We study peer-to-peer packet traffic arising from passive VoIP and video measurements that are generated bySkype and IPTV clients.We provide a common methodology for the statisticalcharacterization of the packet flows, discuss the user's satisfaction and load estimation.Two main ideas are used in our analysis.Due to the dependence of the data we firstpartition the observations into independent blocks and deal further withthe block-wise independent data.Secondly, loss is generated by packet lengths which exceeda channel capacity in a time unit if the inter-arrival times coincide with this time unit. If the inter-arrival times arerandom,loss is generated by those packet lengths corresponding totransmission rates thatexceed the channel capacity.

The previously developed methods for investigation of the above question include such advanced tools as Harnack inequalities and estimates of fundamental solutions. Here we adopt another approach that originates and that uses only very basic tools as capacities and volumes. As a consequence of this inequality, we obtain various interesting comparison inequalities for heat semigroups and heat kernels, which can be used for obtaining pointwise estimates of heat kernels. As an example of application, we present a new method of deducing sub-Gaussian upper bounds of the heat kernel from on-diagonal bounds and tail estimates.