ABPS: An Accurate Backup Path Selecting Approach in ... - IEEE Xplore

2012 IEEE 14th International Conference on High Performance Computing and Communications

ABPS: An Accurate Backup Path Selecting Approach in Overlay Networks Xiaolei Zhou, Deke Guo, Tao Chen, Zhen Shu and Xueshan Luo Science and Technology on Information Systems Engineering Laboratory National University of Defense Technology Email: {zhouxiaolei,dekeguo,chentao,shuzhen,xsluo}@nudt.edu.cn shares some common segments on the physical path with the default one. And if those overlapped path segments fail, the backup path will fail with the default one simultaneously. Unfortunately, the current backup path selecting approaches either based on delay metric merely or AS-level path information, are inadequate to identify a backup path that can detour around the failing path segments. In this paper, we focus on a challenging issue that how to find a proper backup path for any pair of nodes, which can bypass the failures on the sharing path segments. Therefore we employ traceroute probing to acquire IP-level path information of the default paths for all pairs of nodes in a full-mesh overlay network. Meanwhile, this paper utilizes Grid Quorum System, which enable that each node only distribute its probed link state table to a small subset of the nodes in the overlay network, and thus can reduce the communicating overhead as well as balance the traffic loads among the entire network. We propose an accurate backup path selecting approach, which is named as ABPS, to identify an appropriate backup path based on the simultaneous failure probability model. Besides, the selected backup path exhibits low end-to-end delay and less fraction of overlapping with the default path of the node pair. It is revealed that the overlap between the default and backup path is the root cause of simultaneous failure problem in this paper. To the best of our knowledge, ABPS is the first effort to apply traceroute probing with Grid Quorum System together to address the simultaneous problem. Besides, the simultaneous failure probability model proposed in this paper contributes to integrate the two different metrics, delay and overlaps, together. We further evaluate the impacts on the performance of ABPS from the aspects of the simultaneous failure probability, overlapping and communicating overhead of ABPS. In summary, the backup path derived from our ABPS approach is able to detour around failed links with high probability. And the simultaneous failure probability is reduced by about 50 percent, irrespective of the different single point failure probabilities. Especially when the failure probability of single default path rises to 50%, ABPS maintains that probability 25% below. At the same time, the fraction of overlap between the backup path and the default one for any node pair is dramatically reduced. The rest of this paper is organized as follows. Section II summarizes the most related work. Section III demonstrates the existence of the simultaneous failure problems of the

Abstract—Routing overlay offers an ideal methodology to improve the end-to-end communicating performance by providing a backup path for any pair of nodes. The current solutions, however, suffer from the simultaneous failures between the default and the selected backup paths. This paper focuses on a crucial issue of selecting a proper backup path to detour around the failures on the default path with high probability. Experiments were conducted to clarify the influence of overlaps between the default and backup paths, which indicated that the overlaps were the root cause of such simultaneous failures. Therefore, we propose ABPS to select a one-hop backup path with both lower communicating delay and less overlaps with the default path. It employs the traceroute probing to enable each node to acquire IP-level path information of the default paths to the other nodes in a full-mesh overlay network. Meanwhile, with the help of Grid Quorum System, when each node distributes its probing results, there is at least one rendezvous node receives enough information for further discovering a backup path for arbitrary pair of nodes. The evaluation results show that ABPS succeeds in improving the availability of the selected backup paths. And the simultaneous failure probability is reduced by about 50 percent, while the fraction of overlapping between the backup path and the default one is dramatically reduced. Index Terms—Overlay Network; Full-mesh network; Ono-hop Routing; Traceroute; Grid Quorum System

