J. Parallel Distrib. Comput. A multi-dimensional trust evaluation model for large-scale P2P computing

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1 J. Parallel Distrib. Comput. 71 (2011) Contents lists available at ScienceDirect J. Parallel Distrib. Comput. journal homepage: A multi-dimensional trust evaluation model for large-scale P2P computing Xiaoyong Li, Feng Zhou, Xudong Yang Beijing Key Laboratory of Intelligent Telecommunications Software and Multimedia, Beijing University of Posts and Telecommunications, Beijing , China a r t i c l e i n f o a b s t r a c t Article history: Received 26 February 2010 Received in revised form 27 December 2010 Accepted 19 January 2011 Available online 23 February 2011 Keywords: Large-scale P2P computing Trust model Trust factor WMA OWA combination algorithms In large-scale peer-to-peer (P2P) computing, trust management technology has become a key requirement for network security. However, trust is one of the most complex concepts in network communities. It involves many factors, such as, assumptions, expectations, behaviors, risks, and so on. As a result, trustworthiness has multi-dimensional properties. In this paper, an innovative trust model is proposed for large-scale P2P computing, in which multiple factors are incorporated to reflect the complexity of trust. More importantly, the properties (weights) of these factors are dynamically assigned by weighted moving average and ordered weighted averaging (WMA OWA) combination algorithms. This model surpasses the limitations of existing approaches, wherein weights are assigned subjectively. The simulation results show that, compared with the existing approaches, the proposed model provides greater accuracy and a more detailed analysis in trust evaluation Elsevier Inc. All rights reserved. 1. Introduction 1.1. Background In open P2P computing systems, networks consist of groups of peers acting as clients and servers. These groups of peers communicate directly among themselves through wide-area networks. Peers make a portion of their resources, such as processing power, disk storage or network bandwidth, directly available to other network participants, without the need for central coordination by servers or stable hosts. Peers are both suppliers and consumers of resources, in contrast to the traditional client server model where only the servers supply, and the clients consume. Some of the benefits of fully distributed P2P systems are scalability, resource aggregation and inter-operability without administration cost or centralized infrastructure support. Features of the distributed P2P networks include distributed file-sharing [20], digital content delivery [21], and P2P grid computing [6]. To encourage resource sharing among peers and combat malicious peer behavior, trust management is essential for peers to assess the trustworthiness of others and to interact selectively with more reputable ones [28]. Without an efficient trust management mechanism, peers will have little incentive to contribute their computing or bandwidth resources. Peers may hesitate to interact with This project is supported by the National Nature Science Foundation of China (No ) and the Fundamental Research Funds for the Central Universities of China (No. BUPT2009RC0201). Corresponding author. address: lxyxjtu@163.com (X. Li). unknown peers because of the possibility of receiving corrupted or poisoned files or being exploited by malware. P2P trust management is especially necessary in commercial P2P applications, and potential areas in which P2P trust management systems may have applications include P2P auctions [18], trusted content delivery [21], pay-per-transaction operations [25], P2P service discovery [19], P2P resource sharing [5], and others. In the past few years, many state-of-the-art trust models have been proposed, such as [28,25,19,5,11,23,34,13 15]. Some of them are very creative and elaborate, but most of them still have two key limitations which need to be addressed: (1) Many current trust models use simple or one-sided trust factors to quantify and predict the trustworthiness of P2P service providers or requesters. This may lead to inaccurate trustworthiness perceptions. When trust factors between peers cannot be accurately defined, trust cannot be evaluated or managed. (2) In many previous studies, subjective methods were used to assign weights to trust factors. This does not reflect the complexity and adaptability of the trust evaluation process. Furthermore, it may lead to misinformation and preclude an accurate evaluation of trustworthiness Ideas and contributions to the model In the human cognitive process, the brain routinely carries out information processing and fusion. The objectives are to collect observations from various similar or dissimilar sources, to extract the required information (inferences), and to combine or fuse these steps to obtain the status and identity of a perceived object. This process is very crucial for survival and growth of human /$ see front matter 2011 Elsevier Inc. All rights reserved. doi: /j.jpdc

