MMPP-2 approximation of aggregate IPPs with application to expedited forwarding class in ipbased networks

In this paper, we investigate the suitability of a two state Markov Modulated Poisson Process (MMPP-2) approximation to the superposition of n homogeneous Interrupted Poisson Process (IPP) streams which pass through a series of m homogeneous network nodes. Earlier, such approximations have been attempted with the following restrictions: a) only a single node, b) deterministic service rate and c) at most a few hundred streams. We compare the performance of an MMPP-2 approximation to superposed IPPs for increased number of nodes (5, 7, 10), for exponential service rates and for 500 to 2500 IPP streams, each of which is better reflective of a real IP network scenario. Detailed simulation results show that the MMPP-2 approximation works exceedingly well with less than 4% average relative error and less than 6% maximum error. Furthermore, the approximation improves as the number of arriving IPPs, i.e., n increases. A subsequent example shows that this model can be utilized to calculate bandwidth bounds to ensure QoS for aggregate VoIP calls using the Expedited Forwarding class in the IP network.