- tolerance in the different parts of the network. The designed network is less expensive than the network designed by other existing algorithms. Moreover, the algorithm is able to work with the nodes that have different numbers of communication ports and addition of communication ports to nodes is not possible. The algorithm uses information, which can be received from the application engineers, about unsuitable structures of the network topology and is able to avoid designing of the network that contains these unsuitable structures. The proposed algorithm contains the part that verifies network ability to transfer every data-flow in demanded time.

    It is often necessary to change the network topology if the controlled technology is changed. Thus, the modification of the proposed algorithm for the network topology design is described in the thesis. The redesigned network meets all demands for the fault-tolerance, application of nodes with the limited number of communication ports etc. as a brand new network. On the contrary, the redesigned network is less expensive than the new network since it uses as a big part of the original network as possible. Moreover, the modification for the tree topology was proposed.

    The algorithm is designed as a modular iterative task on the basis of the genetic algorithm. The modularity allows application of the more accurate model of the net- work behaviour if it is needed. Moreover, it is possible to design the topology of the pipeline or electrical grid if the module for the verification of the network delays is substituted with model desribing behaviour of electrical grid or pipelines.

  • Goals and Objectives The goals of this work were set as follows:

    1. To design an algorithm for the design of the network with the different fault- tolerance in different parts of the network while the network allows in time data delivery.

    2. Modifications of the basic algorithm for the limited number of communication ports of nodes (different physical layers can be applied) and an application of a priori information about unsuitable topologies.

    3. To design an algorithm for the mesh network expansion and reduction.

    4. To design an algorithm for the network topology design. The tree network has limited depth and use nodes with the limited number of communication ports of the different type of physical layers.

    5. To design an algorithm for the tree topology expansion or reduction.

  • viii

  • Contents

    1 Introduction 1 1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Objectives and outlines . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.3 Genetic algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

    2 Reliability 9 2.1 Requested network . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.2 Reliability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

    2.2.1 Ring topology . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.2.2 Node degree as an approximation . . . . . . . . . . . . . . . 17 2.2.3 Node degree as a reliability measure . . . . . . . . . . . . . . 18

    3 Related works 19

    4 Network topology design 33 4.1 Problem formulation . . . . . . . . . . . . . . . . . . . . . . . . . . 33 4.2 Topology with different levels of fault-tolerance . . . . . . . . . . . . 36

    4.2.1 Chromosome representation . . . . . . . . . . . . . . . . . . 36 4.2.2 Genetic functions . . . . . . . . . . . . . . . . . . . . . . . . 37

    4.2.2.1 Genetic mutation . . . . . . . . . . . . . . . . . . 38 4.2.2.2 Crossover operator . . . . . . . . . . . . . . . . . . 38 4.2.2.3 Fitness function . . . . . . . . . . . . . . . . . . . 39

    4.3 Topology with same level of fault-tolerance . . . . . . . . . . . . . . 41 4.3.1 Node de