2 838 X. Li et al. / J. Parallel Distrib. Comput. 71 (2011) beings and is known as multi-source information fusion [33,4]. This method is rapidly emerging as a discipline, and is finding an increasing number of applications in industrial automation, aerospace systems, and computer engineering. This method is expected to give better spatial coverage, reduced redundancy, improved robustness, and increased accuracy. Trust has existed in the entire history of human beings. Almost every aspect of a person s life is based on some form of trust. Undoubtedly, trust is vital for humanity to be able to have meaningful relationships. Presently, however, researchers have difficulty in operationalizing trust. They disagree even on the basic definitions [13]. In any case, trust is a social phenomenon inherent in human beings. Therefore, a useful trust model should be in line with human patterns of behavior. In this paper, an innovative trust model is proposed based on human cognitive behavior. Multiple factors (multi-source information) are incorporated to mirror the complexity and uncertainty characteristic of trust in human relationships. The weights of these factors are dynamically assigned by weighted moving average and ordered weighted averaging (WMA OWA) combination algorithms [31,32,27,1]. This model overcomes limitations of existing approaches in which weights are assigned subjectively. The simulation results show that the proposed model provides greater accuracy and a more detailed analysis in trust evaluation. The main contributions of this paper go beyond the existing approaches in the following ways: (1) Multi-dimensional Trust Factors. In the open P2P systems, trust is one of the most complex concepts in network communities. It involves many factors, such as assumptions, expectations, behaviors, risks, and so on. As a result, trustworthiness has multi-dimensional properties. Thus, it is very difficult to quantify and predict peer trust. The concepts of extended and multi-dimensional trust factors based on human behavior patterns are proposed. Not only can this reduce networking risk and improve the system efficiency, it can also significantly enhance the accuracy of trust perception and evaluation. (2) An Adaptive Weight Assigning Method. Many previous studies used artificial or subjective means to assign various weights for trust factors. The adaptability of these models has limitations. Based on multi-source information fusion theory, WMA OWA combination algorithms are used to integrate multiple trust factors into an overall trust evaluation. This can overcome the impact of the rigidity of assigned weights on the overall trust perception and evaluation. This paper provides the theoretical foundations and experimental results to validate the design of the trust aggregating mechanism. The remaining parts of this paper are organized as follows. Section 2 gives an overview of related research. Section 3 is the sketch of the approach. Section 4 outlines the details of the trust model based on WMA OWA combination algorithms. The simulation results are presented in Section 5. Section 6 concludes the paper and suggests future directions for improvement. 2. Related work Shi and Liang of Wayne State University proposed the Trust- Ware system [11], a trusted middle-ware for P2P applications. Their approach consists of two models: the Multiple Currency Based Economic model (M-CUBE) and the Personalized Trust model (PET). The M-CUBE model provides a general and flexible substrate to support high-level P2P resource management services. PET derives peer trustworthiness from long-term reputation evaluation and short-term risk evaluation. Satsiou and Tassiulas proposed a distributed reputation-based system in which peers earn reputation analogous to their contributions [23]. In this way, each peer has a trade-off between the capacity that she will dedicate for uploading to increase her reputation and revenue, and the capacity she will dedicate for her downloads. All peers act rationally to maximize their utility. Their proposed policies lead rational peers to cooperate while promoting fairness, as peers receive resources in proportion to their contributions. At Georgia Tech., Liu and Xiong have developed the Peer Trust model [28]. Their model is based on a weighted sum of five peer feedback factors, namely, peer records, scope, credibility, transaction context, and community context. This model is fully distributed. It uses overlay for trust propagation and public key infrastructure for securing remote scores, and it prevents peers from some malicious abuses. At the University of Southern California, Hwang and Zhou developed a robust and scalable P2P reputation system, Power- Trust [34], to leverage the power-law feedback characteristics. The Power-Trust system dynamically selects