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Maximizing Restorable Throughput in MPLS Networks

Reuven CohenDept. of Computer Science, TechnionGabi NakiblyNational 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

1. 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

2. 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

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a standard MPLS scheme

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The protection schemes we study (cont.)

3. A Restricted Local Recovery scheme (RLR)

– The backup path for link A-B is established between A and B

4. A Facility Local Recovery scheme (FLR)

– Same as RLR, except that the new path serves all the LSPs that use the failed link

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A B

a standard MPLS scheme

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The protection schemes we study (cont.)

5. 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

6. An Unrestricted Recovery scheme (UR)

– The backup path for every link can use any route and can protect any number of LSPs

A B

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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

1. We show that the splittable version of the problem is in P and we offer a polynomial time algorithm for it.

2. We show that the unsplittable version of the problem is NP-complete and has no approximation algorithm with a ratio better than |E|½.

3. We propose an approximation algorithm with that ratio.4. We present efficient heuristics for the various recovery schemes.5. 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 k=2 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)

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 fMaximize the profit

S-PRFPprimary route is already given

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LP common constraints

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

S-PRFP

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The recovery-specific LP constraints for LR

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.

S-PRFP

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The recovery-specific LP constraints for RLR

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.

S-PRFP

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The recovery-specific LP constraints for UR

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.

S-PRFP

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The recovery-specific LP constraints for GR

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.

S-PRFP

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The Splittable Restorable Flow Problem (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.

S-RFP

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Examples for some of the constraints imposed by the LP for RLR

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 D E

F G H I J

K L M N O

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The Unsplittable Primary-restricted Restorable Flow Problem (U-PRFP)

There are two differences between U-PRFP and S-PRFP. 1. In U-PRFP, profit can be obtained for a flow only when its entire

demand is satisfied. 2. In U-PRFP, the traffic of each flow can be restored using only a

single backup LSP.

U-PRFP

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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 |E|½

– The same approximation algorithm is applicable also to U-PRFP

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

U-PRFP

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The Splittable Restorable Flow Problem (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)

S-RFP

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

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

don’t have a polynomial time solution.

S-RFP

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The Unplittable Restorable Flow Problem (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 |E|½

– Like for U-PRFP, we did find an approximation with this ratio

U-RFP

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A Practical Heuristics for 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:

1. The flow can indeed be routed2. A backup LSP can be found using the specific recovery scheme

– If both conditions are satisfied, the flow is admitted

U-RFP and U-PRFP

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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

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

optimal algorithm w/ restoration

optimal algorithm w/o restoration

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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S DA B LR

RLR

S DA B GR

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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

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