  Network calculus is a min-plus system theory for performance evaluation of
queuing networks. Its elegance stems from intuitive convolution formulas for
concatenation of deterministic servers. Recent research dispenses with the
worst-case assumptions of network calculus to develop a probabilistic
equivalent that benefits from statistical multiplexing. Significant
achievements have been made, owing for example to the theory of effective
bandwidths, however, the outstanding scalability set up by concatenation of
deterministic servers has not been shown.
  This paper establishes a concise, probabilistic network calculus with moment
generating functions. The presented work features closed-form, end-to-end,
probabilistic performance bounds that achieve the objective of scaling linearly
in the number of servers in series. The consistent application of moment
generating functions put forth in this paper utilizes independence beyond the
scope of current statistical multiplexing of flows. A relevant additional gain
is demonstrated for tandem servers with independent cross-traffic.
