Maximizing Restorable Throughput in MPLS Networks

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Maximizing Restorable Throughput in MPLS Networks

• Reuven Cohen
• Dept. of Computer Science, Technion
• Gabi Nakibly
• National EW Research Center

Published in Infocom 2008 mini-conference
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Motivation

• IP networks are required to service real-time
  applications such as phone conversation
• These services demand high availability and
  reliability, and in particular
• Fast restoration
• Guaranteed QoS even in the case of failures
• IP routing protocols are not able to provide
  these features
• MPLS protection mechanisms are able to provide
  these features
• by pre-establishment of backup LSPs
• We study the effectiveness of the various MPLS
  protections schemes

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Outline

• Define the various MPLS protection schemes
• Define our optimization metric
• Define four different problem models
• Present algorithms for the various protections
  mechanisms and models
• Present simulations results for the various
  algorithms

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The protection schemes we study

• A Global Recovery scheme (GR)
• For each LSP we find a path between the same
  (S,D) pair that does not use any link of the LSP
• The backup path can protect against any failure
  along the LSP
• A Local Recovery scheme (LR)
• For each link A-B we find a path that starts at A
  and ends between B and D
• Recovery is faster than GR (because it is
  initiated by the detecting node)
• However, more backup LSPs are needed for the
  protection of each LSP

D
A
B
S
D
A
B
S
a standard MPLS scheme
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The protection schemes we study (cont.)

• A Restricted Local Recovery scheme (RLR)
• The backup path for link A-B is established
  between A and B
• A Facility Local Recovery scheme (FLR)
• Same as RLR, except that the new path serves all
  the LSPs that use the failed link

D
A
B
S
A
B
a standard MPLS scheme
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The protection schemes we study (cont.)

• An extended k-facility Local Recovery scheme
  (EkFLR)
• Same as FLR, except that the number of LSPs
  protected by each backup path is limited to k
• Hence, we can use more backup paths for the
  failed LSPs
• An Unrestricted Recovery scheme (UR)
• The backup path for every link can use any route
  and can protect any number of LSPs

A
B
D
A
B
S
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Our optimization criterion

• Most past research aims at minimizing the total
  bandwidth reserved for the backup LSPs (Spare
  Capacity Allocation).
• Such models consider a network with unbounded
  capacities, and a cost function associated with
  bandwidth usage.
• We believe that network operators struggle with a
  different problem
• They have a network with finite link capacities
  and seek to maximize the traffic that can be
  admitted with protection.
• Our optimization criterion constructing primary
  and backup LSPs while maximizing throughput.

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Our four problem models

• A capacitated directed network
• We make the common single-failure assumption.
• A set of source-destination pairs with associated
  BW demands and profits.

Splittable Unsplittable
Each flow can be split over several primary or backup paths Each flow can be partially satisfied One primary LSP and one backup LSP All or nothing
Primary-restricted Primary Backup
the primary LSPs are given in advance We also need to establish the primary LSPs (joint optimization)
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Our results

• We show that the splittable version of the
  problem is in P and we offer a polynomial time
  algorithm for it.
• We show that the unsplittable version of the
  problem is NP-complete and has no approximation
  algorithm with a ratio better than E½.
• We propose an approximation algorithm with that
  ratio.
• We present efficient heuristics for the various
  recovery schemes.
• We compare the various recovery schemes with
  respect to our throughput maximization criterion.
  
• We show that UR, GR and, LR differ only
  marginally in their performance.
• Since LR has the fastest restoration time of the
  three schemes, it should be the scheme of choice.
• We show that EkFLR with k2 has almost the same
  performance as RLR and should be preferred over
  it.
• Due to its lower administrative overhead (fewer
  backup LSPs).

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Complexity results - summary

1. S-PRFP (Splitable, Primary restricted)
2. U-PRFP (Unsplitable, Primary restricted)
3. S-RFP (Splitable, joint primary/backup
   optimization)
4. U-RFP (Unplitable, joint primary/backup
   optimization)

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The Splittable Primary-restricted Restorable Flow
Problem (S-PRFP)
S-PRFP
primary route is already given

• It is in P for all recovery schemes.
• We showed it using the following linear program
• - the fraction of flow f routed over edge e
  when edge e fails
• - the routed fraction of f
• Maximize the profit

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LP common constraints
S-PRFP

• The following constraints are common to all
  recovery schemes
• (C1) flow conservation
• (C2) capacity constraints
• (C3) a flow is routed on its primary LSP as
  long as there is no failure
• (C4) a flow is not routed over a failed link

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The recovery-specific LP constraints for LR
S-PRFP
D
A
B
S

• This rule ensures that the backup LSP will follow
  the primary LSP all the way from the source to A.
  
• From node A to the destination node, the backup
  LSP is not constrained.

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The recovery-specific LP constraints for RLR
S-PRFP
D
A
B
S

• RLR-1 is similar to LR-1, except that it also
  ensures that the backup LSP will follow the
  primary LSP from B to the destination.

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The recovery-specific LP constraints for UR
S-PRFP
D
A
B
S

• UR-1 ensures that the backup LSP will follow the
  primary LSP unless it fails.
• In case a link on the Primary LSP fails the
  backup LSP is unrestricted.

