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Service Chain Placement in SDNs
Gilad Kutiel 1 Dror Rawitz 2
1Technion 2Bar Ilan University
ALGOCLOUD 2017
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Service Chain (Customer’s Perspective)
◮ An ordered set of Virtual Functions
Service Chain Placement in SDNs Gilad Kutiel 1 Dror Rawitz 2 1 - - PowerPoint PPT Presentation
Service Chain Placement in SDNs Gilad Kutiel 1 Dror Rawitz 2 1 - - PowerPoint PPT Presentation
Service Chain Placement in SDNs Gilad Kutiel 1 Dror Rawitz 2 1 Technion 2 Bar Ilan University ALGOCLOUD 2017 1/15 Service Chain (Customers Perspective) An ordered set of Virtual Functions 2/15 Service
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SLIDE 3
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Service Chain (Customer’s Perspective)
◮ An ordered set of Virtual Functions ◮ Bandwidth requirement
- 100mb/s
60mb/s
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Service Chain (Customer’s Perspective)
◮ An ordered set of Virtual Functions ◮ Bandwidth requirement ◮ Latency constraint
- 100mb/s
60mb/s 90ms
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Service Chain (Customer’s Perspective)
◮ An ordered set of Virtual Functions ◮ Bandwidth requirement ◮ Latency constraint ◮ Several alternatives
- 100mb/s
60mb/s 90ms
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Problem (ISP’s Perspective)
SDN Service Chain
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Problem (ISP’s Perspective)
SDN Service Chain
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Problem (ISP’s Perspective)
SDN Service Chain
- ≥ 8CPU
≥ 12CPU ≥ 5CPU 3CPU 5CPU 2CPU 4CPU 6CPU 5CPU
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Problem (ISP’s Perspective)
SDN Service Chain
- ≥ 80mb/s
≥ 80mb/s ≥ 40mb/s ≥ 40mb/s
- 80mb/s
40mb/s
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Problem (ISP’s Perspective)
SDN Service Chain
- ≤ 90ms
90ms
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Problem (ISP’s Perspective)
SDN Service Chain
- ≤ 90ms
90ms 7$ 4$ 9$
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Problem cont.
Minimize Placement Cost s.t.
◮ CPU ◮ Bandwidth ◮ Latency
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Related Work
◮ System
SLIDE 14
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Related Work
◮ System
◮ A. Gember-Jacobson et al. 2014
SLIDE 15
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Related Work
◮ System
◮ A. Gember-Jacobson et al. 2014 ◮ R. Hartert et al. 2015
SLIDE 16
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Related Work
◮ System
◮ A. Gember-Jacobson et al. 2014 ◮ R. Hartert et al. 2015
◮ Online Service Chain Embedding Problem
SLIDE 17
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Related Work
◮ System
◮ A. Gember-Jacobson et al. 2014 ◮ R. Hartert et al. 2015
◮ Online Service Chain Embedding Problem
◮ T. Lukovszki and S. Schmid 2015
SLIDE 18
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Related Work
◮ System
◮ A. Gember-Jacobson et al. 2014 ◮ R. Hartert et al. 2015
◮ Online Service Chain Embedding Problem
◮ T. Lukovszki and S. Schmid 2015 ◮ Even et al. 2016
SLIDE 19
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Related Work
◮ System
◮ A. Gember-Jacobson et al. 2014 ◮ R. Hartert et al. 2015
◮ Online Service Chain Embedding Problem
◮ T. Lukovszki and S. Schmid 2015 ◮ Even et al. 2016
◮ Different Model / Objective
SLIDE 20
