Fitting simulation input models for correlated traffic data

Abstract

The adequate representation of input models is an important step in building valid simulation models. Modeling independent and identically distributed data is well established in simulation, but for some application areas like computer and communication networks it is known, that the assumption of independent and identically distributed data is violated in practice and that for example interarrival times or packet sizes exhibit autocorrelation over a large number of lags. Moreover, it is known that negligence of these correlations can result in a serious loss of validity of the simulation model.

Although different stochastic processes, which can model these autocorrelations, like e.g. Autoregressive-To-Anything (ARTA) processes and Markovian Arrival Processes (MAPs), have been proposed in the past and more recently fitting algorithms to set the parameters of these processes such that they resemble the behavior of observations from a real system have been developed, the integration of correlated processes into simulation models is still a challenge.

In this work ARTA processes are extended in several ways to account for the requirements when simulating models of computer and communication systems. In a first step ARTA processes are extended to use an Autoregressive Moving Average (ARMA) process instead of a pure Autoregressive (AR) base process to be able to capture a large number of autocorrelation lags, while keeping the model size small. In a second step they are enabled to use the flexible class of acyclic Phase-type distributions as marginal distribution.

To support the usage of these novel processes in simulation models a fitting algorithm is presented, software for fitting and simulating these processes is developed and the tools are integrated into the toolkit ProFiDo, which provides a complete framework for fitting and analyzing different stochastic processes.

By means of synthetically generated and real network traces it is shown that the presented stochastic processes are able to provide a good approximation of the marginal distribution as well as the correlation structure of the different traces and result in a compact process description.