deterministic network calculus. background ● queueing theory gives probabilistic results ●...
Post on 20-Dec-2015
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Deterministic Network Calculus
Background
● Queueing Theory gives probabilistic results● Critical applications need hard bounds● Queueing theory extends only partially to
networks.● Scheduling theory accounts only for CPU sharing
and bounded blocking.● Periodic studies do not account for bursty traffic.
Cirquit analysis
Concatenation of Network Elements
Converging Flows
Feedback
Definition and Range Spaces
Definition and Range Spaces
The Playout Buffer
Arrival Curves
Arrival Curves
Spacing and Staircases
An Equivalence
The Leaky Bucket in Words
Leaky Bucket in Graphics
Nice to know about Leaky Buckets
Some DN-Calculus in Play
Henrik should prove this on the blackboard
The Generic Cell Rate Algorithm
GCRA
tat
Non conformant Conformant
T
t
Conformant
tT
GCRA facts
Leaky Buckets and GCRAs
Subadditivity
● We assume (0) = 0● Subadditive if t+s) <= (t) + (s)● Subadditive closure of
The largest subadditive function
less than or equal to
Subadditivity
Sufficiency of Subadditive Arrivals