small numbers of power nodes that are most reputable using a distributed ranking mechanism. By using a look-ahead random walk strategy and leveraging on the power nodes, it significantly improves the global reputation accuracy and aggregation speed. Power-Trust is adaptable to the dynamics of peer joining and leaving. It is robust to disturbance by malicious peers. Two types of basic trust information, namely, the interactionderived information (or first-hand information) and the rating (or second-hand information), necessary to build a trust model have been proposed and used in several studies [11,23,28,34]. These are similar to traditional trust models based on 2-dimensional trust factors. Apparently, these models use simple or one-sided trust factors to quantify and predict trustworthiness between peers. This may lead to misinformation, and preclude an accurate evaluation of trustworthiness. More importantly, they use subjective methods to weight the trust factors, which may lead to inaccurate perceptions of trustworthiness. From [11,23,28,34], we can find, in traditional trust models based on 2-dimensional trust factors, two types of basic trust information, namely, interaction-derived information (or first-hand information) and rating (or second-hand information), are necessary to build a trust model. Apparently, these models use simple or one-sided trust factors to quantify and predict trustworthiness between peers. This may lead to misinformation, and preclude an accurate evaluation of trustworthiness. More importantly, they use subjective methods to weight the trust factors, which may lead to inaccurate perceptions of trustworthiness. 3. Sketch of the approach 3.1. Basic architecture Based on the various peer roles in the P2P system, peers can be divided into three types: service provider (SP), service requester (SR), and feedback rater (FR). The notion of the SP is used to represent peers who provide services for others, SR for the peers who request services, and FR for peers who report feedback to others. A quantified trust value of trustworthiness is an integrated opinion rating of a transaction. Our trust evaluation model monitors the behaviors of an entity by collecting, aggregating, and distributing such trust ratings. The basic architecture of this trust evaluation mechanism is designed as in Fig. 1. For ease of reference, a list of key notations is given in Table 1. The P2P trust management system monitors an entity s behavior by collecting, aggregating, and distributing trust rating values. Conceptually, the proposed trust model mainly consists of the following components (right part of Fig. 1): evidence

3 X. Li et al. / J. Parallel Distrib. Comput. 71 (2011) Fusion Calculation of Multiple Trust Factors based on WMA-OWA Combination Algorithms Fig. 1. P2P trust management architecture based on multi-dimensional trust factors. Table 1 Acronyms of key notations and variables. Acronym Entity SR SP FR Feedback DTT HEW Definition An user, a process or a resource in peers Service requester Service provider Feedback rater The recommendation information provided by FR Direct trust tree History evidence window base (EB), knowledge base (KB), trust information fusion center (TIFC), access control base (ACB), trust decision function (TDF), and so on. In the course of interaction between the two entities, related information is monitored and saved in EB, assuming that P i is an SP, and P j is an SR. From Fig. 1, the value of T(P i, P j ) between P i and P j, is calculated by the OWA-WMA combination algorithms. This fusion function includes five subfunctions (input), known as the history factor (HF), the availability factor (AF), the feedback factor (FF), the motivation factor (MF) and the risk factor (RF). Thus, trustworthiness between P i and P j can be determined by the following vector: D = (H f (P i, P j ), A f (P i, P j ), R f (P i, P j ), M f (P i, P j ), F f (P i, P j )) (1) where H f (P i, P j ) is used to evaluate P j s trustworthiness based on historical data. Thus H f (P i, P j ) reflects a long-term trust between P i and P j. A f (P i, P j ) is used to evaluate P j s trustworthiness based on availability-based monitoring data, such as data transfer rate, data throughput, service time, responding time, establish-connection delay, data transfer delay, and so on. Generally, A f (P i, P j ) is a real-time and short-term trust factor. F f (P i, P j ) is used to evaluate feedback trust to this service requester. R f (P i, P j ) is used to evaluate risk before a transaction. Analyzing the risk involved in a transaction is important to decide whether or not to proceed with the transaction. M f (P i, P j ) is used to evaluate a peer s activity level before a transaction. As there are many free-riding peers in P2P networks, M f (P i, P j ) is used to reduce peer free-riding behaviors and motivate these peers to cooperate with others. In short, a trust evaluation vector includes five