**1. Introduction**

250 Telecommunications Networks – Current Status and Future Trends

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Modern telecommunication networks, irrespectively of their organization and type of the transmitted information, become more complex and possess many specific characteristics. The new generation of telecommunication networks and systems support a wide range of various communication-intensive real-time and non real-time various applications. All these net applications have their own different quality-of-service requirements in terms of throughput, reliability, and bounds on end-to-end delay, jitter, and packet-loss ratio etc. Thus, telecommunication network is a type of the information system considered as an ordered set of elements, relations and their properties. Their unique setting defines the goal searching system.

For such a type of information system as a telecommunication network it is necessary to perform a preliminary long-term planning (with structure designing and system relation defining) and a short-term operating control within networks functioning. The problem of the optimal planning, designing and controlling in the telecommunication networks involves: definition of an initial set of decisions, formation of a subset of system permissible variants, definition of an optimal criteria, and also a choice of the structure variants and network parameters, optimal by such a criteria. It is the task of a general decision making theory reduced to the implementation of some choice function of the best (optimal) system based on the set of valid variants. For the decision making tasks the following optimizing methods can be used: scalar and vector optimization, linear and nonlinear optimization, parametric and structure optimization, etc (Figueira, 2005; Taha, 1997; Saaty, 2005). We propose a method of the multicriteria optimization for optimum variants choice taking into account the set of quality indicators both in long-term and short-term planning and controlling.

The initial set of permissible variants of a telecommunication network is being formed through the definition of the different network topologies, transmission capacities of communication channels, various disciplines of service requests applied to different routing ways, etc. Obtained variants of the telecommunication network construction are estimated

Multicriteria Optimization in Telecommunication Networks Planning, Designing and Controlling 253

The choice of the optimal criteria is related to the formalization of the knowledge about an optimality. There exist two ways of describing the customer's preference of one variant to

An ordinal approach is order-oriented (better-worse) and is based on introducing certain binary relations on a set of permissible alternatives. In this case the customer's preference is the binary relation R on the set ΦD which reflects the customer's knowledge that the

Assume that a customer sticks to a certain rigorous preference , which is asymmetric and transitive, as he decides on a set of permissible alternative ΦD. The solution ϕ0 D ∈ Φ is called optimal with respect to , unless there are other solution ϕ∈ ΦD for which (0) ϕ ϕ holds true. A set of all optimal solutions in relation to is denoted by opt . ΦD A set of optimal solutions can comprise the only element, a finite or infinite number of elements as a function of the structure of a permissible set or properties of the relation . If the discernibility relation coincides with that of equality =, then the set optΦD (provided it is

A cardinal approach to describe the customer's preference assigns to each alternative ϕ∈ Φ<sup>D</sup> , a certain number U being interpreted as the utility of the alternative ϕ. Each utility function determines a corresponding order (or a preference) R on die set ΦD(R) ϕ ϕ ′ ′ if and only if U( ) U( ). ϕ′ ′′ ≥ ϕ In this case they say that the utility function U( )⋅ is a preference indicator R. In point of fact this approach is related to assigning a certain scalar-objective function (a conventional preference criteria) whose optimization in a general case may result

The choice of the optimal criteria is based on formalizing the knowledge of a die system customer (i.e. a person who makes a decision) about its optimality. However, one often fails to formalize the knowledge of a decision-making person about the system optimality rigorously. Therefore, it appears impossible to assign the implicitly of the scalar optimal

a certain objective function of the system utility (or usefulness). Therefore, at the initial

k( ) (k ( ),...,k ( ),...,k ( )), <sup>ϕ</sup> <sup>=</sup> 1im ϕϕ ϕ

the system ϕ= β (s, ) upon the system quality indicators. In this connection one has to deal with the newly emerged issues of optimizing approaches in terms of a collection of quality indicators, which likewise are called the problems of multicriteria or vector optimization. Basically, the statement and the solution of a multicriteria problems is related to replacing (approximation) customer's knowledge about the system optimality with a different optimality conception which can be formalized as a certain vector optimal criteria (1) and, consequently, the problem will be solved through the effective

D (0) extr U( ) ϕ∈Φ

ϕ = ϕ , where U( ) ϕ is

(1)

of the variant of

criteria resulting in the choice of the only decision variant [ ]

design stages the system is characterized by a set of objective functions:

which determines the influence of the structure *s* and the parameters β

the other, i.e. ordinal and cardinal .

not empty) contains the only element.

optimization procedure.

alternative ϕ′ is better than the alternative: ϕ ϕϕ ′′ ′ ′′ : R.

in the selection of the only optimal variant of the system.

on a totality of given metrics describing the messages transmission quality. Thus, the formed set of the permissible design decisions is represented in the space of criteria ratings of quality indicators where, used of unconditional criteria of a preference, the subset of effective (Pareto-optimal) variants of the telecommunication network is selected. On a final stage of optimization any obtained effective variants of the network can be selected for usage. The unique variant choice of a telecommunication network with introducing some conventional criteria of preference as some scalar goal function is also possible.

In the present work some generalizations are made and all stages of solving multicriteria problems are analyzed with reference to telecommunication networks including the statement of a problem, finding the Pareto-optimal systems and selecting the only system variant. This chapter also considers the application particularities of multicriteria optimization methods at the operating control within telecommunication systems. The investigation results are provided on the example of solving of a particular management problem considering planning of cellular networks, optimal routing and choice of the speech codec, controlling network resources, etc.
