HIERARCHICAL APPROXIMATION OF TELECOMMUNICATIONS NETWORKS

With the fibre optic revolution in communications technology, the industry is currently planning for network architectures in which switches rather than communication channels have become the economic and the performance bottleneck. A systems approach to planning is therefore required which considers the network and its supported services as an integrated whole, in order to achieve joint, rather than independent isolated optimisations. Three-level hierarchical stochastic optimisation models for network planning and management - involving mainly the transport and network layers of the seven-level OSI architecture - are introduced in support of this integrated systems approach. Corresponding to these three-level models are successive mathematical approximations to data traffic flows. Analysis for routeing of traditional switched networks involves queueing networks, but for design and flow control of current packet switched and future multiservice photonic networks, operating at gigabit transmission rates, reflected Brownian motion and, particularly, deterministic and Markov fluid approximations become more appropriate. Functional central limit theory may be used to derive these three successive approximations from the underlying discrete network traffic processes in a stationary environment, paralleling on the network graph the micro, meso and macro scales of classical physics in free space. These ideas are explored in a preliminary way for some simple network planning problems and directions are indicated for future mathematical research which would improve their practical applicability.