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A Novel Method for Survivability Test Based on End Nodes in Large Scale Network
A Novel Method for Survivability Test Based on End Nodes in Large Scale Network
KSII Transactions on Internet and Information Systems (TIIS). 2015. Feb, 9(2): 620-636
Copyright © 2015, Korean Society For Internet Information
  • Received : January 23, 2014
  • Accepted : December 13, 2014
  • Published : February 28, 2015
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Ming Liang
Zhao Gang
Wang Dongxia
Huang Minhuan
Li Xiang
Miao Qing
Xu Fei

Abstract
Survivability is a necessary property of network system in disturbed environment. Recovery ability is a key actor of survivability. This paper concludes network survivability into a novel composite metric, i.e. Network Recovery Degree (NRD) . In order to measure this metric in quantity, a concept of Source-Destination Pair (SD Pair) , is created to abstract end-to-end activity based on end nodes in network, and the quality of SD Pair is also used to describe network performance, such as connectivity, quality of service, link degree, and so on. After that, a Survivability Test method in large scale Network based on SD pairs, called STNSD , is provided. How to select SD Pairs effectively in large scale network is also provided. We set up simulation environment to validate the test method in a severe destroy scenario and evaluate the method scalability in different large scale network scenarios. Experiment and analysis shows that the metric NRD correctly reflects the effort of different survivability strategy, and the proposed test method STNSD has good scalability and can be used to test and evaluate quantitative survivability in large scale network.
Keywords
1. Introduction
S urvivability is a research hotspot in network area during recent twenty years, but how to measure network survivability accurately and quantitatively is still a challenge, especially in a large scale network. The generally accepted definition of network system survivability was proposed by Ellison et al. [1] . Survivability is the capability of a system to fulfill its mission, in a timely manner, in the presence of attacks, failures, or accidents. The goal of network survivability is to maintain the fundamental network system services in the face of faults/failures and to support the fulfillment of organization missions. As for this definition, survivability is not mathematically well defined since this concept does not directly refer to a measurable sense. In order to solve this problem, this paper research to provide a novel metric and a test method for measuring network survivability in quantity, which help network survivability evaluation more accurately, experiment result shows the metric is valid and the method can work well in large scale network.
The rest of this paper is organized as follows: Section 2 reviews previous work on the network survivability test methods and metric. Section 3 analyzes the fundamental attributes of network survivability and the network survivability lifecycle, which is a general survivable process when a network suffering disturbances. Section 4 provides a novel quantifiable metric of network survivability, i.e. Network Recovery Degree (NRD) . Section 5 presents a method called STNSD to test the metric NRD , and section 6 makes an experiment and analysis to validate the proposed method STNSD . Finally section 7 presents conclusions and future work.
2. Related Work
Existing survivability test methods including survivability indexes for network system can be classified into two categories by different research ideas: effect-based survivability test methods [5] [7] [8] and scheme-based survivability test methods [9] [10] [11] .
The idea of effect-based survivability test methods is analysing survivability definition of network system, abstracting key effect and characteristic of survivability for some requirements, and then providing survivability indexes, metrics and test method. These researchers think that survivability could be measured and evaluated using its quantitative attributes, especially the availability and fault-tolerance attributes which can be statistically modeled using the metrics of failure rate [2] , repair rate [3] , fault-coverage [4] [5] , and so on. Therefore survivability test is usually replaced by measuring its fundamental attributes which comes from survivability definition and effect. Under this methodology, Carmichael [5] analysed two kinds of typical Layer-2 Ethernet protocols available for increasing the survivability of a network on live networks and via simulation, and gave some survivability index in Layer-2, including forward delay, packet latency, Hello Time, Maxi age of packet, and so on. These works are made effectively on a small network with serval links in the experiment, but they are hard to work well in large scale network. Zuo [7] regarded survivability characteristic as adaptability, recoverability, fault tolerance, reliability, and performance degrading. And he has also listed 15 kinds of representative survivability primitives for these five characteristics, but he did not present quantifiable test method for these characteristics. Wang etc. [8] defined three quantifiable metrics: network robustness, cumulative failure probability and performance benefit to evaluate capacity allocation strategy for network survivability in the condition of limited redundant resources, and also gave corresponding calculation methods, but these methods only fit for survivability measurement of the largest connected component of network after failures, and does not fit for testing the whole network survivability obviously.
