On Polynomial-Time Congestion-Free Software-Defined Network Updates - - PowerPoint PPT Presentation

On Polynomial-Time Congestion-Free Software-Defined Network Updates

Saeed Akhoondian Amiri (MPI, Saarland, Germany) Szymon Dudycz (6 University of Wroclaw, Poland) Mahmoud Parham and Stefan Schmid (University of Vienna, Austria) Sebastian Wiederrecht (TU Berlin, Germany)

IFIP NETWORKING 2019, May 21, 2019 – Warsaw, Poland

• 1

Why reroute?

• many reasons, including security and policy changes
• traffic engineering, optimizations, demand changes etc.
• rerouting involves distribution of new (forwarding) rules
• while maintaining certain consistency properties
• in a SDN, rules are distributed by a controller

2

S w v u T S w v u T

• ld routes

new routes Dashed: new route Solid: old route Task: reroute red and blue flows to their new route

SDN controller issues update commands

update(node, Red/Blue)

3

Task: reroute red and blue flows to their new route

S w v u T

2 1 2 1 1 1 1 Dashed: new route Solid: old route Let’s reroute!

update(node, Red/Blue)

update(S, Red) update(w, Red) update(u, Blue) update(S, Blue) update(u, Red) update(v, Red) update(v, Blue) update(w, Blue)

4

1-update(w, Red) Rerouting red and blue flows to their new route, congestion-free!

S w v u T

2 1 2 1 1 1 1 Dashed: new route Solid: old route update(S, Red) update(w, Red) update(S, Blue) update(u, Red) update(v, Red) update(v, Blue) update(w, Blue)

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1-update(w, Red)

S w v u T

2 1 2 1 1 1 1 2-update(S, Red)

congestion!

Rerouting red and blue flows to their new route, congestion-free! Dashed: new route Solid: old route

infeasible transient state

update(S, Red) update(w, Red) update(u, Red) update(v, Red) update(v, Blue) update(w, Blue)

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S w v u T

2 1 2 1 1 1 1 Let’s try again! Rerouting red and blue flows to their new route, congestion-free! Dashed: new route Solid: old route 4-update(S, Red) 3-update(w, Red) 1-update(u, Blue) 2-update(S, Blue) 5-update(u, Red) 6-update(v, Red) 7-update(v, Blue) 8-update(w, Blue)

7

S w v u T

2 1 2 1 1 1 1 4-update(S, Red) 3-update(w, Red) 1-update(u, Blue) 2-update(S, Blue) 5-update(u, Red) 6-update(v, Red) 7-update(v, Blue) 8-update(w, Blue) Rerouting red and blue flows to their new route, congestion-free! Dashed: new route Solid: old route

• ne update per round

8

S w v u T

2 1 2 1 1 1 1 1-update(u, Blue) 4-update(S, Red) 3-update(w, Red) 1-update(u, Blue) 2-update(S, Blue) 5-update(u, Red) 6-update(v, Red) 7-update(v, Blue) 8-update(w, Blue) Rerouting red and blue flows to their new route, congestion-free! Dashed: new route Solid: old route

9

S w v u T

2 1 2 1 1 1 1 4-update(S, Red) 3-update(w, Red) 1-update(u, Blue) 2-update(S, Blue) 5-update(u, Red) 6-update(v, Red) 7-update(v, Blue) 8-update(w, Blue) Rerouting red and blue flows to their new route, congestion-free! Dashed: new route Solid: old route

10

S w v u T

2 1 2 1 1 1 1 4-update(S, Red) 3-update(w, Red) 1-update(u, Blue) 2-update(S, Blue) 5-update(u, Red) 6-update(v, Red) 7-update(v, Blue) 8-update(w, Blue) Rerouting red and blue flows to their new route, congestion-free! Dashed: new route Solid: old route

11

S w v u T

2 1 2 1 1 1 1 4-update(S, Red) 3-update(w, Red) 1-update(u, Blue) 2-update(S, Blue) 5-update(u, Red) 6-update(v, Red) 7-update(v, Blue) 8-update(w, Blue) Rerouting red and blue flows to their new route, congestion-free! Dashed: new route Solid: old route

12

S w v u T

2 1 2 1 1 1 1 4-update(S, Red) 3-update(w, Red) 1-update(u, Blue) 2-update(S, Blue) 5-update(u, Red) 6-update(v, Red) 7-update(v, Blue) 8-update(w, Blue) Rerouting red and blue flows to their new route, congestion-free! Dashed: new route Solid: old route

13

S w v u T

2 1 2 1 1 1 1 4-update(S, Red) 3-update(w, Red) 1-update(u, Blue) 2-update(S, Blue) 5-update(u, Red) 6-update(v, Red) 7-update(v, Blue) 8-update(w, Blue) Rerouting red and blue flows to their new route, congestion-free! Dashed: new route Solid: old route

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Observations

• 8 updates, 8 rounds in this example
• Multiple updates could be scheduled for a same round
• Updates in a same round finish in arbitrary order ⇒ transient states
• All transient states must respect capacity constraints
• The example admits a feasible schedule in only 4 rounds

