Compartmental Models for Nonhierarchical Communications Networks

In this paper we use compartmental models to study the dynamics and control of stressed nonhierarchical communications networks. Such networks are frequently used in voice and data communications. Not only are nonhierarchical structures important for network reliability and survivability (robustness under damage), but they are useful for economic reasons, as in the cases of major inter-exchange carriers' long distance networks. Detailed steady state analytic models are often used to evaluate steady state performance measures. These analytic models can produce point-to-point grades-of-service; however, the time resolution is necessarily lost. Simulations for circuit-switched networks can yield the time behavior and performance characteristics of stressed networks, but the purpose of this paper is to show that a set of simple difference equations among the most important network resource variables will produce a variety of network behaviors which are observed both in simulation and in the analytic steady-state models. The compartmental network models are complementary to the steady state analytic models because they possess time resolution but are spatially homogeneous. Oscillations from feedback control mechanisms and the time-dependent congestion effects related to the presence of significant damage and overload are observed, and optimal control parameter setting is investigated.