The idea of scheme-based survivability test methods is developing and measuring survivability index by means of analysing survivability policies or schemes. Zhang [9] proposes a new network survivability paradigm, called heterogeneous networking, for improving a network’s defence capabilities. So they develop a quantifiable survivability metric, called diversity distance, to capture the extent of required redundancy and reduce the likelihood of network elements for each level of functional capability. Wang [10] views that the key policy of survivability is the dynamic reconfiguration. So many metrics, such as available battery power, varying communication bandwidth, available memory or faults in software components, should be considered in order to preserve desired application level quality of service, so he proposes corresponding methods for these metrics. Sasitharan [11] focuses on researching self-governance, such as self-organization, self-management, to support network survivability, and uses average link gradients and average node load as network survivability index, and propose bio-inspired mechanisms to support network survivability that is integrated with policy based management. All these methods above focuse on measuring survivability characters for some survivability schemes, such as diversity distance for the method in [9] , available battery power for the method in [10] , average node load for the method in [11] , which are all not universal test methods in a general sense for different survivability mechnisms.
In a word, contrast with the survivability definition [1] , the survivability metrics and test methods above are limited in network scale, or only measure some phrase(s) or aspect(s) of network survivability. So how to measure network survivability quantitatively in the whole and make a test method independent of mechnisms is still a challenge.
3. Network Survivability Lifecycle
In this section, we will analize the attributes of network survivability in detail, and make a theory preparation for proposing novel network survivability metric NRD.
Survivability is an important dynamic system attribute, and network survivable process can pass through five phases, which are normal phase, resistance phase, destroyed phase, recovery phase, and adaptation and evolution phase [12] . We call this five-phase process as a network survivability lifecycle. In the network survivability lifecycle, normal phase is a healthy and undestroyed stage; resistance phase is a degradation stage of network performance after attacks, failures, or accidents; destroyed phase is a bottom stage in which network performance lies at the lowest level; recovery phase is a rising stage of network performance since survivability mechanism runs; adaptation and evolution phase is a self-adaptation stage of network with the implementation of adaptation policies. When a disturbance is coming, the survivable process of network is shown in Fig. 1 , where horizontal coordinate is time t , and vertical coordinate is network performance V ( t ), and V 0 is the normal performance, and Vr is the required performance threshold of network system, and Ve is emergency performance threshold of network system. From Fig. 1 , network is in normal phase initially, and V ( t ) is at a high level. When network is disturbed in resistance phase, V ( t ) degrades in evidence. With the further degradation of V ( t ), network goes into destroyed phase and V ( t ) reaches the lowest value (i.e. bottom level). Then, V ( t ) rises gradually and network goes into recovery phase since survivability mechanism works. When self-adaptation policies work, network comes into evolution phase, during which the performance of network will become much better.
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Performance curve in a survivability lifecycle
In a survivability lifecycle, the recovery time of network performance from phase 2 to 4 is a key index of network survivability, so we can grasp each phase by measuring the wave of network performance, and then get quantifiable survivability of a network by calculating the recovery time or analogous index in this survivable process.
4. Network Survivability Metric Based on SD Pair
Network survivability metric is the basic of the test and evaluation of network survivability. This section will set up two notions, SD Pair and SD Quality , to analyze the wave of network performance during a network survivability lifecycle, and then proposes a novel quantifiable metric of network survivability, i.e. NRD , based on SD Pair .
- 4.1 Analysis on Network Performance
According to the discussion in section 3, by means of analyzing the variety index of network performance, we can measure the survivability of network system in quantity. From our survey, methods that attempt to quantitatively analyze the survivability can be classified into two categories: connectivity or performance [13] - [15] .
The analysis of network connectivity is based on two factors: the Node Connectivity Factor (NCF) and the Link Connectivity Factor (LCF). The former deals with the removal of nodes, while the latter is concerned with the removal of links. Several methodologies can be used to analyze the connectivity of networks, among which linear/non-linear programming and simulation with given metrics are the most popular [13] .