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3-update(S, Red) 2-update(w, Red) 1-update(u, Blue) 2-update(S, Blue) 4-update(u, Red) 4-update(v, Red) 2-update(v, Blue) 4-update(w, Blue) Rerouting red and blue flows to their new route, congestion-free! Dashed: new route Solid: old route

S w v u T

2 1 2 1 1 1 1

Feasible Transient States

2^3=8 possible transient states for round 2

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Problem Definition

• Input: two flow pairs (old,new), unit demands, unsplittable.
• Task: reroute each flow, from its old route to its new route, consistently.
• Consistent: Loop-free + Congestion-free.
• For every pair, (old ∪ new) is a DAG ⇒ Loop-freedom for free!
• Feasibility: is there a sequence of congestion-free updates?
• Optimality: how to minimize the number of rounds efficiently?

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Dashed: new route Solid: old route

Block Decomposition

block1 block2 block3 block4 S T v1 v2 v3

Block1 Block2 Block3 Block4

the union of the old and new routes

1) Take the union of old and new routes => a DAG 2) Obtain its nodes in a topologically sorted oder 3) Intersections consecutive in that order are block’s endpoints

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Block Update

start of block

(1) activate all new route links not incident to u (2) update(u, blue) (3) deactivate links on the old route Dashed: new route Solid: old route

block update in 3 rounds

u v

Block i

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• Update the whole flow route block by block
• A block takes up to 3 rounds to update
• Blocks of the same flow can be updated independently
• Blocks of different flows may have dependencies

block1 block2 block3 block4 S T v1 v2 v3

Block1 Block2 Block3 Block4

Towards an Efficient Algorithm

20

Towards an Efficient Algorithm for 2 Flows

Block B

L

Block A

L

dependency

• Link L has capacity 1
• Blue cannot reroute before Red reroutes away from L
• Block A depends on Block B
• Any feasible schedule updates B before A

Dashed: new route Solid: old route

21

Overview of the Algorithm 1) Compute the block composition for the two flows. 2) Compute the dependency graph D of G. 3) If there is a cycle in D then terminate. 4) While D is not empty, repeat:

1) Update all blocks that correspond to the sink vertices of D. 2) Remove all the sink vertices from D.

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# of rounds

• All sink blocks are updated together, in 3 rounds.
• 3 rounds per iteration is not always necessary.
• Allocating the necessary rounds yields the optimal schedule

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Hardness

The complexity for 3 to 5 flows remains open.

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Summary

• NP-hard from 6 flows
• special case: 2 flows, every route pair forms a DAG
• optimal schedule for 2 flows, given acyclic pairs
• congestion-free schedule for 3 ≤ k ≤ 5 flows? open

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Summary

• NP-hard from 6 flows
• special case: 2 flows, every route pair forms a DAG
• optimal schedule for 2 flows, given acyclic pairs
• congestion-free schedule for 3 ≤ k ≤ 5 flows? open

26

Thank you!

Backup slides

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10 20 30 40 50 60 2 3 4 5 6 Percentage

The frequency of each possible number of rounds (in %) in optimal schedules from Algorithm 2

20 40 60 80 100 120 140 160 180 200 Dataxchange Airtel Garr199901 Garr199905 Garr200109 Garr200112 Belnet2003 Belnet2004 BtEurope Garr199904 Garr200404 Navigata Sprint Ans Arnes Esnet Garr201104 Garr201107 Geant2001 Internode Peer1 Cesnet201006 Cwix Garr201105 Garr201108 Runtime (per update pair) ISP Topologies (Zoo)

10 20 30 40 50 60 2 3 4 5 6 7 8 9 1011121314

arbitrary feasible schedules from Algorithm 1 Distribution of runtime (in microsecond) over all the problem instances from some of the evaluated graphs

28

S 1 2 3 T Let’s update S first!

Loop-free Rerouting

Dashed: new route Solid: old route

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S 1 2 3 T Let’s update S first!

so far so good!

Then update 3?

Loop-free Rerouting

Dashed: new route Solid: old route

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S 1 2 3 T Then update 3? Not consistent!

Loop-free Rerouting

Dashed: new route Solid: old route

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S 1 2 3 T

Loop-free Rerouting

Dashed: new route Solid: old route

No loop would occur if the union was acyclic.

32

S v w

Let’s update S, first!

rerouting the old route to the new route

T

Dashed: new route Solid: old route

33

S v w

S first, is not consistent!

T

Dead end!

rerouting the old route to the new route Dashed: new route Solid: old route

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S v w

first update W

T

rerouting the old route to the new route Dashed: new route Solid: old route

35

S v w

first update W

T

rerouting the old route to the new route Dashed: new route Solid: old route

36

S v w

first update W

T

then update S

rerouting the old route to the new route Dashed: new route Solid: old route

37

S v w

first update W

T

then update S

rerouting the old route to the new route Dashed: new route Solid: old route

38

S v w

first update W

T

then update S

rerouting the old route to the new route

lastly, update V

Dashed: new route Solid: old route

39

S v w

first update W

T

then update S lastly, update V

rerouting the old route to the new route Dashed: new route Solid: old route

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