Half-modelling of shaping in FIFO net Marc Boyer Half-modelling of shaping in FIFO net with network calculus Context Network calculus: overview Marc Boyer Network calculus: topologies Previous works (tandem topologies) Local delay and shaping LUB RTNS 2010 – nov. 4th 2010 Our contribution Conclusion Marc Boyer (ONERA, France) Half-modelling of shaping in FIFO net RTNS 2010 – nov. 4th 2010 1 / 24
Outline Half-modelling of shaping in FIFO net 1 Context Marc Boyer 2 Network calculus: overview Context 3 Network calculus: topologies Network calculus: overview 4 Previous works (tandem topologies) Network calculus: Local delay and shaping topologies PBOO without shaping (LUB) Previous works (tandem topologies) 5 Our contribution Local delay and shaping LUB 6 Conclusion Our contribution Conclusion Marc Boyer (ONERA, France) Half-modelling of shaping in FIFO net RTNS 2010 – nov. 4th 2010 2 / 24
Outline Half-modelling of shaping in FIFO net 1 Context Marc Boyer 2 Network calculus: overview Context 3 Network calculus: topologies Network calculus: overview 4 Previous works (tandem topologies) Network calculus: Local delay and shaping topologies PBOO without shaping (LUB) Previous works (tandem topologies) 5 Our contribution Local delay and shaping LUB 6 Conclusion Our contribution Conclusion Marc Boyer (ONERA, France) Half-modelling of shaping in FIFO net RTNS 2010 – nov. 4th 2010 3 / 24
Worst Case Traversal Time: What and Why Half-modelling of shaping in Net in real-time systems FIFO net Embedded systems are: Marc Boyer real-time ( = ⇒ real-time scheduling) Context communicating: Network calculus: overview Network calculus: topologies Previous works (tandem real-time real-time topologies) net app. app. Local delay and shaping LUB Our contribution Conclusion Marc Boyer (ONERA, France) Half-modelling of shaping in FIFO net RTNS 2010 – nov. 4th 2010 4 / 24
Worst Case Traversal Time: What and Why Half-modelling of shaping in Net in real-time systems FIFO net Embedded systems are: Marc Boyer real-time ( = ⇒ real-time scheduling) Context communicating: network delay (traversal time) Network calculus: overview Network calculus: topologies Previous works (tandem real-time real-time topologies) net app. app. Local delay and shaping LUB Our Traversal time contribution Conclusion Marc Boyer (ONERA, France) Half-modelling of shaping in FIFO net RTNS 2010 – nov. 4th 2010 4 / 24
Worst Case Traversal Time: What and Why Half-modelling of shaping in Net in real-time systems FIFO net Embedded systems are: Marc Boyer real-time ( = ⇒ real-time scheduling) Context communicating: network delay (traversal time) Network calculus: = ⇒ need of end-to-end delay bound (WCTT) overview Network calculus: topologies Previous works (tandem real-time real-time topologies) net app. app. Local delay and shaping LUB Our Traversal time contribution ≤ WCTT ≤ WCTT-bound Conclusion Marc Boyer (ONERA, France) Half-modelling of shaping in FIFO net RTNS 2010 – nov. 4th 2010 4 / 24
Worst Case Traversal Time: What and Why Half-modelling of shaping in Net in real-time systems FIFO net Embedded systems are: Marc Boyer real-time ( = ⇒ real-time scheduling) Context communicating: network delay (traversal time) Network calculus: = ⇒ need of end-to-end delay bound (WCTT) overview Network = ⇒ traffic contract and service guarantee calculus: topologies Previous works (tandem real-time real-time topologies) net app. app. Local delay and shaping LUB Our Traversal time contribution ≤ WCTT ≤ WCTT-bound Conclusion Marc Boyer (ONERA, France) Half-modelling of shaping in FIFO net RTNS 2010 – nov. 4th 2010 4 / 24
Outline Half-modelling of shaping in FIFO net 1 Context Marc Boyer 2 Network calculus: overview Context 3 Network calculus: topologies Network calculus: overview 4 Previous works (tandem topologies) Network calculus: Local delay and shaping topologies PBOO without shaping (LUB) Previous works (tandem topologies) 5 Our contribution Local delay and shaping LUB 6 Conclusion Our contribution Conclusion Marc Boyer (ONERA, France) Half-modelling of shaping in FIFO net RTNS 2010 – nov. 4th 2010 5 / 24
