Performance and Stability of Communication Networks via Robust Exponential Bounds

We propose a new way for evaluating the performance of packet switching communication networks under a fixed (session-based) routing strategy. Our approach is based on properly bounding the probability distribution functions of the system input processes. The bounds we suggest, which are decaying exponentials, possess three convenient properties. When the inputs to an isolated network element are all bounded, they result in bounded outputs, and assure that the delays and queues in this element have exponentially decaying distributions. In some network settings, bounded inputs result in bounded outputs. Natural traffic processes can be shown to satisfy such bounds. Consequently, our method enables the analysis of various previously intractable setups. We provide sufficient conditions for the stability of such networks, and derive upper bounds for the interesting parameters of network performance.