### Server Models for Probabilistic Network Calculus

*M. Fidler*

#### Abstract

Network calculus is a deterministic queuing theory that has gained increasing attention in recent time. Founded on min-plus algebra it resorts to intuitive convolution formulae for efficient concatenation of servers and derivation of related performance bounds. Yet, the pessimistic worst-case analysis of deterministic network calculus gave rise to probabilistic counterparts that aim at utilizing the smoothing effects of statistical multiplexing by allowing for certain violation probabilities. Related theories are, however, significantly more complicated and still subject to research. To advance theory this paper evolves server models for probabilistic network calculus that are based on moment generating functions to efficiently utilize statistical multiplexing and the independence of flows.

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