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Related Work
◮ System
◮ A. Gember-Jacobson et al. 2014 ◮ R. Hartert et al. 2015
◮ Online Service Chain Embedding Problem
◮ T. Lukovszki and S. Schmid 2015 ◮ Even et al. 2016
◮ Different Model / Objective
◮ Even et al. 2016
SLIDE 21
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Related Work
◮ System
◮ A. Gember-Jacobson et al. 2014 ◮ R. Hartert et al. 2015
◮ Online Service Chain Embedding Problem
◮ T. Lukovszki and S. Schmid 2015 ◮ Even et al. 2016
◮ Different Model / Objective
◮ Even et al. 2016 ◮ Cohen et al. 2015
SLIDE 22
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Our Results
◮ NP-hardness in many cases
1
SLIDE 23
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Our Results
◮ NP-hardness in many cases
SDN Costs Our Result
1
SLIDE 24
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Our Results
◮ NP-hardness in many cases
SDN Costs Our Result DAG Integral, Polynomial Optimal
1
SLIDE 25
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Our Results
◮ NP-hardness in many cases
SDN Costs Our Result DAG Integral, Polynomial Optimal DAG Any FPTAS - (1 + ε)-apx
1
SLIDE 26
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Our Results
◮ NP-hardness in many cases
SDN Costs Our Result DAG Integral, Polynomial Optimal DAG Any FPTAS - (1 + ε)-apx Any Any FPTAS - (1 + ε)-apx
1
SLIDE 27
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Our Results
◮ NP-hardness in many cases
SDN Costs Our Result DAG Integral, Polynomial Optimal DAG Any FPTAS - (1 + ε)-apx Any Any FPTAS - (1 + ε)-apx1
1running time depends on SDN’s typology
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Hardness (Feasibility)
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Hardness (Feasibility)
- 1 CPU
1 CPU 1 CPU 1 CPU 1 CPU 1 CPU
- 1 CPU
1 CPU 1 CPU 1 CPU 1 CPU 1 CPU
Hamiltonian path ⇐ ⇒ Feasible Placement
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Hardness (SDN with a single node)
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Hardness (SDN with a single node)
{2, 3, 6, 7, 4, 8}
- 15 CPU
- 2$ / 0 CPU
0$ / 2 CPU 3$ / 0 CPU 0$ / 3 CPU 6$ / 0 CPU 0$ / 6 CPU 7$ / 0 CPU 0$ / 7 CPU 4$ / 0 CPU 0$ / 4 CPU 8$ / 0 CPU 0$ / 8 CPU
Partition ⇐ ⇒ Placement that costs 15$
SLIDE 32
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Hardness (SDN with a single node)
{2, 3, 6, 7, 4, 8}
- 15 CPU
- 2$ / 0 CPU
0$ / 2 CPU 3$ / 0 CPU 0$ / 3 CPU 6$ / 0 CPU 0$ / 6 CPU 7$ / 0 CPU 0$ / 7 CPU 4$ / 0 CPU 0$ / 4 CPU 8$ / 0 CPU 0$ / 8 CPU
Partition ⇐ ⇒ Placement that costs 15$
* Not hard for integral, polynomial values
SLIDE 33
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Hardness (simple paths)
SLIDE 34
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Hardness (simple paths)
- · · ·
· · · · · · · · ·
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Hardness (simple paths)
- · · ·
· · · · · · · · · See paper...
SLIDE 36
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Integral Polynomial Costs, Single Node
Min CPU per Cost Budget.
- 10CPU
- 1$
3CPU 1$ 3CPU 2$ 2CPU 1$ 3CPU 2$ 1CPU 1$ 3CPU
$
- 7
6 5 4 3 2 1
SLIDE 37
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Integral Polynomial Costs, Single Node
Min CPU per Cost Budget.
- 10CPU
- 1$
3CPU 1$ 3CPU 2$ 2CPU 1$ 3CPU 2$ 1CPU 1$ 3CPU
$
- 7
6 5 4 3 2 1
SLIDE 38
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Integral Polynomial Costs, Single Node
Min CPU per Cost Budget.