I. I NTRODUCTION Recent works has demonstrated that path diversity is an effective way for improving the end-to-end performance of network applications [1]. This paper focuses on a specific class of distributed applications, which have extremely strict demands on the delay of end-to-end communication. The performance of these applications is sensitive to the state of networks. When the default path between a node pair occurs failure or performance degradation, the end-to-end delay between the pair of communicating nodes will raise dozens of times. And therefore, a one-hop backup path with lower delay will be selected to instead of the default one. Employing the default and backup paths alternatively will provide persistent low-delay communication capability to the large-scale distributed systems. Researchers have already proposed a wide array of solutions [2] [9] [10], to find the optimal one-hop backup path for any pair of nodes in an overlay network. Unfortunately, the current solutions suffer from the simultaneous failure problem, i.e. both the default and backup paths fail at the same time. Our experiment results in Fig.3 indicate taht the path overlapping is the root cause of such failures. The backup path usually 978-0-7695-4749-7/12 $26.00 © 2012 IEEE DOI 10.1109/HPCC.2012.183

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backup path and default path, and reveals that the root cause of such a problem is the overlaps between the default and backup paths. Section IV proposes the ABPS approach that can identify an appropriate one-hop path with both lower end-to-end delay and less fraction of overlapping with the default path, for any pair of nodes . Section V evaluates our approaches. We conclude this work in section VI.

































II. R ELATED W ORK A number of remarkable researches have been proposed in the last decade to address the issue of backup path selecting in overlay networks under various contexts. As the network rapidly scales, the approaches aimed at improving scalability has been proposed to reduce the probing and sending overhead. The conventional approaches, including RON [2] and Tapestry [3], make each node actively monitor all the other nodes and broadcast a full copy of its link state table of 𝑛 − 1 entries, where 𝑛 denotes the network size. As a result, every node in the network is aware of the link state of all the other nodes and hence is able to discover the best backup path for arbitrary pair of nodes. Such approaches generate 𝑂(𝑛2 ) per node probing and communicating overhead, which limits the scalability in deployment. Gummadi et.al. [9] proposes an approach based on correlated failure probability model, which achieves acceptable accuracy when the probability is assumed given as a prior via long-term observation. However, the assumption is not feasible in current large-scale distributed systems. The proposal in [6] employes IP-level path information as well as delay to help selecting the path with maximum disjointness.It is regarded as the first attempt to utilize IP addresses sequence to estimate the overlap between the default and backup paths. However, this approach suffers the extra large overhead and thus is lack of feasibility. Routing Underlay [5] employs the BGP (Border Gateway Protocol) information to discover disjointed AS (Autonomous System) level backup path. Similarly, [7] proposes a heuristic approach, based on an intuitive earliest-divergence rule, to identify an AS-level backup path that diverges with the default one earliest or detours farthermost around the default path. Typically, these approaches based on AS-level information are coarse-grained and thus may not capture the feature of path overlapping. Additionally, [10] firstly introduces Grid Quorum System (as shown in Fig.1) to this issue. It reduces the overhead to √ 𝑂(𝑛1.5 ) when every node exchanges routing states with 𝑂( 𝑛) nodes selected by the quorum system. For every pair of nodes, it ensures that at least one rendezvous node receives the link state tables from both side of the nodes pair, and thus is able to identify the best candidate path from 𝑛 − 2 indirect paths. In summary, neither the delay-based nor the BGP information based approaches are adequate to select an appropriate backup path that can detour around the failure on the default path. It motivates us to combine traceroute probing and Grid Quorum System together to address this issue.

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III. PATH OVERLAPPING P ROBLEM A series of experiments were conducted to investigate the actual simultaneous failure problem in the large-scale distributed systems, based on a 4 days’ (from April.1.2005 to April.4.2005 in a size of about 440 nodes) all-pairs-ping dataset [15] that collects the delay data between all pairs of communicating nodes on the PlanetLab testbed. The result (see Fig.2) shows that, when the direct paths failed, the selected one-hop backup paths with minimum end-to-end delay would fail simultaneously with a probability of 10% around. More seriously, such probability may even rise up to more than 60%, which may make the whole system stuck. Based on a dataset published by the iPlane service [14], further experiments were conducted to find out the root cause of such problem. We derived a dataset of a full-mesh network in scale of 200 nodes in 67 days (from March.1.2011 to May.10,2011, with 4 days absent). In such experiments, delay was taken as the single metric to select a one-hop backup path, and compare the overlaps between the default and backup paths hop by hop. Fig.3(a) indicates that the simultaneous failure probability between the backup path and the default one is about 20% , and may increase to more than 55%. The failure probability jitters frequently, which may make the backup path unavailable. Fig.4(a) indicates the actual overlapping between the default and backup paths. Fig.4(a) shows that the peak emerges at 9 hops overlaps between the default and backup paths, with a probability of 8.01%, while Fig.4(a) plots the cumulative distribution function, which indicates that the probability of overlapping between the default and backup paths will achieve 75.5% at 25 hops. The maximum overlapping length between the default and backup paths even archives 32 hops. Furthermore, we derive the number of backup paths whose failures are caused by the overlapping problem. The result is shown in Fig.3(b). Obviously, the number of the

