@comment{ generated by <http://infoscience.epfl.ch/> }

@TechReport{136/LCA,
   abstract    = {We analyze some queueing problems arising in guaranteed
                 service and controlled load networks using min-plus
                 algebra. We find an explicit representation for the
                 sub-additive closure of the minimum of two operators, and
                 we introduce a new, useful family of idempotent,
                 time-varying, and min-plus linear operators. We model
                 queueing systems arising in networks networks as
                 non-linear min-plus systems that can be bounded by linear
                 systems, and apply our concepts to: the optimal shaper
                 studied by Anantharam and Konstantopoulos, the window
                 flow control problem previously studied by: Cruz and
                 Okino, Chang, Agrawal and Rajan. In all these cases we
                 explain the existing bounds and in the latter case derive
                 another bound. We then show how the same method enables
                 us to give a representation for the losses in a shaper
                 with finite buffer constraints or with delay constraints.
                 We apply the result to bound the losses in a variable bit
                 rate (VBR) trunk system by the losses in simpler,
                 constant bit rate trunk systems (CBR) systems. Finally,
                 as a by-product of the concepts proposed in the paper, we
                 show how it provides an explicit solution to the
                 deterministic Skorokhod reflection mapping problem with
                 two boundaries.},
   affiliation = {EPFL},
   author      = {Le Boudec, Jean-Yves and Thiran, Patrick},
   details     = {http://infoscience.epfl.ch/record/29},
   keywords    = {Guaranteed Quality of Service; ATM; Queueing Systems;
                 Network Calculus; Min-Plus Algebra; ReflectionMapping;
                 Window Flow Control; Optimal Leaky Bucket},
   oai-id      = {oai:infoscience.epfl.ch:29},
   oai-set     = {report},
   status      = {PUBLISHED},
   title       = {Network {C}alculus viewed as a {M}in-plus {S}ystem {T}heory},
   unit        = {LCA LCA2 LCA3},
   year        = 1998
}