In general, network performance is analyzed by calculating the capability that the network will fulfill its given QoS metrics. Because of the variety of network performance metrics, many diverse methodologies, such as Markov chain, game theory and simulation with given metrics, can be used for analysis [14] .
We can easily find out that two kinds of analysis methods on network performance above are both concerned with the end-to-end activity in the network. In fact, the end-to-end activity is primary task of computer network and is also the most concern of users [15] . Users always rather care the ability of end-to-end activity than that in the midway. So it is an effective way to measure the performance of a large scale network system by means of analyzing the ability of end-to-end activity.
- 4.2 SD Pair and SD Quality
There are a lot of end-to-end activities in network system, such as a community between two nodes, a request between user and server or a web request between two web services, and so on. In order to describe these end-to-end activities and its capability, some concepts are defined as follows.
DEFINITION 1. Source-Destination Pair , for short SD Pair , is an abstraction of end-to-end activity of network system, denoted as r = { s,d } , r R,s,d V , where s and d denote the requester side and the target side in the end-to-end activity respectively, and R is the set of SD Pairs , and V is the set of nodes in the network.
According to the discussion in section 4.1, we categorized the SD Pairs to into two subcategories: the Connectivity-type SD Pair and the Service-type SD Pair . The Connectivity-type SD Pair is those SD Pair whose function focuses on network connectivity, and the Service-type SD Pair is those SD Pair whose function focuses on network application.
DEFINITION 2. SD Quality , denoted as pr , is the degree to which end-to-end performance of SD Pair r fulfils connectivity or service requirement. SD Quality shows the capability of end-to-end activity of SD Pair .
By means of the two concepts SD Pair and SD Quality , we can make formal description for some general index of network performance, such as link degree, bandwidth, quality of service (QoS), and so on. In the Connectivity-type SD Pair, S and D denote two ends of the communication path separately, and SD Quality denotes the communication quality, such as bandwidth, delay, and so on. While in the Service-type SD Pair, S and D denotes the service requester and responder separately, and SD Quality denotes the service providing quality, such as service response time. In order to accurately describe the communication quality and service response quality, we further make another two definitions about SD Quality : the Connectivity-type SD Pair and the Service-type SD Pair , and give corresponding calculation method for each.
DEFINITION 3. Connectivity-type SD Quality, pr , is the degree to which end-to-end performance of r fulfils connectivity requirement, and can be calculated by Formula (1):
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In Formula (1), RTTreal denotes the measured RTT (Round-Trip Time) in the Connectivity-type SD Pair , and RTTreqr denotes the required RTT in the Connectivity-type SD Pair .
DEFINITION 4. Service-type SD Quality, pr , is the degree to which end-to-end performance of r fulfils service requirement, and can be calculated by Formula (2):
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In Formula (2), RSTreal denotes measured service response time in the Service-type SD Pair , and RSTreqr denotes the required service response time in the Service-type SD Pair .
In general, considering survivability measurement only for network communication system, Connectivity-type SD Quality is enough; while considering survivability measurement for network application system, Service-type SD Quality is much more suitable. With the definitions above, we can get a formal description of the network performance in the whole. Given a network, any end-to-end function can be denoted as r , and its performance can be denoted as pr , then all the end-to-end function in the network can be denoted as R = { r 1 , r 2 , ..., rN }, where N is the total number of the end-to-end functions, and all the end-to-end performance in the network can be denoted as PR = { P 1 , P 2 , ..., PN }. If we only consider the end-to-end performance in a large scale network, we can accurately analyze network performance and then measure network survivability by calculating PR .
- 4.3 Network Survivability Metric Based on SD Pair
SD Quality denotes the end-to-end performance in the network, so, as discussion in section 3, SD Quality will wave in a survivability lifecycle. Now we will make another two definitions to further describe this survivable process, and then propose a composite metric, NRD , to measure network survivability in quantity.
