HIERARCHICAL APPROXIMATION OF TELECOMMUNICATIONS NETWORKS

With the fibre optic revolution in communications technology, the indu stry is currently planning for network architectures in which switches rather than communication channels have become the economic and the p erformance bottleneck. A systems approach to planning is therefore req uired which considers the network and its supported services as an int egrated whole, in order to achieve joint, rather than independent isol ated optimisations. Three-level hierarchical stochastic optimisation m odels for network planning and management - involving mainly the trans port and network layers of the seven-level OSI architecture - are intr oduced in support of this integrated systems approach. Corresponding t o these three-level models are successive mathematical approximations to data traffic flows. Analysis for routeing of traditional switched n etworks involves queueing networks, but for design and flow control of current packet switched and future multiservice photonic networks, op erating at gigabit transmission rates, reflected Brownian motion and, particularly, deterministic and Markov fluid approximations become mor e appropriate. Functional central limit theory may be used to derive t hese three successive approximations from the underlying discrete netw ork 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 si mple network planning problems and directions are indicated for future mathematical research which would improve their practical applicabili ty.