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Contextual Trust Aided Enhancement of Data Availability in Peer-to-Peer Backup Storage Systems

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Abstract

Peer-to-peer storage services are a cost-effective alternative for data backup. A basic question that arises in the design of such systems is: In which peers do we store redundant data? Choosing appropmailriate peers for data backup is important at a microscopic level, from an end-user’s perspective to guarantee good performance, e.g., quick access, high availability, etc., as well as at a macroscopic level, e.g., for system optimization, fairness, etc. Existing systems apply different techniques, including random selection, based on a distributed hash table (DHT) or based on the peers’ past availability pattern. In this paper, we propose as an alternative, a contextual trust based data placement scheme to select suitable data holders. It is originally designed for and applicable to scenarios where there is inadequate historical information about peers, a common scenario in large-scale systems. Specifically, our scheme estimates trustworthiness of a peer based on stereotypes, formed by aggregating information of interactions with other (similar) peers. Simulation experiments show that our placement scheme outperforms not only random selection but also schemes using historical information, in terms of both achieved data availability as well as bandwidth overheads to sustain the system.

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Notes

  1. Peers leave the system permanently.

  2. Note that for backup storage application, typically only the data owner needs access to the data. However, if multiple users are to access the data round the clock, storing at peers with different time-zones is desirable [28]. The proposed approach can be applied for such a scenario as well, but then the function needs to be changed.

  3. Dealing with and preventing such malicious behaviors will require other security mechanisms, possibly including conventional trust based approaches. That is a somewhat orthogonal issue, beyond the scope of the presented work, where we are using trust abstraction as an alternative to explicit multi-objective optimization of the system.

  4. The data transfer rate is influenced by many factors such as bandwidth, connection type, ISP latency, etc. However, for simplicity, we assume that the data transfer rate is only determined by bandwidth in the simulation.

  5. We define a session as a process that a peer joins the system, contributes/provides resources and leaves the system.

  6. Note that in a real PlanetLab trace, node’s online pattern is already known, while in synthetic trace, node’s availability is generated artificially according to its time zones, time of day effects, and unique failure model characterized by the inter-arrival time and session length (see Sect. 4.1.2) and is hence, again known a priori for the experiments

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Acknowledgments

The authors wish to thank Krzysztof Rzadca for his valuable comments. This work has been supported in part by AcRF Tier 1 Grant RG 29/09 for the CrowdStore project.

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Authors and Affiliations

  1. CAIS-NGII, Nanyang Technological University, Nanyang Avenue, Singapore, 639798, Singapore

    Xin Liu

  2. School of Computer Engineering, Blk N4, North Spine, Nanyang Avenue, Singapore, 639798, Singapore

    Anwitaman Datta

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Correspondence to Xin Liu.

Appendix

Appendix

1.1 Trust Modeling

Modeling trust using beta distribution is a very popular approach. In our work, a transaction is binary, i.e., successful or unsuccessful, and we model the transactions between p o and p h as observations of independent Bernoulli trials. In each trial, the success probability, that is, the trust p is modeled by Beta distribution. Equation 4 shows the probability density function of Beta distribution:

$$ f(p;\alpha,\beta) = \frac{\Upgamma(\alpha + \beta)}{\Upgamma(\alpha)\Upgamma(\beta)}p^{\alpha-1}(1-p)^{\beta-1} $$
(4)

α and β are the shape parameters representing numbers of successful and unsuccessful transactions between a pair of peers. We start with α = β = 1, that translate into a complete uncertainty about the distribution of the parameter, modeled by the uniform distribution: Beta(1;1) = U(0;1). After observing s successes in n trials, the posterior density of p is Beta(α + s; β + n − s). Figure 7 shows three examples of beta pdf with different parameters. The curves express the relative likelihood of the probability that the target peer is trustworthy in the future transaction. When α > β (there are more successful transactions), the target peer is trustworthy with a higher probability, otherwise, it is trustworthy with a lower probability.

Fig. 7
figure 7

Probability density function of beta distribution

Full size image

So trust is modeled as a function and not as a single value. In this way, we can understand various aspects of trust like its expectation, confidence, etc., by studying the function.

The following definition defines the trust function between entities (an individual peer or a group of peers) based on a beta function. By E t , we denote the entity participating in the trust calculation.

Definition 1

(Trust Function) Entity E 1 evaluates entity E 2. From the viewpoint of E 1,  S E1,E2 and U E1,E2 represent, respectively, the number of successful transactions and unsuccessful transactions between E 1 and E 2 (S E1,E2 ≥ 0 and U E1,E2 ≥ 0). Trust function T E1,E2(p|S E1,E2, U E1,E2) mapping trust rating p (0 ≤ p ≤ 1) to its probability is defined by:

$$ \begin{aligned} T_{E_1,E_2}(p | S_{E_1,E_2},U_{E_1,E_2}) &= \frac{\Upgamma(S_{E_1,E_2} + U_{E_1,E_2} + 2)} {\Upgamma(S_{E_1,E_2} + 1)\Upgamma(U_{E_1,E_2} + 1)}\\ &\times p^{S_{E_1,E_2}}(1 - p)^{U_{E_1,E_2}}. \end{aligned} $$
(5)

The expected value of the trust function is equal to:

$$ E_{E_1,E_2}(T_{E_1,E_2}(p|S_{E_1,E_2},U_{E_1,E_2})) = \frac{(S_{E_1,E_2} + 1)}{(S_{E_1,E_2} + U_{E_1,E_2} + 2)} $$
(6)

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Liu, X., Datta, A. Contextual Trust Aided Enhancement of Data Availability in Peer-to-Peer Backup Storage Systems. J Netw Syst Manage 20, 200–225 (2012). https://doi.org/10.1007/s10922-011-9198-9

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