New stochastic network calculus for loss analysis

Recently some stochastic (probabilistic) extensions of the deterministic network calculus have been developed, mainly for exploiting the statistical multiplexing of flows aggregated in packet based communication networks. This exploitation could result ”better” stochastic performance bounds than those bounds provided by the inherently worst case analysis of the deterministic network calculus. The core of these stochastic extensions is the re-definition of the so-called arrival and service curve in a probabilistic manner. Until this time the re-definitions of these curves are based on tail probability like functionals. In this paper we perform a new kind of stochastic network calculus based on defining arrival and service curves using a different functional called tail weight. The power of this approach is demonstrated by presenting fundamental results on backlog and delay bounds and concatenation of nodes, furthermore suitable service curves and numerical examples are also presented for one of the most complicated packet service disciplines, the generalized processor sharing scheduler.