Deterministic Network Calculus. DNC history Queueing Theory, Agner Krarup Erlang, 1909 Queueing Networks, James R. Jackson, 1957 Scheduling Theory, Liu.

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Presentation transcript:

Deterministic Network Calculus

DNC history Queueing Theory, Agner Krarup Erlang, 1909 Queueing Networks, James R. Jackson, 1957 Scheduling Theory, Liu & Layland, 1972 Network Calculus, Rene Cruz, 1991, J. Y. Le Boudec

DNC motivation Queueing Networks predict backlogs and waiting in networks of servers and buffers (production, computer networks, traffic) QN theory is probabilistic – not suited for real time analysis Scheduling theory gives worst case (non-deterministic) results for single queues under restricting assumptions Deterministic Network Calculus extends scheduling theory to a non deterministic theory for networks.

Cirquit analysis

Concatenation of Network Elements

Converging Flows

Feedback

Definition and Range Spaces

The Playout Buffer

Arrival Curves

Spacing and Staircases

Left Continuity

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 facts

Leaky Buckets and GCRAs

Good Functions

Subadditivity

Sufficiency of Subadditive Arrivals

Minimum Arrival Curves

Minimum Arrival Curves (example)