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Algorithm 1 Achieving a Grid Quorum System Require: √ set of nodes ℚ, node 𝑞𝑚 ∈ ℚ, scale of network 𝑛 1: if 𝑛 ∈ ℕ then 2: for any node √ 𝑞𝑚 ∈ ℚ do 3: 𝑎 ← 𝑛√ 4: 𝑖←𝑚∣ 𝑛√ 5: 𝑗 ← 𝑚 mod 𝑛 6: locate node 𝑞𝑚 at (𝑖, 𝑗) 7: end for 8: else √ √ 9: 𝑎 ← 𝑛 − ⌊ 𝑛⌋ 10: if 𝑎 ≤ 0.5 then 11: for any node 𝑞𝑚 ∈ √ ℚ do 12: 𝑖 ← 𝑚 mod ⌊ √𝑛⌋ 13: 𝑗 ← 𝑚 mod ⌈ 𝑛⌉ 14: end for 15: else 16: for any node 𝑞𝑚 ∈ √ ℚ do 17: 𝑖 ← 𝑚 mod ⌈ √𝑛⌉ 18: 𝑗 ← 𝑚 mod ⌈ 𝑛⌉ 19: end for 20: end if 21: end if

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(b) Number of failing backup paths affected by path overlapping.

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Fig. 3. Simultaneous failure problem between the default and backup paths selected by delay metric based approach.

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(a) Overlapping probability (b) CDF of Overlapping probability Fig. 4. Overlapping probability between the default and backup paths selected by the delay metric based approach.

default paths failure caused by overlapping jitters along with the changing of simultaneous failure. We can see that about that 38.7% of the backup paths each of which overlaps with the related default path will fail on average. Therefore, a definite conclusion can be drawn that the simultaneous failure problem is mainly induced by the overlaps between the default and backup paths. It is critical to propose another metric that could help selecting an appropriate onehop backup path with less overlaps.

nodes in row 1 and column 1 except the node (1, 1), denoted as ℚ1,1 = {(1, 2), (1, 3), (1, 4), (2, 1), (3, 1), (4, 1)}. Similarly, we have ℚ4,4 = {(4, 1), (4, 2), (4, 3), (1, 4), (2, 4), (3, 4)}. Interestingly, we find that the common rendezvous of ℚ1,1 and ℚ4,4 are nodes (1, 4) and (4, 1). Actually, any two Grid Quorums share two rendezvous nodes, since any pair of row and column intersects. With the help of Grid Quorum System, each node √ is required to sent its local link state probing results to 2( 𝑛 − 1) nodes, compared with 𝑛 nodes in approaches without Grid Quorum System.

IV. ACCURATE BACKUP PATH S ELECTING A PPROACH Due to the fundamental limitation, the prior distributed approaches are not widely deployed in real world large-scale distributed systems. We propose ABPS that utilize traceroute probing with Grad Quorum System, to address such an issue.

