1 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

2 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

3 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

4 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 S DAB S DAB a standard MPLS scheme

5 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 S DAB AB a standard MPLS scheme

6 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 AB S DAB

7 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.

8 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. SplittableUnsplittable  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-restrictedPrimary + Backup the primary LSPs are given in advance We also need to establish the primary LSPs (joint optimization)

9 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).

10 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)

11 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 f Maximize the profit S-PRFP primary route is already given

12 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

13 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 S DAB

14 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 S DAB

15 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 S DAB

16 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 S DAB

17 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

18 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! ABC D E FGH I J KLM N O S DAB

19 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

20 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

21 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

22 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

23 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

24 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 w f /d f (profit/bandwidth) – Apply randomized rounding to select integral flows – For each selected flow, verify that: 1. The flow can indeed be routed 2. 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

25 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

26 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 S DAB S DAB LR RLR S DAB GR

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

28 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

29 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.

30 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.

31 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 S DAB