DEFINITION 5. SD Recovery Rate , ηr , is the rate at which SD Quality is recovered. It can be calculated by Formula (3):
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In Formula (3), p recovery denotes the SD Quality in recovery phase of survivable network, and p normal denotes the SD Quality in normal phase of survivable network.
DEFINITION 6. SD Recovery Time , tr , is the time from being destroyed to that 80% SD Recovery Rate is reached, which is calculated by Formula (4):
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In Formula (4), 80% is a reference value that can be adjusted as necessary.
DEFINITION 7. Network Recovery Degree (NRD) . Given a network, each SD Pair r , r ∈ R , has a SD Recovery Time tr , then the NRD of the network can be calculated by Formula (5):
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In Formula (5), ωr is the weight of SD Pair r , which reflects the importance of r and can be got by experience, and tr is the recovery time of SD Pair r , and R is the set of SD Pairs . In fact, NRD is a composite metric, which reflects how much performance of the whole network can be recovered from destroyed state in a unit of time, so the more NRD is, the better network survivability is.
5. Survivability Test Method in the Large Scale Network Based on SD Pairs
- 5.1 Test Idea
The Survivability Test method in the large scale Network based on SD pairs , called STNSD , firstly abstracts the network function with SD Pair , and describes connectivity and service performance with SD Quality . Then considering different failure scenes in a large scale network, we will make different test cases and use an active measurement tool to keep monitoring the RTT (Round-Trip Time) of each SD Pair , and then calculate SD Recovery Rate and SD Recovery Time . Finally, by using Formula (5), we can calculate the NRD and get quantifiable survivability of the network.
- 5.2 Test Steps
Under the test idea, we have detailed test steps of the method STNSD below.
Step 1: Construct failures. For connectivity-type SD Pair , the failure situation focuses on communication link or node whose effect is disconnection or link congestion. For Service-type SD Pair , the failure situation focuses on quality of service whose effect is Deny of Service or Congestion of Service.
Step 2: Select SD Pairs for survivability test, in which SD Pairs should pass though the affected area including compromised nodes, links and services. Sometimes key nodes, links, and services in the network also should be selected into SD Pair set. The selection of SD Pair is described in section 5.3 in detailed.
Step 3: Measure SD Quality of each SD Pair by Formula (1) or Formula (2).
Step 4: Measure SD Recovery Rate and SD Recovery Time for each SD Pair by Formula (3) and Formula (4), and then calculate the NRD of the whole network by using Formula (5), and network survivability is got in quantity.
- 5.3 Selection of SD Pair Set
The SD Pairs set can be selected according to the type of failure: for service failure, The SD Pair between the compromised server and a user node should be considered; for link failure, node failure, protocol error, etc., the SD Pairs should be selected by an effective and general approach for different failure positions and types in the network. The idea of selection of SD Pair set is selecting a part of SD Pairs to get the response of all the SD pairs based on end node so as to watch the performance of network inside as full as possible. By this means, we need not consider positions and number of destroyed area in the network, because all the failures which can affect end-to-end performance based on end nodes can be found by such optimal SD Pairs . This work can be translated to resolve a set cover problem, which is a NP-complete problem of Karp [16] . In this section, we propose an Optimal SD Selection (OSDS) algorithm based on end nodes for selecting SD Pair set in large scale network.
In order to describe this algorithm, we should define a Cover-Degree Function f (R). The Cover-Degree Function reflects the degree with which the set R covers the network links. For each SD Pair set R , there exists:
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In which, the r is a SD Pair in R , and r = { s,d } where s and d are both end nodes. As a SD Pair cross through an end-to-end path, to simplify it we also define r = {s,d} = {(s,x),...,(y,d)} , where x,…,y are the nodes crossed through by SD Pair r , and (s,x),...,(y,d) are a group of links in SD Pair path. L is network link set, and |L| is the total number of network links.
Given a set of end nodes V end in a network, the OSDS algorithm has four steps.
Step1: initialize SD Pair set R with empty, and set precision parameter M and balance parameter N . Generally let M = | V end | / 5 and N=10 by experience.