B. Selection Metric Based on Failure Probability Model

A. Configuration of Grid Quorum System

Selecting an appropriate one-hop backup path for any pair of nodes requires both the low end-to-end delay between the node pair and minimal overlaps between the default and backup paths. However, The lengths of paths between different pairs of nodes range from several hops to more than 30 hops, while the end-to-end delays range from several milliseconds to thousands of milliseconds. Thus we propose the simultaneous failure probability model to integrate the two different factors. 1) Simultaneous Failure Probability Model Suppose that there are 𝑛 nodes in a full-mesh overlay networks. The source and destination node are denoted as 𝑠 and 𝑑 respectively. Node 𝑖 denotes the intermediate node through which to generate a one-hop candidate path. The default path from 𝑠 to 𝐼 is denoted as 𝑃 𝑎𝑡ℎ , while 𝑃 𝑎𝑡ℎ denotes the default path from 𝑖 to 𝑑. Similarly, a one-hop path through the intermediate node 𝑖 is denoted as 𝑃 𝑎𝑡ℎ . The overlapping length is denoted as 𝛾, while the length of 𝑃 𝑎𝑡ℎ and 𝑃 𝑎𝑡ℎ are denoted as 𝛼

Grid Quorum System [10] is an ingenuity that utilize the property that any pair of row and column intersects. In this paper, we adopt such a novel structure to implement the traceroute probing backup path selecting. The definition of Grid Quorum System is described in Definition1. Definition 1. Grid Quorum System Suppose that the scale of network is √ 𝑛, which √ is a perfect square number, and locate n nodes in a 𝑛× 𝑛 square. For each node located at (𝑥𝑖 , 𝑦𝑗 ), Quorum ℚ𝑖,𝑗 consists of all nodes in Row 𝑖 and Column 𝑗 except (𝑥𝑚 , 𝑦𝑛 ),and then ℚ𝑖𝑗 ∩ ℚ𝑚,𝑛 = {(𝑥𝑖 , 𝑦𝑛 ), (𝑥𝑚 , 𝑦𝑗 )}. ℚ𝑖,𝑗 and ℚ𝑚,𝑛 denote two Grid Quorums, the elements in the intersection of ℚ𝑖,𝑗 and ℚ𝑚,𝑛 are named as rendezvous nodes. The algorithm of achieving a Grid Quorum System is shown in Algorithm 1. Here we take the Grid Quorum System scale of 16 in Fig.1 as an example. We first locate 𝑛 = 16 nodes in a 4 × 4 square in any order. In this case, ℚ1,1 will contain all

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and 𝛽 respectively. Let 𝜌 denote the failure probability at a single point on the physical path, which represents the failure of both the network devices and physical links. The simultaneous failure probability model is built upon the following two assumptions: 1) the delay of 𝑃 𝑎𝑡ℎ is equal to that of 𝑃 𝑎𝑡ℎ ; 2) the physical path between arbitrary node pair is symmetrical, i.e., the IP addresses sequence of 𝑃 𝑎𝑡ℎ is in the reverse order of that of 𝑃 𝑎𝑡ℎ . 𝑃 𝑎𝑡ℎ 𝐷𝑒𝑙𝑎𝑦(𝑃 𝑎𝑡ℎ )

= =

𝑃 𝑎𝑡ℎ + 𝑃 𝑎𝑡ℎ 𝑃 𝑎𝑡ℎ + 𝑃 𝑎𝑡ℎ (1)

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(2)

𝑇 𝑟𝑎𝑐𝑒(𝑃 𝑎𝑡ℎ ) 𝑇 𝑟𝑎𝑐𝑒(𝑃 𝑎𝑡ℎ )

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+ 𝑇 𝑟𝑎𝑐𝑒(𝑃 𝑎𝑡ℎ )

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DstID 3 4 5 6 7 Fig. 5.

Delay(ms) 57.39 1134.32 561.48 342.09 94.39

IPTrace 217.149.196.50;217.149.196.51;. . . 145.99.179.145;217.149.196.50;. . . 217.149.196.51;145.145.19.61;. . . 145.99.19.61;145.145.80.65;. . . 216.24.184.85;216.24.186.85;. . .

Sample of the link state table maintained by node 2 locally.