- 10CPU
- 1$
3CPU 1$ 3CPU 2$ 2CPU 1$ 3CPU 2$ 1CPU 1$ 3CPU
$
- 7
3 6 5 4 3 2 1
SLIDE 39
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Integral Polynomial Costs, Single Node
Min CPU per Cost Budget.
- 10CPU
- 1$
3CPU 1$ 3CPU 2$ 2CPU 1$ 3CPU 2$ 1CPU 1$ 3CPU
$
- 7
3 6 3 5 3 4 3 3 3 2 3 1 3
SLIDE 40
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Integral Polynomial Costs, Single Node
Min CPU per Cost Budget.
- 10CPU
- 1$
3CPU 1$ 3CPU 2$ 2CPU 1$ 3CPU 2$ 1CPU 1$ 3CPU
$
- 7
3 6 3 5 3 4 3 3 3 2 3 1 3
SLIDE 41
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Integral Polynomial Costs, Single Node
Min CPU per Cost Budget.
- 10CPU
- 1$
3CPU 1$ 3CPU 2$ 2CPU 1$ 3CPU 2$ 1CPU 1$ 3CPU
$
- 7
3 6 6 3 5 3 4 3 3 3 2 3 1 3
SLIDE 42
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Integral Polynomial Costs, Single Node
Min CPU per Cost Budget.
- 10CPU
- 1$
3CPU 1$ 3CPU 2$ 2CPU 1$ 3CPU 2$ 1CPU 1$ 3CPU
$
- 7
3 6 6 3 6 5 3 6 4 3 6 3 3 6 2 3 6 1 3
SLIDE 43
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Integral Polynomial Costs, Single Node
Min CPU per Cost Budget.
- 10CPU
- 1$
3CPU 1$ 3CPU 2$ 2CPU 1$ 3CPU 2$ 1CPU 1$ 3CPU
$
- 7
3 6 6 3 6 5 3 6 4 3 6 3 3 6 2 3 6 1 3
SLIDE 44
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Integral Polynomial Costs, Single Node
Min CPU per Cost Budget.
- 10CPU
- 1$
3CPU 1$ 3CPU 2$ 2CPU 1$ 3CPU 2$ 1CPU 1$ 3CPU
$
- 7
3 6 5 6 3 6 5 3 6 4 3 6 3 3 6 2 3 6 1 3
SLIDE 45
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Integral Polynomial Costs, Single Node
Min CPU per Cost Budget.
- 10CPU
- 1$
3CPU 1$ 3CPU 2$ 2CPU 1$ 3CPU 2$ 1CPU 1$ 3CPU
$
- 7
3 6 5 6 3 6 5 5 3 6 5 4 3 6 5 3 3 6 5 2 3 6
- 1
3
SLIDE 46
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Integral Polynomial Costs, Single Node
Min CPU per Cost Budget.
- 10CPU
- 1$
3CPU 1$ 3CPU 2$ 2CPU 1$ 3CPU 2$ 1CPU 1$ 3CPU
$
- 7
3 6 5 6 3 6 5 5 3 6 5 4 3 6 5 3 3 6 5 2 3 6
- 1
3
SLIDE 47
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Integral Polynomial Costs, Single Node
Min CPU per Cost Budget.
- 10CPU
- 1$
3CPU 1$ 3CPU 2$ 2CPU 1$ 3CPU 2$ 1CPU 1$ 3CPU
$
- 7
3 6 5 9 6 3 6 5 9 5 3 6 5 9 4 3 6 5 9 3 3 6 5 9 2 3 6
- 1
3
SLIDE 48
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Integral Polynomial Costs, Single Node
Min CPU per Cost Budget.
- 10CPU
- 1$
3CPU 1$ 3CPU 2$ 2CPU 1$ 3CPU 2$ 1CPU 1$ 3CPU
$
- 7
3 6 5 9 6 3 6 5 9 5 3 6 5 9 4 3 6 5 9 3 3 6 5 9 2 3 6
- 1
3
SLIDE 49
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Integral Polynomial Costs, Single Node
Min CPU per Cost Budget.