Step2: for each node s in V end , select other N nodes, d 1 , d 2 , .., di ,..., d N V' and s ≠ d i from V end , and make up of N candidate SD Pair of node s : r 1 = { s,d 1 }, r 2 = { s,d 2 },..., rN = { s,dN }. Add each candidate SD Pair , r 1 , r 2 , …, rN , to SD Pair set R respectively, and calculate the new Cover-Degree Function f (R).
Step3: for end node s , select the SD Pair r max which makes f (R) be the largest one in the candidate SD Pairs of node s , and then add r max to the SD Pair set R . If all the N candidate SD Pairs of node s cannot enlarge f (R), then we regard node s as an invalid node, and compute the number of continuous invalid nodes.
Step4: When the number of continuous invalid nodes is below M , repeat Step2 and Step3, otherwise finish the algorithm. When algorithm is finished, R is the optimal SD Pair set that we required.
The OSDS algorithm is shown in Algorithm 1 .
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In OSDS algorithm above, the precision parameter M is used to adjust the precision of the algorithm. The larger M results in larger cover degree of SD Pair set. But meanwhile, the computation complexity of OSDS algorithm is enlarged evidently. The balance parameter N is used to adjust the size of SD Pair set and computing speed of algorithm. The more N, OSDS algorithm has larger probability to find new valid SD Pairs . On the other side, computation complexity is also enlarged evidently. But the computation complexity of OSDS algorithm is no more than O(M*N*| V end |). Experience shows that we can obtain acceptable calculation precision and speed, when N = 10 and M = | V end | / 5, where | V end | is the total number of end nodes of network.
The SD Pairs above fall into different types: the SD Pair on server failure is Service-type SD Pair , and the SD Pair selected by OSDS algorithm are all Connectivity-type SD Pair . So these SD Pairs should use different formulas to calculate SD Quality in the test step 3 in section 5.2.
- 5.4 Weight of SD Pair
For the Service-type SD , the weight is assigned by experience, and the more important the path of SD Pair is and the larger weight is. For Connectivity-type SD , its weight is decided by its largest link bandwidth in the SD Pair path, the higher the link bandwidth of SD Pair is and the larger weight is. Formula (7) is given for calculate the weight, ωi of No. i SD Pair .
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In Formula (7), Wi is the largest link bandwidth (Mb/s) in No. i SD Pair , and n is the total number of SD Pairs .
6. Experiment and Analysis
The test experiment aims: (i) to assess the STNSD method’s ability including OSDS algorithm for selecting SD Pairs ; (ii) to validate the STNSD method to calculate quantifiable survivability in large scale network; (iii) compare the performance gain of the STNSD method facing different survivability strategy. For this purpose, a use case of the STNSD is given, and the scalability analysis of the STNSD method is also given.
- 6.1 Experiment Scenarios
To demo the test process of the STNSD method, we set up a network with 66 routers (Scenario 1) labeled by from n0 to n65 and simulated by CORE v4.3 [17] tools. Another five scenarios are also set up to analyze the scalability of the STNSD method in large scale network. Although the Scenario 1 is not large enough, it embraces the network core, network aggregation layer, and network access layer, and can be seen as a branch of large scale network. The topology of Scenario 1 includes four areas: one backbone area and three not-so-stubby areas shown in Fig. 2 . Supposed 15 links (33% percent links in aggregation layer) of the network are destroyed, which lie in the three not-so-stubby areas randomly. The destroyed links are labeled by dotted lines in Fig. 2 . In order to test the network survivability, we apply two kinds of strategies with different route protocols: distributed route strategy (Strategy 1) and centralized route strategy (Strategy 2). In distributed route strategy the new route table is calculated in each router by OSPF protocol after a failure, while in centralized route strategy the new route tables are calculated by some centralized servers and then spread them to routers, which is appeared in many research papers. For just giving the survivability test as a sample we do not describe the centralized route strategy in detail.
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Network topology in experiment Scenario 1
In order to assess scalability of the STNSD method, we also generate another 5 network scenarios with number of nodes from 145 to 1467 by a popular topology generator, GT-ITM. The nodes include both internal nodes and end nodes (leaf nodes).
• Scenario 2: network with 145 nodes (including 132 end nodes) and 147 links. Network run with OSPF routing protocol.
