  A basic calculus is presented for stochastic service guarantee analysis in
communication networks. Central to the calculus are two definitions,
maximum-(virtual)-backlog-centric (m.b.c) stochastic arrival curve and
stochastic service curve, which respectively generalize arrival curve and
service curve in the deterministic network calculus framework. With m.b.c
stochastic arrival curve and stochastic service curve, various basic results
are derived under the (min, +) algebra for the general case analysis, which are
crucial to the development of stochastic network calculus. These results
include (i) superposition of flows, (ii) concatenation of servers, (iii) output
characterization, (iv) per-flow service under aggregation, and (v) stochastic
backlog and delay guarantees. In addition, to perform independent case
analysis, stochastic strict server is defined, which uses an ideal service
process and an impairment process to characterize a server. The concept of
stochastic strict server not only allows us to improve the basic results (i) --
(v) under the independent case, but also provides a convenient way to find the
stochastic service curve of a serve. Moreover, an approach is introduced to
find the m.b.c stochastic arrival curve of a flow and the stochastic service
curve of a server.
