Sojourn time of elastic flows under perturbation of unresponsive traffic

Motivated by the need to develop simple models to obtain qualitative results for evaluating the impact of unresponsive traffic on elastic flows, we assume that transmission capacity is offered to elastic flows in a processor sharing fashion as function of the unresponsive traffic and quantified by means of a perturbation parameter e. For such a system, we analyze the impact of the perturbation on the mean sojourn time of an elastic flow, which represents a useful measure for the transfer delay of digital documents. Specifically, we derive the first two terms of the power series expansion in e of the mean sojourn time. The first order term is consistent with the reduced service rate (RSR) approximation, which corresponds to the service rate for elastic flows being constant and equal to the mean value of the perturbed service rate. The complexity of the expansion increases for the second order term and correlations created by the unresponsive traffic appear. Qualitative results show that variability in the service rate degrades the performance of elastic flows