Offered-load model for Pareto inter-arrival network traffic

In the network data, interarrival times are heavy-tail distributed. Weibull, Pareto and Lognormal are the best examples of heavy-tail distributions. These distributions give time-varying arrival rates. Also, renewal processes for these interarrivals are non-homogeneous Poisson processes. The network traffic is, thus, non-stationary. Many of the theoretical tools, such as equilibrium probabilities for Markov chains, matrix geometric solutions and Laplace transforms are not available for queue with time varying rates. Since no closed form expressions of Laplace transform of Weibull, Pareto and Lognormal distributions are available, the queueing analysis becomes complicated. In this paper we present queueing analysis of heavy-tail network traffic, and thus, time dependent queuing model M_t/G/¿ is analyzed for heavy-tail Pareto arrivals. In particular, we find analytical expressions for the time-dependent mean function (offered load), denoted here as m(t), which depends on the time-dependent arrival rate function ¿(t) and service time distribution.