Basic ideas Half-modelling of shaping in FIFO net Marc Boyer Theory designed to compute WCTT bounds Used to certify A380 Context Strong mathematical background: (min , +) dioid Network calculus: overview � � x < y = ⇒ f ( x ) ≤ f ( y ) F = f : ❘ → ❘ Network x < 0 = ⇒ f ( x ) = 0 calculus: topologies ( f ∗ g )( t ) = 0 ≤ u ≤ t ( f ( t − u ) + g ( u )) inf (1) Previous works (tandem topologies) ( f ⊘ g )( t ) = sup ( f ( t + u ) − g ( u )) (2) Local delay and shaping 0 ≤ u LUB Our contribution Conclusion Marc Boyer (ONERA, France) Half-modelling of shaping in FIFO net RTNS 2010 – nov. 4th 2010 6 / 24
Reality modelling Half-modelling Data flow: R ( t ) amount of data up to time t (cumulative of shaping in FIFO net curve) Marc Boyer S → R ′ Server: transforms input into output R − Arrival curve: α Context Network ∀ t , d ≥ 0 : R ( t + d ) − R ( t ) ≤ α ( d ) ⇐ ⇒ R ≤ R ∗ α calculus: overview Service curve: β iff R ′ ≥ R ∗ β Network calculus: topologies Traffic contract Service guarantee Previous works (tandem Token bucket Periodic Delay Rate-latency topologies) γ r , b Local delay and β R , T shaping δ d r LUB b Our b R contribution Conclusion t t t t d T Marc Boyer (ONERA, France) Half-modelling of shaping in FIFO net RTNS 2010 – nov. 4th 2010 7 / 24
First results Half-modelling Given: of shaping in FIFO net an arrival traffic contract Marc Boyer a service guarantee Context Network calculus: overview Network α β calculus: topologies Previous works (tandem topologies) Local delay and shaping LUB R S R’ Our contribution Conclusion Marc Boyer (ONERA, France) Half-modelling of shaping in FIFO net RTNS 2010 – nov. 4th 2010 8 / 24
First results Half-modelling Given: it can compute of shaping in FIFO net an arrival traffic contract a delay bound ( h ) Marc Boyer a service guarantee output traffic contract Context Network calculus: overview α Network α β calculus: topologies h α ′ = α ⊘ β Previous works (tandem topologies) Local delay and shaping LUB R S R’ Our contribution Conclusion Marc Boyer (ONERA, France) Half-modelling of shaping in FIFO net RTNS 2010 – nov. 4th 2010 8 / 24
Outline Half-modelling of shaping in FIFO net 1 Context Marc Boyer 2 Network calculus: overview Context 3 Network calculus: topologies Network calculus: overview 4 Previous works (tandem topologies) Network calculus: Local delay and shaping topologies PBOO without shaping (LUB) Previous works (tandem topologies) 5 Our contribution Local delay and shaping LUB 6 Conclusion Our contribution Conclusion Marc Boyer (ONERA, France) Half-modelling of shaping in FIFO net RTNS 2010 – nov. 4th 2010 9 / 24
Pay burst only once principle Half-modelling of shaping in FIFO net R ′ S ′ R ′′ R S Marc Boyer Context Pay burst only once Network calculus: The sequence S , S ′ can be replaced by a virtual server S ; S ′ overview Network with service curve β ∗ β ′ . calculus: topologies Interest End-to-end delay is less than sum of individual delays. Previous works (tandem topologies) h ( α, β ∗ β ′ ) ≤ h ( α, β ) + h ( α, β ′ ) Local delay and (3) shaping LUB Our contribution Proof R ′′ ≥ R ′ ∗ β ≥ ( R ∗ β ) ∗ β ′ = R ∗ ( β ∗ β ′ ) Conclusion Marc Boyer (ONERA, France) Half-modelling of shaping in FIFO net RTNS 2010 – nov. 4th 2010 10 / 24
✶ ✶ FIFO Aggregate scheduling Half-modelling R ′ of shaping in R 1 1 FIFO net S R ′ Marc Boyer R 2 2 Context Network calculus: overview Network calculus: topologies Previous works (tandem topologies) Local delay and shaping LUB Our contribution Conclusion Marc Boyer (ONERA, France) Half-modelling of shaping in FIFO net RTNS 2010 – nov. 4th 2010 11 / 24
✶ ✶ FIFO Aggregate scheduling Half-modelling R ′ of shaping in R 1 1 FIFO net S R ′ Marc Boyer R 2 2 Context First FIFO result: aggregated delay (Th. 1) Network calculus: If d = h ( α 1 + α 2 , β ) is the delay for the aggregated flow, then overview δ d is a service curve for each flow. Network calculus: α ′ i ( t ) = ( α ′ i ⊘ δ d )( t ) = α ( t + d ) topologies Previous works (tandem topologies) Local delay and shaping LUB Our contribution Conclusion Marc Boyer (ONERA, France) Half-modelling of shaping in FIFO net RTNS 2010 – nov. 4th 2010 11 / 24
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