• Scenario 3: network with 322 nodes (including 277 end nodes) and 349 links. Network run with OSPF routing protocol.
• Scenario 4: network with 528 nodes (including 428 end nodes) and 635 links. Network run with OSPF routing protocol.
• Scenario 5: network with 712 nodes (including 559 end nodes) and 887 links. Network run with OSPF routing protocol.
• Scenario 6: network with 1467 nodes (including 1126 end nodes) and 1898 links. Network run with OSPF routing protocol.
- 6.2 A Use Case of STNSD Method
We realize a tool for the STNSD method, the panel is shown in Fig. 3 . The tool can collect and monitor information for each SD Pair , and calculate the NRD in the whole network on different scenarios. We use the Scenario 1 as an example to demo the STNSD Method . For the Scenario 1, 22 pairs of nodes are selected using the OSDS algorithm: {n56,n25}, {n43,n60}, {n20,n46}, {n62,n22}, {n65,n40}, {n14,n32}, {n17,n54}, {n63,n37}, {n66,n57}, {n39,n42}, {n26,n23}, {n13,n16}, {n59,n53}, {n36,n33}, {n25,n19}, {n56,n45}, {n56,n54}, {n43,n37}, {n60,n65}, {n20,n17}, {n22,n14}, {n40,n32}. According to end-to-end bandwidth of each pairs, we calculate weights of all pairs by the Formula (6) in Table 1 .
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The panel of network survivability test by the STNSD Method
SD Pairsand its Weights
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SD Pairs and its Weights
In the experiment, as all the pairs are Connectivity-type SD Pairs except {n56,n25}, we use an active measurement tool, like Ping command, to keep measuring the RTT (Round-Trip Time) of each Connectivity-type SD Pair . For Service-type SD Pair {n56,n25}, we use an request tool written with python language to open the url of web application server deployed in node 25, and measuring the service response time. In the test steps descripted in section 5.2, given RTTreqr = 50 ms and RSTreqr = 100 ms , Connectivity-type SD Quality is calculated by the Formula (1) and Service-type SD Quality is calculated by the Formula (2), and then the SD Recovery Rate and the SD Recovery Time of each SD Pair are achieved by the Formula (3) and the Formula (4) respectively, As all the pairs, except {n66,n57}, {n26,n23}, {n13,n16}, {n59,n53}, {n36,n33}, {n25,n19} and {n43,n37}, in both the distributed route strategy and the centralized route strategy are recovered completely, so ηr = 100% for each pair. We repeat the test 10 times and calculate average value of each pair. The result of two survivability strategy is shown in Table 2 . Because the SD Pair {n66,n57}, {n26,n23}, {n13,n16}, {n59,n53}, {n36,n33}, {n25,n19} and {n43,n37} are not affected by 15 destroyed links, so the two survivability strategies have no effect on network, and the value of the SD Recovery Rate and SD Recovery Time are all zero in the Table 2 .
SD Pairsand itsηrandtr
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SD Pairs and its ηr and tr
In the test, the network survivability metric NRD is got by the Formula (5) using the data above, and the NRD of the distributed route strategy is 0.0315 while the NRD of the centralized route strategy is 0.1413. For a large scale network, generally NRD in [0.1, +∞) means excellent survivability, and NRD in [0.033, 0.1) means good survivability, and NRD in [0.02, 0.033) means acceptable survivability, and NRD in (-∞, 0.033) means bad survivability. So in this scenario the network with the distributed route strategy has an acceptable survivability, while the network with the centralized route strategy has an excellent survivability. It is obviously that much more performance of network is recovered by the centralized route strategy , so the centralized route strategy brings network better survivability than the distributed route strategy does in this scenario.
After analyzing the difference between two recovery strategies, we find out because route information update much faster in the centralized route strategy than that in the distributed route strategy , which makes much more SD Pairs come back to communication soon, so the NRD of the centralized route strategy is larger than that of the distributed route strategy . From experiment result, we can see that the STNSD method can be used to test network survivability well and the proposed metric NRD can perfectly reflect network survivability in a quantitative way.
