A linear system approach to serving Gaussian traffic in packet-switching networks

We present a novel service discipline, called linear service discipline, to serve multiple QoS queues sharing a resource and analyze its properties. The linear server makes the output traffic and the queueing dynamics of individual queues as a linear function of its input traffic. In particular, if input traffic is Gaussian, the distributions of queue length and output traffic are also Gaussian with their mean and variance being a function of input mean and input power spectrum (equivalently, autocorrelation function of input). Important QoS measures including buffer overflow probability and queueing delay distribution are also expressed as a function of input mean and input power spectrum. This study explores a new direction for networkwide traffic management based on linear system theories by letting us view the queueing process at each node as a linear filter.