hyper-Erlang Model Research Articles

Segment-based adaptive hyper-Erlang model for long-tailed network traffic approximation

Modeling the long-tailedness property of network traffic with phase-type distributions is a powerful means to facilitate the consequent performance evaluation and queuing based analysis. This paper improves the recently proposed Fixed Hyper-Erlang model (FHE) by introducing an adaptive framework (Adaptive Hyper-Erlang model, AHE) to determine the crucially performance-sensitive model parameters. The adaptive model fits long-tailed traffic data set directly with a mixed Erlang distribution in a new divide-and-conquer manner. Compared with the well-known hyperexponential based models and the Fixed Hyper-Erlang model, the Adaptive Hyper-Erlang model is more flexible and practicable in addition to its accuracy in fitting the tail behavior.

Comment on “A general model for long-tailed network traffic approximation”

The recent paper by Wang et al. (J. Supercomput. 38:155---172, 2006) proposed a Hyper Erlang model for long-tailed network traffic approximation. The paper argued that traditional models such as the Pareto, Weibull and log normal distributions are difficult to apply because of "their complex representations and theoretical properties". The paper went on to say that the Pareto distribution "does not have analytic Laplace transform, and many other heavy-tailed distributions, such as Weibull and log normal also do not have closed-form Laplace transforms". In the following, we would like to show that one can actually derive explicit expressions for Laplace transforms of heavy-tailed distributions. The next three sections provide explicit expressions for the Laplace transforms of the Pareto, Weibull and the log-normal distributions. To the best of our knowledge, these are the first known results on Laplace transforms of heavy-tailed distributions.

Hyper-Erlang Distribution Model and its Application in Wireless Mobile Networks

This paper presents the study of the hyper-Erlang distribution model and its applications in wireless networks and mobile computing systems. We demonstrate that the hyper-Erlang model provides a very general model for users' mobility and may provide a viable approximation to fat-tailed distribution which leads to the self-similar traffic. The significant difference from the traditional approach in the self-similarity study is that we want to provide an approximation model which preserves the Markovian property of the resulting queueing systems. We also illustrate that the hyper-Erlang distribution is a natural model for the characterization of the systems with mixed types of traffics. As an application, we apply the hyper-Erlang distribution to model the cell residence time (for users' mobility) and demonstrate the effect on channel holding time. This research may open a new avenue for traffic modeling and performance evaluation for future wireless networks and mobile computing systems, over which multiple types of services (voice, data or multimedia) will be supported.