To eliminate the divergence existing in the two different dimensions, we normalize the values of each dimension, i.e., make 𝑑𝑖 , 𝜌𝑖 ∈ [0, 1]. Besides, the value of 𝑚−module is set to be 2−module. The detail of the best one-hop path selecting approach is given by Equation (7).   [ ] 2 2 1/2   ′ (𝑑(0) − 𝑑𝑖 ) + (𝜌(0) − 𝜌𝑖 ) 𝑃 − 𝑃 (0)  = min 1≤𝑖≤𝑛−2

(7)

C. 3-Phases Accurate Backup path selecting

Let an event 𝐴 denote that the default path occurs a failure, while an event 𝐵 denotes that the backup path occurs a failure. The simultaneous failure probability of the default and backup paths is denoted as 𝑃 (𝐵∣𝐴), which is given by Equation (4).

With the employing of Grid Quorum System and simultaneous failure probability model, we propose 3-phases ABPS approach. Phase 1: Probing For a given consisting of 𝑛 nodes, a Grid Quorum √ √ network System of 𝑛 × 𝑛 is achieved. Any node located at (𝑥𝑖 , 𝑦𝑗 ) actively probes the other n-1 nodes in the network with traceroute probing periodically. When the messages return, the node maintains a link state table locally. There are three fields in the link state table, including DstID, Delay and IPTrace. The DstID field records the IDs of the destinations, while the Delay field records the delays along the default path. Besides, the IPTrace field records the IP addresses sequence. A sample of the link state table maintained by node 2 is shown in Fig.7. Phase 2: Distribution Any node (𝑥𝑖 , 𝑦𝑗 ) sends its local link state table to all the nodes in ℚ𝑖,𝑗 . When a node received link state tables from different nodes, it has a partial view of the global link state and thus is able to identify an appropriate one-hop path, which can detour around the failure in the default path with high probability, for a given number of the node pairs in the network. Therefore, all of the nodes in ℚ𝑖,𝑗 are aware of the link state of node (𝑥𝑖 , 𝑦𝑗 ). In a global scope, any node (𝑥𝑖 , 𝑦𝑗 ) is able to recommend an appropriate one-hop path for nodes in ℚ𝑖,𝑗 . Phase 3: Recommendation Here we assume that the node at (𝑥𝑖 , 𝑦𝑛 ) is preferred while the other one acts as a redundant. Node (𝑥𝑖 , 𝑦𝑛 ) will select an appropriate backup path according to the metrics based on the simultaneous failure probability model, and send recommendation messages to the nodes in Grid Quorum ℚ𝑖,𝑗 . An illustrative example is presented in Fig.1. In Phase 1, node 2 sends traceroute probing message to all of the other 15 nodes in the network every 15 minutes. When node 2 receives the returned messages, it will immediately add a new entry to the link state table maintained locally. If the entry already exists, it will update the current entry. In Phase 2, node 2 sends its link state table to all the nodes in Grid Quorum ℚ1,2 = (1, 1), (1, 3), (1, 4), (2, 2), (2, 3), (2, 4). Finally, node

1 + (1 − 𝜌)𝛼−𝛾 − (1 − 𝜌)(𝛼+𝛽)𝛽 − (1 − 𝜌)(𝛼+𝛽)𝛼 1 − (1 − 𝜌)(𝛼+𝛽)𝛼 (4) Additionally, Equation (4) suggests that when the overlapping 𝛾 grows larger, 𝑃 (𝐵∣𝐴) will increase much higher. It demonstrates that the conclusion that overlapping between the default and backup path is the root cause of simultaneous failures, as we have inferred in section III. 2) Selection Metric of ABPS First a two-dimensions reference frame of the delay between arbitrary node pair and the simultaneous failure probability between the default and paths is constructed. Then, we plot the value of a vector in the reference frame, which represents all possible paths between any pair of nodes. An ideal point is a point with the minimum values of both the delay between arbitrary node pair and simultaneous failure probability of the default and backup paths. Actually, the ideal point never really exists. However, we can still compute the module between existing points and the ideal point, and then identify the point with the minimum module. Assume that the candidate path 𝑃𝑖 𝑇 is denoted as a vector, and 𝑃𝑖 = {𝑑𝑖 , 𝜌𝑖 } , where 𝑑𝑖 denotes the delay of 𝑃𝑖 while 𝜌𝑖 denotes the length of the overlapping between a pair of nodes. The ideal point is denoted as 𝑃 (0) . And the module between any two different point is denoted as ∥𝑃𝑖 − 𝑃 (0) ∥. The selected path between any node pair 𝑃 ′ ought to satisfy Equation (5).         ′ (5) 𝑃 − 𝑃 (0)  ← min 𝑃𝑖 − 𝑃 (0) 

