Traffic Modeling with Phase-Type Distributions and VARMA Processes

In discrete event systems event times are often correlated among events of one event stream and also between different event streams. If this correlation is neglected, then resulting simulation models do not describe the real behavior in a sufficiently accurate way. In most input modeling approaches, no correlation or at most the autocorrelation of one event stream is considered, correlation between different event streams is usually neglected. In this paper we present an approach to combine multi-dimensional time series and acyclic phase type distributions as a general model for event streams in discrete event simulation models. The paper presents the basic model and methods to determine its parameters from measured traces.