- 10CPU
- 1$
3CPU 1$ 3CPU 2$ 2CPU 1$ 3CPU 2$ 1CPU 1$ 3CPU
$
- 7
3 6 5 9 6 6 3 6 5 9 6 5 3 6 5 9 6 4 3 6 5 9 3 3 6 5 9 2 3 6
- 1
3
SLIDE 50
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Integral Polynomial Costs, Single Node
Min CPU per Cost Budget.
- 10CPU
- 1$
3CPU 1$ 3CPU 2$ 2CPU 1$ 3CPU 2$ 1CPU 1$ 3CPU
$
- 7
3 6 5 9 6 6 3 6 5 9 6 5 3 6 5 9 6 4 3 6 5 9 7 3 3 6 5 9
- 2
3 6
- 1
3
SLIDE 51
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Integral Polynomial Costs, Single Node
Min CPU per Cost Budget.
- 10CPU
- 1$
3CPU 1$ 3CPU 2$ 2CPU 1$ 3CPU 2$ 1CPU 1$ 3CPU
$
- 7
3 6 5 9 6 6 3 6 5 9 6 5 3 6 5 9 6 4 3 6 5 9 7 3 3 6 5 9
- 2
3 6
- 1
3
SLIDE 52
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Integral Polynomial Costs, Single Node
Min CPU per Cost Budget.
- 10CPU
- 1$
3CPU 1$ 3CPU 2$ 2CPU 1$ 3CPU 2$ 1CPU 1$ 3CPU
$
- 7
3 6 5 9 6 9 6 3 6 5 9 6 9 5 3 6 5 9 6 10 4 3 6 5 9 7 12 3 3 6 5 9
- 2
3 6
- 1
3
SLIDE 53
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Integral Polynomial Costs, Single Node
Min CPU per Cost Budget.
- 10CPU
- 1$
3CPU 1$ 3CPU 2$ 2CPU 1$ 3CPU 2$ 1CPU 1$ 3CPU
$
- 7
3 6 5 9 6 9 6 3 6 5 9 6 9 5 3 6 5 9 6 10 4 3 6 5 9 7 12 3 3 6 5 9
- 2
3 6
- 1
3
SLIDE 54
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Integral Polynomial Costs, Single Node
Min CPU per Cost Budget.
- 10CPU
- 1$
3CPU 1$ 3CPU 2$ 2CPU 1$ 3CPU 2$ 1CPU 1$ 3CPU
$
- 7
3 6 5 9 6 9 6 3 6 5 9 6 9 5 3 6 5 9 6 10 4 3 6 5 9 7 12 3 3 6 5 9
- 2
3 6
- 1
3
SLIDE 55
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Integral Polynomial Costs, Single Node
Min CPU per Cost Budget.
- 10CPU
- 1$
3CPU 1$ 3CPU 2$ 2CPU 1$ 3CPU 2$ 1CPU 1$ 3CPU
$
- 7
3 6 5 9 6 9 6 3 6 5 9 6 9 5 3 6 5 9 6 10 4 3 6 5 9 7 12 3 3 6 5 9
- 2
3 6
- 1
3
- Search for min Budget s.t. CPU constraint.
SLIDE 56
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Small, Integral Costs, DAG
Min Latency s.t. Cost Budget.
SLIDE 57
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Small, Integral Costs, DAG
Min Latency s.t. Cost Budget.
◮ Pick 2 arcs (x ≥ y)
- x
m b / s
- ymb/s
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Small, Integral Costs, DAG
Min Latency s.t. Cost Budget.
◮ Pick 2 arcs (x ≥ y) ◮ Orange Problem - Single Node
- x
m b / s
- ymb/s
SLIDE 59
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Small, Integral Costs, DAG
Min Latency s.t. Cost Budget.