𝑃 (𝐵∣𝐴) =

1≤𝑖≤𝑛−2

For different module definitions, the meanings of ideal point are different as well. Here we employ 𝑚-module in ABPS as shown in Equation (6).  [  ] 𝑚 𝑚 1/𝑚   ′ (6) 𝑃 − 𝑃 (0)  = (𝑑(0) − 𝑑𝑖 ) + (𝜌(0) − 𝜌𝑖 )

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5 receives the link state tables form both node 2 and 8, and hence can identify an appropriate one-hop path for the pair of nodes. Node 6 sends a recommendation message back to node 2 and 8. Besides, in a global scope, node 6 sends one-hop path recommendation messages to all nodes in ℚ2,2 = (1, 2), (3, 2), (4, 2), (2, 1), (2, 3), (2, 4). And thus all of the node pairs in this network get an appropriate one-hop backup path recommendation. When the default path fails, the nodes pair is able to communicate along the backup one, in order to detour around the failure with high probability. The average path length of end-to-end paths in the collected iPlane dataset is 15.76. Thus we assume that the path length is 16 to estimate the communicating overhead in ABPS, which is given by Theorem 1.The pernode communicating overhead is bound by 𝑂(𝑛1.5 ) in Theorem 1.

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Theorem 1. Identifying the best √ √ one-hop backup path in ABPS makes every√node incur 𝑛+4 𝑛−3 messages and 160𝑛 𝑛− 152𝑛 − 144 𝑛 + 136 bytes in total.

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Proof: First of all, in phase 1, ABPS requires that node (𝑥𝑖 , 𝑦𝑗 ) probing its link state to all the other 𝑛−1 nodes in the network. Such a process generates 𝑛 − 1 messages of 8𝑛 − 8 bytes in total. As a result, a link state table of size 80(𝑛 − 1) bytes for every node is formed to distribute to the other nodes. Furthermore, node at (𝑥𝑖 , 𝑦𝑗 ) sends its link state √ table all nodes in ℚ𝑖,𝑗 in the phase√2, which results in 2( 𝑛 − 1) messages of size 160(𝑛 − 1)( 𝑛 − 1) bytes in total. Finally, in phase 3, node 𝑞𝑖 sends the routing recommendation √ messages back to all the nodes √ in ℚ𝑖,𝑗 , hence causing 2( 𝑛 − 1) messages of total size 16( 𝑛 − 1) bytes.

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(a) Overlapping probability (b) CDF of Overlapping probability Fig. 7. Overlapping probability between default and backup paths selected by ABPS.

by the delay-based approach, rapidly jitter in large range with a average value of about 25.4%, while that failure probabilities of the backup paths selected by ABPS are reduced by about 50% on average and remaining steady. Especially, the failure probability of the backup path selected by the delay-based approach frequently rise up to more than 50%, while that probabilities of the backup path selected by ABPS remain below 20%. Despite the slight jitters, the failure probabilities are much more steady than that of the delay-based approach. The value of parameter 𝜌 is set to be 0.05 under low-level single point failure mode. Fig.6(b) indicates that the failure probabilities of the backup paths selected by ABPS are 17.6% on average, ranging from 2.97% to 24.23%, which are beyond 2 times better than the backup paths selected by the delaybased approaches. In summary, the evaluation results show that ABPS is able to select an appropriate one-hop backup path that can detour around the failure in the overlapping segments between the default and backup paths with a higher probability. Consequently, the availability of the selected backup path is improved by ABPS.