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The recovery-specific LP constraints for GR
S-PRFP
D
A
B
S

• GR-1 ensures that the backup LSPs must be edge
  disjoint with the primary LSP.
• GR-2 and GR-3 ensures that the backup LSPs are
  identical for every failure.

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The Splittable Restorable Flow Problem (S-RFP)
S-RFP

• Joint primary and backup LSP optimization
• The same linear program but without the primary
  LSP constraint (C-3).
• Can only be applied to RLR scheme.

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Examples for some of the constraints imposed by
the LP for RLR
D
A
B
S

• Each link has a capacity of 10Mb/s, and each LSP
  needs 5Mb/s.
• We have 3 primary LSPs A ? E, F? J and K ? O
• We can backup a possible failure of C-D using
  C-H-I-D
• Then, we can backup a possible failure of M-N
  using M-H-I-N
• The LP needs to understand that there is no
  conflict on H-I because we protect against a
  single failure!

A
B
C
E
D
F
G
H
J
I
K
L
M
O
N
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The Unsplittable Primary-restricted Restorable
Flow Problem (U-PRFP)
U-PRFP

• There are two differences between U-PRFP and
  S-PRFP.
• In U-PRFP, profit can be obtained for a flow only
  when its entire demand is satisfied.
• In U-PRFP, the traffic of each flow can be
  restored using only a single backup LSP.

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The proof for the hardness of the Unsplittable
Primary-restricted Restorable Flow Problem
(U-PRFP)
U-PRFP

• An approximation preserving reduction from the
  Unsplitable Flow Problem (UFP)
• The construction of G
• All primary LSPs must go through (u,v)
• Every pair of solutions in both problems has the
  same value
• UFP does not have an approximation better than
  E½
• The same approximation algorithm is applicable
  also to U-PRFP

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The Splittable Restorable Flow Problem (S-RFP)
S-RFP

• Unlike in S-PRFP, here the primary route is not
  given in advance
• Hence, the problem is at least as computationally
  difficult as S-PRFP
• We use the same linear program but without
  constraint (C-3).
• Because C-3 sticks the primary LSP to a given
  route
• This solves RLR and its related schemes (FLR and
  EkFLR)

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The Splittable Restorable Flow Problem (S-RFP)
(cont.)
S-RFP

• However, for GR, LR, and UR we need to use
  path-indexed variables,
• Namely, variables that indicate for each flow the
  routed bandwidth on every possible path in the
  graph.
• Since the number of such paths is exponential in
  the size of the graph, we dont have a polynomial
  time solution.

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The Unplittable Restorable Flow Problem (U-RFP)
U-RFP

• U-RFP is at least as computationally harder as
  U-PRFP
• Therefore, it is not only NP-complete, but also
  cannot be approximated better than E½
• Like for U-PRFP, we did find an approximation
  with this ratio

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A Practical Heuristics for U-RFP and U-PRFP
U-RFP and U-PRFP

• Heuristic 1
• Solve the LP without the recovery requirement.
• Sort the flows in non-increasing order of wf /df
  (profit/bandwidth)
• Apply randomized rounding to select integral
  flows
• For each selected flow, verify that
• The flow can indeed be routed
• A backup LSP can be found using the specific
  recovery scheme
• If both conditions are satisfied, the flow is
  admitted

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Some simulation results

• We use the BRITE simulator to simulate MPLS
  topologies, according to the Barabasi-Albert
  model
• This model captures two important characteristics
  of the topology
• Incremental growth
• Preferentail connectivity (? power-law degree
  distribution of the MPLS routers)
• We also used actual ISP topologies, taken from
  the RocketFuel project

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The penalty of reliability in the Splittable
Primary-restricted model
optimal algorithm w/ restoration
optimal algorithm w/o restoration

• For each backup scheme we find the ratio
  OPT_S-PRFP/OPT_S-PFP
• For all schemes it is easier to protect when
  load is lower

• As expected, UR is the best
• As expected, LR is better than RLR
• The advantage of GR over LR is interesting

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When the network is smaller

• When the network is smaller, the various schemes
  perform very closely, except that RLR is still
  inferior

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The penalty of unsplittable backup LSPs (for
primary-restricted)

• We see here the penalty ratio for using
  unsplittable backup
• Recall that for splittable routing we have an
  optimal algorithm
• Two different heuristics are used for the
  unsplittable version
• We see that splittable is better by 25 for all
  schemes
• With FLR the penalty is even higher, because FLR
  needs to find high capacity LSPs

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The penalty of unsplittable backup LSPs (for
primary-restricted)

• We see here the penalty ratio for using
  unsplittable backup
• As a function of the load in the network
• Surprisingly, the penalty decreases as the load
  increases.
• Can be explained by the fact that the primary
  LSPs traverse the shortest-paths.

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The benefit of joint optimization (primary
backup)

• As expected, as the load in the network increases
  so does the penalty of using primary LSP set in
  advance.
• The penalty increases for network with higher
  average degree.

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Conclusions

• The first comprehensive study of maximizing
  restorable throughput in MPLS networks
• We considered 4 models of the problem and 6
  restoration schemes
• The splittable versions are in P
• The unsplittable versions are all NP-complete,
  and they cannot be approximated within E ½-?
• LR should be the recovery scheme of choice

D
A
B
S