A Nonstationary Offered-Load Model for Packet Networks

Motivated by the desire to appropriately account for complex features of network traffic revealed in traffic measurements, such as heavy-tail probability distributions, long-range dependence, self similarity and nonstationarity, we propose a nonstationary offered-load model. Connections of multiple types arrive according to independent nonhomogeneous Poisson processes, and general bandwidth stochastic processes (not necessarily Markovian) describe the individual user bandwidth requirements at multiple links of a communication network during their connections. We obtain expressions for the moment generating function, mean and variance of the total required bandwidth of all customers on each link at any designated time. We justify Gaussian approximations by establishing a central limit theorem for the offered-load process. We also obtain a Gaussian approximation for the time-dependent buffer-content distribution in an infinite-capacity buffer with constant processing rate. The offered-load model can be used for predicting future bandwidth requirements; we then advocate exploiting information about the history of connections in progress.