V. E VALUATION A threefold trace-driven evaluation of ABPS was conducted based on a 67 days’ full-mesh dataset of traceroute probing derived from the iPlane service [14]. The approaches in [2] and [10] are chosen as comparison. Typically, both of the above approaches select a one-hop backup path by the delay metric solely, denoted as delay based approaches for short. To evaluate our ABPS approach thoroughly, we implement a threefold trace-driven evaluation. A. Simultaneous Failure Probability The main objective of ABPS is to improve the availability of the selected one-hop backup path. The simultaneous failure probability is taken as a counter criterion of availability. The simultaneous failure probabilities of ABPS with different values of parameter 𝜌 were evaluated. The results are presented in Fig. 6, comparing with the backup path selected by the delay-based approaches. 1) High-level single point failure mode: Under some certain conditions, the failure probability at a single point in the physical path will be quite high. We set the parameter 𝜌 to be 0.05 to evaluate the simultaneous failure probability of the backup path selected by ABPS, under the high-level single point failure mode. As shown in Fig.6(a), the simultaneous failure probabilities of the backup paths, which are selected

B. Overlapping The overlapping between the default and backup paths is measured to validate the performance of ABPS. The evaluation results are presented in Fig.7. As is clear from Fig.7, the overlapping problem gets well addressed in ABPS. The peak of the overlapping between the default and backup paths in ABPS emerges at 4 hops with a probability of 13.74%, compared with 9 hops with a probability of 8.01% in the delay-based approaches. It is noteworthy that the maximum length of overlapping between these two paths in ABPS is 11, where is nearly the peak of the overlapping in the delay-

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of overlap between the backup path and the default one for any node pair is dramatically reduced. Additionally, we have demonstrated that our backup path selecting method incurs less communication cost of 𝑂(𝑛1.5 ) due to the use of the Grid Quorum System. Following this paper, we intend to extend our current work to further address the issue of path overlapping in the future. First of all, We plan to reduce the overhead with some IP address compression techniques, such as Bloom Filter [13] and Trie [11], in order to achieve the better scalability. Moreover, A IP-level path is assumed to be symmetrical in order to simplify the problem, which is not the true in practice. Therefore, we will propose another backup path selecting approach with the reverse traceroute [12] in our future works. Furthermore, we will extend the Grid Quorum System to higher dimensions to acquire more desirable properties to improve the scalability of ABPS deployment in large-scale distributed systems.

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Fig. 8. Overhead Comparison among ABPS, Scaling Routing Overlay and delay metric based approaches.

based approaches. ABPS reduces the overlapping between the default and backup path by about 50%. The cumulative distribution function of overlapping probability (see Fig.7(b)) denotes that the backup paths selected by ABPS overlapped with the default paths with a probability of 70.88%, while a probability of 75.52% in the delaybased approaches. Therefore, ABPS succeeds in selecting an appropriate one-hop backup path with less overlaps with the default path.

VII. ACKNOWLEDGEMENT This work is supported in part by the NSF China under Grant Nos. 61170284, 60903206, the China Postdoctoral Science Foundation under Grant Nos. 20100480898, 201104439, and the Research Foundation of National University of Defense Technology under Grant No. JC10-05-01.

C. Communication Overhead The per-node communication overhead required in our approaches is simulated and compared with both the approaches of delay-based [2] and Scaling Overlay Routing [10], which is the current best delay-based approach before our proposals. ABPS employs traceroute while the other two approaches only select the backup path by the delay metric merely. As is clear from Fig.8 that our approach indeed dramatically reduces the per-node communication overhead than the delay-based approach, irrespective the size of the network. ABPS incurs some larger communication overhead than the Scaling Overlay Routing approach. However, the overhead produced by ABPS is bound by 𝑂(𝑛1.5 ), as we have proved in Theorem 1. Additionally, the size of link state tables is considered as the root cause of extra communication overhead when employing ABPS. Each IP address contributes 4 bytes to the link state tables. We intend to reduce the communication overhead with some effective IP address compression techniques in our future works. VI. C ONCLUSION