- 6.3 Scalability Analysis
- (1) Experiment Methodology
In large scale network, scalability of the method STNSD is very important. After analyzing the steps of the method STNSD , the OSDS algorithm is the key of the method STNSD to achieve good scalability for selection of SD Pairs . So we use the Scenario 1, 2, 3, 4, 5 and 6 which have different node number from 64 to 1467 to assess the scalability of OSDS algorithm.
For comparison, except for OSDS algorithm, another three algorithms: all SD Pair algorithm, random SD Pair algorithm, and prediction algorithm [18] , are all considered. In all SD Pair algorithm, all end-to-end SD Pairs in the network are selected into SD Pair set. In random SD Pair algorithm, a number of SD Pairs are selected randomly into SD Pair set. In prediction algorithm [18] , about 20% of SD Pairs in the network are considered based on algebraic prediction.
- (2) Metrics
In order to evaluating the scalability of OSDS algorithm including its other performance, three metrics are used: cover rate, time cost, and SD Pair rate.
Cover rate reflects the validity of the SD Pair selection algorithm. Let the whole end-to-end SD Pair set in a network is Rall , the SD Pair subset obtained by the SD Pair selection algorithm is R , then the cover rate of the SD Pair selection algorithm is calculated by Formula (8):
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where f ( Rall ) and f ( R ) are Cover-Degree Function of SD Pair set Rall and R respectively, which is already defined in section 5.3.
Time cost is cost time of the SD Pair selection algorithm, which reflects the efficiency of the algorithm.
SD Pair rate is the number of selected SD Pairs compared to the number of the total SD Pairs in the network. Let N be the number of the total SD Pairs, Np be the number of SD Pairs that are obtained by the SD Pair selection algorithm. SD Pair rate is calculated by Formula (9).
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- (3) Experiment Results
The metric results of OSDS algorithm, all SD Pair algorithm, random SD Pair algorithm and prediction algorithm [18] in five scenarios are shown in Fig. 4 .
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The result of metrics by four algorithms in different scale networks ( x axis is node number of network, and y axis is cover rate, time cost, and SD Pair rate separately )
In Fig. 4 , the horizontal axis is the node number of network according to the five scenarios, and the vertical axis is three metrics: cover rate, time cost, and SD Pair rate separately. Fig. 4 (a) shows the cover rate by four algorithms in the different topologies. From Fig. 4 (a), we can clearly find out that cover rate of OSDS algorithm and all SD Pair algorithm always have the top value with 100%, while the other two algorithms are evidently lower. Fig. 4 (b) shows the time cost by three algorithms in the different topologies. From Fig. 4 (b), we can clearly find out that the time cost by OSDS algorithm and random SD Pair algorithm both have much less time than all SD Pair algorithm. Even in Scenario 6 with 1467 nodes, the time cost is 248.60s, which is also acceptable. For lack of enough information, the time cost of prediction algorithm is unknown for us [18] . Fig. 4 (c) shows the SD Pair rate by four algorithms in the different topologies. From Fig. 4 (c), we can clearly find out that SD Pair rate by OSDS algorithm is much lower than all SD Pair algorithm and prediction algorithm [18] . Even in Scenario 6 with 1467 nodes, the SD Pair rate of OSDS algorithm is as low as 0.12% (752 SD Pairs), which is much less contrast to other algorithms. For comparison, we also select the same number of SD Pairs by random SD Pair algorithm. We also find a decreasing trend of SD Pair rate with the increase of network size in Fig. 4 (c). After analyzing the selected SD Pairs by OSDS algorithm, we also find out number of SD Pairs is no more than number of end nodes and there are less than 2 SD Pairs correspond to an end node, which pay little overload on network traffic and end nodes. What’s more, because end-to-end path is mainly necessary for OSDS algorithm, OSDS algorithm can work well without the information of network topology, when using a tool like Traceroute. When all end-to-end paths are known, the computing complex is O(n) where n is the number of network nodes, so OSDS algorithm is scalable and fits large scale network.
