Candidate: Dr. Lazare MATIP ESSOUNGA
On May 23rd, 2008, Mr. Lazare MATIP ESSOUNGA defended his PhD thesis at the Department of Electrical Engineering and Computer Science, Technical University of Berlin of Berlin (Germany). Members of the Jury were (among others) Dr. Pr. Adam Wolisz, Technical University of Berlin (Co-supervisor), Dr. Pr. Leonid I. Abrosimov, Professor in Moscow power engineering Institute-Technical University (Co-supervisor), Dr. Pr. Vladimir M. Vishnevsky, Russian Academy of Sciences Institute for Information Transmission problems. His research was on the « Development and research of a model integrated into the Network administration as used for performance controlling of corporate calculating telecommunication and computer Networks: Method of matrix writing constructing of topological structure».
For details on his research, please contact the author at the following address:
Dr. Matip Essounga Lazare PhD in telecom & computer network Managing Director 250, St-Jacques office 4 Lachine H8R 1E2 Quebec, Canada Office: +1 438 380 6757 Cell: +1 514 503 5745 E-mail: lazare@mateltelecom.com www.mateltelecom.com
Abstract
Using mathematical methods for solving problems of reliability analysis, routing and performance of computer network (CN), which have more than 1000 nodes, requires compiling and operative renovation of CN topology matrix. In the paper such points are stated as: vector description of structure CN and rules, which provide the two-dimensional image of CN structure for manager, as well as algorithmic procedures for constructing and operative modification of the matrix writing the topological structures of CN.
1. Introduction
An object of research is a distributed corporate computer network (CN), which includes workstations, servers, communication devices, and data transmission equipment and communication lines.
It is necessary to have a formalized description of CN structure presented by the matrix form [1-2] for solving problems of CN modernization, reliability estimation and productivity parameters calculation.
The structure is an arrangement of network elements and their interconnections. A topological structure (TS) of CN is used for solving problems that address metric space. Elements of TS are devices and communication lines. TS define a location of devices (servers, communication devices, workstations). TS allows to check technical restrictions of communication lines length, defines communication devices to which it is possible to connect new group of workstations, etc. CN can contain more than hundred devices.
It is difficult to use mathematical methods for automated CN designing, which has more than 1000 units, because of absence of effective, formalized ways of presentation and description of CN structure.
One of the important tasks of building CN, support of its normal operation, analysis of the functional features is a description of all devices in the network.
In the book [3] the author describes the approach for describing of computer network. This method consists of preparing datasheets in which the most important information about all CN devices is placed into specific table cells: information about routers, switches, workstations and servers. However this method doesn’t have a description of communication lines between devices, and description of topology structure. For presentation of communication lines the author offers to draw topology of a physical network up manually. But when there are more then hundred devices in the network, it is very hard to do this.
The second approach for documenting of CN structure is software programs for management of network devices. The most wide-spread are HP OpenVeiw NNM [4-5] and CiscoWorks LMS [6-8]. These programs allow to automate the process of network topology mapping. They also allow automatically collecting important information from devices, such as type of device, IP-address and etc. But they do not give information about physical location of CN devices. Also they do not determine passive devices and types of channels.
2. Purpose of research and formulation of the problem
The purpose of description of topological structure is to obtain such a display of devices and communication lines, which will enable:
– to fix composition devices and communication links between them, then submit them in a tabular, matrix, scheduling and graphic forms to follow formal treatment;
– to order all parameters describing the devices which are the part of CN and necessary for modeling and analyzing CN performance.
The formulation of the problem. For known schemes of the nodes and descriptions interconnection CN nodes, which are set in an arbitrary manner, it is required to develop a methodology that allows:
– to formalize the initial data,
– to formalize representation of interactive working records,
– to formalize representation of the resulting records,
– to generate matrix records of topological structure.
3. Definitions
All devices, which are included in researched CN, it is possible to divide into following classes: WD – workstations, GD – group devices, SD – servers, SWD – switching devices. A parameter is used for taking into account features of functioning devices of various classes. The parameter is type of CN device. The full list of devices types is made for everyone CN and takes into account its features.
Two concepts are used in the description of CN interconnections: a communication line and a communication channel. The communication line (CL) is physical means, which provide the connection of two sockets of devices. An example of CL is a cable or a radio line. The communication channel (CC) is set of functional means, which provide data exchange on the communication line in accordance with the access and transmission protocol. The communication channels of various types can be organized depending on the functioning features through communication lines.
Let’s assign CN device to identifier A. In this case socket k of device A can assign identifier A.k. According to the accepted identifiers of devices the communication line connecting the sockets A.k and B.r of two devices, should have the compound identifier: A.k-B.r. The full identifier of the communication lines «socket – socket» takes into account the type of communication channel and has the form: (A.k-B.r) .
If there are more than hundreds devices in CN, it should be used multilevel (L>1) identification system. In this identification system the identifier A of device is recorded as a vector, i.e. А = (a1. aL-1 aL). Each value al has its own independent numbering system.
Vector representation of the identifier A allows establishing conformity of everyone CN to its technical realization and location in a topological space. However, existing means allow displaying objects only in three-dimensional space. In doing so, to make changes usually use the plane, that is two-dimensional space.
Multidimensional matrix of TS can be presented in a matrix of connections (socket х socket), as shown in figure 8. But in this case, for large CN dimension of TS matrix becomes so big and bulky that it is impossible to work with.
Multidimensional matrix of TS analysis revealed the following properties:
– TS matrix is poorly filled;
– each displayed LC is defined by two sockets, each of which is a vector space identifier L+1;
– if there are same values of corresponding vectors in the identifiers of LC sockets, dimension of the space (necessary for display) is reduced by the number of matches;
– numbers sockets (coordinates of the level L+1) are mandatory in the display CL.
4. Rules for TS creation
Discovered properties of the vector space are used in rules of numbering. Expansion of the vector space which provides a reduction in the vector space is used to build a set of TS schemes.
4.1. Rule numbering
Number 1 element of level L is attributed to the element, which socket is connected using CL to the socket of the element of higher level (L-1). For example:
1. Number 1 is assigned to the building (L = 1), in which device sockets are connected to LC that connect researched CN to external networks such as the Internet.
2. Halls numbering of the building begins with the hall in which there is a room with the switch which is connected to inter halls CL.
3. The numbering of floors in the hall begins with the floor in which there is a room with the switch which is connected to inter halls CL.
4. The numbering of rooms on the floor begins with the room in which there is a switch which is connected to inter floors CL.
5. The numbering of devices in the room begins with the switch, which is connected to inter rooms CL.
4.2.Expansion rule
Expansion rule of two-dimensional vector space mappings of TS:
1. The rule lack of expansion. Topological structures (TS) can be presented as a set of two -dimensional maps, in each of which the vector « sockets » does not exceed a maximum quantity of sockets of switching device, if among all elements of the level l (l =) only sockets of element №1 are connected to the sockets of element №1 levels (l-1).
2. The rule of need to expand. Topological structure (TC) can not be presented as a set of two-dimensional maps, each vector « sockets » does not exceed the maximum quantity of sockets of switching device SWD, if are not implemented at least one of the conditions specified in the rule 1. In order to provide a description of topological structure as a set of two-dimensional mappings, it is necessary to use the expanded vector space of « sockets » coordinate.
3. The rule of forming the expanded vector space of « sockets » coordinates. To ensure orderly display of the expanded vector space, considering each vector as multi digit number, which determines the L=1 «senior level ».
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