Mathematical methods and modelling tools for designing communication networks

The prime subject of the talk is the creation of mathematical fundamentals for designing commu nication networks on the basis of new analytical methods for calculation, optimization, asymptotic analysis and investigation of the stability of multiclass queueing networks. Specifically, the subjects addressed are grouped into four interrelated categories: 1. Creation of new mathematical methods for estimates of characteristics of the functioning of communication networks and their components; gaining (based on these new mathematical methods) new concepts about connections between reliability, serviceability, technical, oper ational and economic aspects of functioning of communication networks; creating methods combining both functional and temporal aspects of communication networks research; the creation of new mathematical methods for investigation of protocols and for optmization of communication networks. 2. Deriving new mathematical formulae for basic characteristics of various types of multiclass queueing networks with product form of solution; finding (on a basis of deriving, generaliza tion, extension and investigation of corresponding integral representations) of new types of multiclass queueing networks with product form of solution. 3. Program realization of the new methods under discussion in library of classes on the algo rithmic language C++. 4. The computationally efficient POLynomial APproximation method, design philosophy and way of packaging used in powerful software package, named POLAP, for definition and ana lytical solution of multiclass queueingnetworks models of communication networks.