A problem of SD Pair selection algorithm, including OSDS algorithm, based on end nodes is that when there are lots of redundant links, such as in Scenario 3, 4, and 5, the SD Pair paths based on end nodes might not cover all the links of network, but this could not affect network survivability test eventually. It’s because: a) network survivability test is user-oriented. The end-users just care about the performance they can obtain, and need not to concern with network internal information. The uncovered links are always redundant, and usually do not work. b) The SD Pair paths have adaptability in the network. When link fault occurs, redundant links would transmit data, and would be immediately covered.
Experiment result and analysis shows that the proposed survivability test method STNSD using OSDS algorithm has an excellent scalability and can be used in large scale network.
- 6.4 Comparison Analysis between STNSD and Existing Survivability Test Methods
As described related works in section 2, existing survivability test methods have two categories by different research ideas: effect-based survivability test methods and scheme-based survivability test methods. Since the scheme-based methods are all related with corresponding survivability schemes closely, they cannot be used in survivability measurement with other schemes always. While the STNSD is a general method, which can be used to measure different survivability schemes for large scale network freely. What’s more, the STNSD also resolves the problems about scale and quantization limitation of existing effect-based survivability test methods, and present a quantifiable test approach for a novel metric NRD and can be used in large scale network. In a word, the STNSD has a better performance compared to existing survivability test methods.
7. Conclusion and Future Work
This paper proposes a novel metric NRD on network survivability and its test method STNSD based on SD Pairs . The metric NRD is based on the abstraction of end-to-end capability of network, which can effectively reflect the network performance in the whole. The survivability test method STNSD can be used in quantifiable survivability test and evaluation for the large scale network. Experiment result shows that the survivability test method is valid and NRD can reflect the network survivability ability correctly, which makes survivability test and evaluation more efficiently. Because OSDS algorithm for selecting SD Pairs has well scalability for network size and is independent of the failure position, so the proposed survivability test method STNSD can be used to measure survivability in large scale network even when the failure position is unknown.
The proposed technique is simple and easy to apply in network measurement points. Presently a test framework is under development aiming to facilitate the technique usage on operational scenarios in real environment.
Acknowledgements
This work has been partially supported by the National Natural Science Foundation of China under Grant No. 61271252.
BIO
Ming Liang received his B.Sc., M.Sc. and Ph.D. degrees in Computer Science Dep artment from Mechanical Engineering College, China, in 2001, 2004 and 2008, respe ctively. Now he is a research assistant in National Key Laboratory of Science and Te chnology on Information System Security, China. His major interests are network sur vivability, mobile wireless network, and social network.
Zhao Gang received his Ph.D. degree in Computer Science from Tsinghua Univers ity, China, in 2009. Now he is a research fellow in National Key Laboratory of Scien ce and Technology on Information System Security, China. His main research interests include computer network, and information security.
Wang Dongxia received her M.Sc. and the Ph.D. degrees in Computer Science fro m the National University of Defense Technology, China, in 1997 and 2000, respecti vely. Now she is a research fellow in National Key Laboratory of Science and Techn ology on Information System Security, China. Her major interests are network surviv ability, network science, and mobile wireless networks.
Huang Minhuan received his B.Sc. and M.Sc. degrees from National University of Defense Technology, China, in 1996 and 1999, respectively. Now he is a research fellow in National Key Laboratory of Science and Technology on Information System Security, China. His major interests are network science, and Internet routing.
Li Xiang received her B.Sc. and M.Sc. degrees from Information Engineering University, China, in 2005 and 2008, respectively. Now she is a research assistant in National Key Laboratory of Science and Technology on Information System Security, China. Her current research interests include delay tolerant network, and mobile wireless network.
Miao Qing received her B.Sc. and M.Sc. degrees from National University of Defense Technology, China, in 1994 and 1997, respectively. Now she is a research assistant in National Key Laboratory of Science and Technology on Information System Security, China. Her current research interests include network science, and mobile wireless network.
Xu Fei received his B.Sc. and M.Sc. degrees from National University of Defense Technology, China, in 2005 and 2008, respectively. Now he is a research assistant in National Key Laboratory of Science and Technology on Information System Security, China. His current research interests include network science, and mobile wireless network.
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