Approximate Model for Merging Markovian Arrival Processes

Traffic-based decomposition models encompass procedures required for modelling of the basic network operations of superposition, departure and splitting, arising due to the common sharing of the resources and routing decisions taking place in packetswitched networks. It is desirable to study such models for Markovian Arrival Processes (MAPs), as these processes are able to match correlations and burstiness, characteristics that are inherent to IP traffic. Using the method of exact superposing of MAPs has limitations, as the computational complexity dramatically increases in practical cases. In order to keep the computational efforts required to a minimum, in analyzing queueing networks using the method of decomposition, one has to use a MAP of small order (e.g., MAP-2) to represent the intermediate node, as well as, the offered traffic inputs in the network. In this paper, we propose an approximate model for evaluation of the exact superposed process of a number of independent MAP processes as a MAP of order two, which provides good accuracy across wide range of burstiness parameters for the individual traffic processes and across various traffic load scenarios. Keywords— Traffic Modelling, Markovian Arrival Process.