◮ Pick 2 arcs (x ≥ y) ◮ Orange Problem - Single Node ◮ Blue Problem - Shortest Path
- x
m b / s
- ymb/s
SLIDE 60
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Small, Integral Costs, DAG
Min Latency s.t. Cost Budget.
◮ Pick 2 arcs (x ≥ y) ◮ Orange Problem - Single Node ◮ Blue Problem - Shortest Path ◮ Green Problem - Recursively
- x
m b / s
- ymb/s
SLIDE 61
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Small, Integral Costs, DAG
Min Latency s.t. Cost Budget.
◮ Pick 2 arcs (x ≥ y) ◮ Orange Problem - Single Node ◮ Blue Problem - Shortest Path ◮ Green Problem - Recursively
◮ At most |V | × |F| × Cost
- x
m b / s
- ymb/s
SLIDE 62
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Small, Integral Costs, DAG
Min Latency s.t. Cost Budget.
◮ Pick 2 arcs (x ≥ y) ◮ Orange Problem - Single Node ◮ Blue Problem - Shortest Path ◮ Green Problem - Recursively
◮ At most |V | × |F| × Cost
- x
m b / s
- ymb/s
Search for the minimum budget s.t. Latency constraint.
SLIDE 63
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Theorem
Costs can be scaled and rounded such that for any ε > 0 an
- ptimal solution w.r.t the rounded value is a 1 + ε-approximation
for the original costs.
SLIDE 64
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General Case
◮ Find unreachable nodes
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General Case
◮ Find unreachable nodes ◮ Mark nodes with deg > 2
SLIDE 66
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General Case
◮ Find unreachable nodes ◮ Mark nodes with deg > 2 ◮ Choose a permutation
SLIDE 67
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General Case
◮ Find unreachable nodes ◮ Mark nodes with deg > 2 ◮ Choose a permutation ◮ Orient the network accordingly
- 1
2 3
SLIDE 68
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General Case
◮ Find unreachable nodes ◮ Mark nodes with deg > 2 ◮ Choose a permutation ◮ Orient the network accordingly ◮ Use the previous algorithm
- 1
2 3
SLIDE 69
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General Case
◮ Find unreachable nodes ◮ Mark nodes with deg > 2 ◮ Choose a permutation ◮ Orient the network accordingly ◮ Use the previous algorithm ◮ Running time is O(k!t(n)) 1
- 1
2 3
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General Case
◮ Find unreachable nodes ◮ Mark nodes with deg > 2 ◮ Choose a permutation ◮ Orient the network accordingly ◮ Use the previous algorithm ◮ Running time is O(k!t(n)) 1
- 1
2 3
1 Can be reduced to O(2kt(n))
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Conclusion
◮ Attracts Attention
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Conclusion
◮ Attracts Attention
◮ System
SLIDE 73
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Conclusion
◮ Attracts Attention
◮ System ◮ Algorithmically
SLIDE 74
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Conclusion
◮ Attracts Attention
◮ System ◮ Algorithmically
◮ Best we can hope solution for DAGs
SLIDE 75
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Conclusion
◮ Attracts Attention
◮ System ◮ Algorithmically
◮ Best we can hope solution for DAGs ◮ Open questions for general SDNs
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Conclusion
◮ Attracts Attention
◮ System ◮ Algorithmically
◮ Best we can hope solution for DAGs ◮ Open questions for general SDNs
◮ Best we can hope solution under some assumptions
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Conclusion
◮ Attracts Attention
◮ System ◮ Algorithmically
◮ Best we can hope solution for DAGs ◮ Open questions for general SDNs
◮ Best we can hope solution under some assumptions
◮ Fault Tolerance
SLIDE 78
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Conclusion
◮ Attracts Attention
◮ System ◮ Algorithmically
◮ Best we can hope solution for DAGs ◮ Open questions for general SDNs
◮ Best we can hope solution under some assumptions
◮ Fault Tolerance ◮ In practice?
SLIDE 79
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