R EFERENCES [1] Jianxin Liao, Jingyu Wanga, Tonghong Li, Xiaomin Zhu, Introducing multipath selection for concurrent multipath transfer in the future internet, Computer Networks, 55(2011) 1024-1035. [2] D. G. Andersen, H. Balakrishnan, M. F. Kaashoek, and R. Morris, Resilient overlay networks,In: Proc. ACM SOSP, 2001. [3] Zhao B.Y., Ling Huang, Stribling, J., Rhea S.C., Joseph A.D. and Kubiatowicz, J.D., Tapestry: a resilient global-scale overlay for service deployment, IEEE Journal on Selected Areas in Communications, vol.22, no.1, pp. 41- 53, Jan., 2004. [4] B. Zhao, L. Huang, J. Stribling, A. Joseph, and J. Kubiatowicz, Exploiting routing redundancy via structured peer-to-peer overlays, In: Proc. IEEE ICNP, 2003. [5] A. Nakao, L. Peterson, and A. Bavier, A routing underlay for overlay networks, In Proc. ACM SIGCOMM, 2003. [6] M. Zhang, J. Lai, A. Krishnamurthy, L. Peterson, and R. Wang, A transport layer approach for improving end-to-end performance and robustness using redundant paths, In: Proc. of USENIX NSDI, 2004. [7] T. Fei, S. Tao, L. Gao, and R. Guerin, How to select a good alternate path in large peer-to-peer systems. In: Proc. of IEEE INFOCOM, Barcelona, Spain, Mar.2006. [8] W. Cui, I. Stoica, and R. H. Katz, Backup path allocation based on a correlated link simultaneous failure probability model in overlay networks, In: IProc. of IEEE ICNP, Paris, France, Nov. 2002. [9] K. P. Gummadi, H. V. Madhyastha, S. D. Gribble, H. M. Levy, and D. Wetherall, Improving the reliability of Internet paths with one-hop source routing, In: Proc. USENIX OSDI, San Francisco, CA, Dec.2004. [10] David Sontag, Yang Zhang, Amar Phanishayee, David G. Andersen and David Karger, Scaling All-Pairs Overlay Routing, In: Proc. ACM CoNEXT, 2009. [11] Masanori Bando and H. Jonathan Chao, FlashTrie: Hash-based PrefixCompressed Trie for IP Route Lookup Beyond 100Gbps, In: Proc. IEEE INFOCOM, 2010. [12] E. Katz-Bassett, H. V. Madhyastha, V. K. Adhikari, C. Scott, J. Sherry, P. van Wesep, T. Anderson, A. Krishnamurthy, Reverse Traceroute In: Proc. USENIX NSDI, 2010 [13] Benoit Donnet, Bamba Gueye and Mohamed Ali Kaafar, Path similarity evaluation using Bloom filters, Computer Networks, 56 (2) (2012) 858869. [14] Datasets of iPlane. [Online]. Available: http://iplane.cs.washington.edu [15] All-pairs-pings. [Online]. Available: http://pdos.csail.mit.edu/˜strib/

Routing resilience is becoming an important issue for largescale distributed systems. Experimental results have shown that path failures in large-scale network are huge, which seriously hinder both the reliability and user experience of the distributed applications. The current solutions, however, suffer from the simultaneous failures of the default and backup paths between any node pair. In this paper, we focus on an essential issue of selecting a proper backup path that is able to detour around the failures at a default path with high probability. To address such an issue, this paper proposes an accurate backup path selecting approach. More precisely, we propose a threephases approach that integrate the delay and IP addresses sequence between a node pair. ABPS employs traceroute probing with Grid Quorum System. The trace-driven evaluation results show that ABPS succeeds in detouring around the failures with high probability, while the simultaneous failure probability is reduced by about 50 percent. At the same time, the fraction

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