  l. Introduction Modern network are multi-layer by their structure. This
requires the development of new mathematical models, which would allow to
adequately describe the existing physical and logical connections between the
elements on its different levels, and to effectively solve the problems of
design. The paper formulates the problem of synthesis of structure of MPLS
network layered with the transport SDH network or WDM and suggests the method
of its solving. The solving is based on the application of mathematical model
of multi-layer graph. II, III, IV. Main Part During the planning of MPLS
networks it is necessary to determine the topology of both the networks: that
of transport one and that of MPLS one. This means that one needs to determine:
- what nodes of the transport network should support the MPLS functionality; -
in what way the LSR nodes should be connected via the transport network; - what
should be the bandwidth between LSR links. According to the general method for
solving the problem of synthesis of multiservice telecommunication systems with
the usage of multi-layer graphs, we have to synthesize the initial redundant .
The solving of the task above can be reduced to the finding of the multi-layer
minimum weight subgraph that provides the transfer of information flows with
the consideration of the requirements to the structure of the multilayer graph
[5] and the flows on its edges [6] observed at the applying of constraints to
the bandwidth of the edges of the multi-layer graph. V. Conclusion The paper
reduces the problem of design of multiservice telecommunication system with the
transferred flows to the problem of finding a multilayer minimum weight
subgraph with the consideration of constraints to the graph edges bandwidth. It
is shown that application of given method provide to reduce MPLS network cost
to 10 - 16 %.
