Network calculus is an elegant theory which uses envelopes to determine the
worst-case performance bounds in a network. Statistical network calculus is the
probabilistic version of network calculus, which strives to retain the
simplicity of envelope approach from network calculus and use the arguments of
statistical multiplexing to determine probabilistic performance bounds in a
network. One of the key results of deterministic network calculus is that the
end-to-end performance measures determined using a network service envelope is
bounded by $ {\cal O} (H) $, where $H$ is the number of nodes traversed by a
flow. There have been many attempts to achieve a similar linear scaling of
probabilistic performance bounds in statistical network calculus but with
limited success. The main contribution of this paper is to show that, if the
statistical network service envelope is derived from stochastic network service
process characterizing the service offered at the network, the resulting
end-to-end performance measures of $(\sigma(\theta),\rho(\theta))$ constrained
traffic model determined using the statistical network service envelope scale
linearly in the number of nodes ($H$) traversed by the arrival traffic.