- •On March 30, 2010
- •Contents
- •1 General conditions
- •2 Key positions
- •2.1 The general concept about problems of telecommunication networks synthesis and analysis
- •2.2 Model representation of a telecommunication networks as object of synthesis and analysis
- •2.3 Elements of optimization theory on graphs and networks
- •2.3.1 Synthesis of the minimal cost network
- •Figure 2.4 Figure 2.5 Figure 2.2 Figure 2.3 Figure 2.6 Figure 2.7 Figure 2.8
- •2.3.2 Determination of a graph median
- •2.3.3 Determination of the graph center
- •The algorithm of finding graph centre (vertex s) follows from the definition:
- •2.3.4 Determination of the minimal length cycle
- •2.3.5 Finding the shortest way in a connecting network
- •2.3.6 Determination of the given transient path sets
- •2.3.7 Problems about flow
- •3 The complex task
- •Construction of telecommunication network models
- •3.2 Synthesis of subscriber access network
- •3.3 Synthesis of the internodal network
- •3.4 Construction of the routing matrixes
- •3.5 Estimation of network capacity between points pair
- •4 The list of literature
- •The variants of individual tasks
3.3 Synthesis of the internodal network
3.3.1 Study sub item 2.1, 2.3.4 of the Key statements.
3.3.2 Define the contour of the least length merging internodal telecommunication network points into the hoist ring.
There given: location of points (n=10), the circuit design of the linearly-cable conduit presented as weight matrix of graph ribs representing a network. Weight characteristics of ribs match to distances in kilometres of linearly-cable constructions between network points. Use the weight matrix obtained while performing the Task 3.1 as mentioned matrix.
Remarks. For the problem solution it is possible to take advantage of heuristic algorithm of «the problem about the travelling salesman» solving. As heuristics it is possible to use the rule shown in the item 2.3.4, or to formulate a heuristic rule independently.
3.3.3 Show the obtained solution and the explanation to it in an explanatory note.
3.3.4 Answer the following key questions in writing:
What does «the problem about the travelling salesman » consist in?
What is the exact solution of «the problem about the travelling salesman»?
What contour is called Hamiltonian cycle?
What is called as heuristics? What algorithms refer to the heuristic ones?
Formulate advantages and disadvantages of exact and heuristic algorithms.
3.4 Construction of the routing matrixes
3.4.1 Study sub item 2.1, 2.3.5, 2.3.6 of the Key statements.
3.4.2 Build routing matrixes for each network knot (n=10) providing main route selecting and also two bypaths while connecting sections setting up from the considered knot to all the others.
For a main route (a way of the first sampling) it is necessary to use the shortest paths from the knot s (s=1.... n) to other network points. For bypaths (paths of the second and third selections) - the shortest paths by transits at maximum admissible transience Т0 = 2. In the presence of several paths of equal transience preference one should favor to the shortest by length path.
For definition of the shortest by length paths as initial matrix of lengths of the lines connecting knot network points, take advantage of the weight matrix obtained while performing the Task 3.1 and for minimum transience path finding - contiguity matrixes.
3.4.3 Methodical instructions.
Routing matrixes are stored in every UКi networks and intended for definition of a direction of the proceeding communication line (communication channel) at connecting section of information message transmitting from initial point to the point of destination. It is possible to forsee additional directions (bypaths) selection in case of the first selection of occupation direction on the definite UКs in the presence of the switching equipment feasibilities. The order of directions selecting is defined by a routing matrix the quantity and line-numbering of which match to paths number p and to the assigned order of their occupation, and columns number - to points of destination numbers (figure 3.1).
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1
2
…
j
i
…
n
1
j
I
2
r
J
… … … … … … … … … … … … … … … … … … ….
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p
l
L
Figure 3.1
Element mij of routing matrix for UКs is the knot number of contiguous UКs in transit of matching selection from UКs to the point of destination J.
3.4.4 Show the general problem assignment (verbal model), results of the solution and explanations matching to them in the explanatory note.
3.4.5 Answer the following key questions in writing:
What class of problems does routing matrixes construction refer to?
What is called the path in a network, a path length, way transience and the shortest way?
Show practical situations where there is a problem of the shortest way definition.
What is Dijkstra's algorithm of the shortest ways searching based on?
What kinds of mark are used at Dijkstra's algorithm operation?
Is it possible by means of Dijkstra's algorithm to find paths variety, the shortest by transience? Which initial data are required for this purpose?
What method is it possible to obtain paths variety of set transience by?
What does the idea of multilevel tree construction method consist in?