complementary factors, including the historical trust factors H f (P i, P j ), the availability-based trust factor A f (P i, P j ), the feedback-based trust factor F f (P i, P j ), the risk-based trust factor R f (P i, P j ) and the motivation-based trust factor M f (P i, P j ). Through WMA OWA combination algorithms [31,32,27,1], these five trust factors can be combined into one overall trustworthiness metric. Definition 1. In general, overall trustworthiness between P i and P j is calculated by the following equation: T(P i, P j ) = W D = w 1 H f (P i, P j ) + w 2 A f (P i, P j ) + w 3 F f (P i, P j ) + w 4 R f (P i, P j ) + w 5 M f (P i, P j ) (2) where W = (w 1, w 2,..., w 5 ), w m [0, 1], 5 m=1 w m = 1. w m is the weight of the related trust factor. In the previous work, three kinds of subjective methods assign the values to these weights [11], namely, expert opinion, random allocation, and average weight. However, within each of the three methods exists a common defect. They all lack dynamic adaptability. Once the value of weights is identified, it is difficult to dynamically adjust the value adaptively. Therefore, assigning adaptive values to (w 1, w 2,..., w 5 ) is one of the key tasks in this work. The WMA OWA combination algorithms combine an OWA operator and a weighted moving average (WMA) model [31,7,32,10,27,8, 30,29,1], which not only considers the degree of varying influence among various data but also focuses on dynamic weighting problems. In the proposed model, the WMA OWA combination algorithms are used to weight these trust factors. This capability allows the model to provide a more detailed and accurate assessment of the trust evaluation process Formal function of trust evaluation Assuming that P i has m levels of service, the set of policy is defined as S = {s 1, s 2,..., s m }. Between P i and P j, the trust decision-making function ρ is a mapping procedure from T(P i, P j ) to its service policy S: s m, c k T(P i, P j ) 1 s m 1, c k 1 T(P i, P j ) < c k ρ(t(p i, P j )) =, (3) s 2, c 1 T(P i, P j ) < c 2 s 1, 0 T(P i, P j ) < c 1 where c 1, c 2,..., c k [0, 1], and c 1 < c 2 < < c k. For example, in a P2P resource-sharing system, an SP P 0 can define its trust evaluation function as: s3, 0.5 T(P 0, P x ) 1 ρ(t(p 0, P x )) = s 2, 0.2 T(P 0, P x ) < 0.5 s 1, 0 T(P 0, P x ) < 0.2 where {s 1, s 2, s 3 } ={no service, download, download and upload}. If T(P 0, P 1 ) is 0.19, then ρ(t(p 0, P 1 )) = ρ(0.19) = s 1, which implies that P 1 has no access privilege for the resources in P 0. If T(P 0, P 1 ) = 0.4, then ρ(t(p 0, P 1 )) = ρ(0.4) = s 2, which implies that P 1 has download privilege. If T(P 0, P 1 ) = 0.79, then ρ(t(p 0, P 1 )) = ρ(0.79) = s 3, which implies that P 1 has both download and upload privileges.

4 840 X. Li et al. / J. Parallel Distrib. Comput. 71 (2011) Monitoring agents for peer behaviors Data transfer rate Data throughput Nodes service time Standardization of availability evidence Availabitlity-based trust factor Fig. 2. Availability-based trust factor and related behavior evidence. 4. Calculation of multi-dimensional trust factors 4.1. History-based trust factor The history trust factor refers to long-term peer behavior. In the model presented here, the value of H f (P i, P j ) is a weighted average value of all past experiences between two interacting peers. In the history of the interaction process, assuming that P i has rated the interaction satisfaction degree of P j as a sequence of probabilistic ratings: K = {x(1), x(2),..., x(t),..., x(h 1), x(h)} (4) where t is a time-stamp and t [1, h]. 0 x(t) 1. In addition, h is known as the history evidence window (HEW, which refers to the largest number of history records considered by the trust model). After an interaction (which is called an experience), P i will give a score for P j in accordance to its performance. For the sake of simple computation, at a time-stamp t of an interaction, the quantization function of an experience is defined as follow: x(t) = o(t) (5) u(t) where o(t) is the resource online time and u(t) is the total time to complete this interaction (such as total download time for the sharing resource). Definition 2. History trust factor between P i and P j is defined as the following equation: h (x(t) γ (t)) H f (P i, P j ) = t=1, h 0 (6) h 0, h = 0 where γ (t)(0 γ (t) 1) is an attenuation function. γ (t) is used to weight a historical experience on the basis of its time-stamp t. In fact, trust changes with time. An early experience would have a small impact on trust, and a recent experience would contribute more to the trust evaluation. The quantity γ (t) is defined as follows: γ (t) = 1, t = h γ (t 1) = γ (t) (1 µ) h (7), t h where h acts as an adjustable positive constant and can be tuned accordingly. The attenuation property of the historical trust factor is reflected by γ (t). As an example, assuming that h = 5 and µ = 0.6, at time-stamp 5, K = {x(1), x(2), x(3), x(4), x(5)} = {0.6, 0.7, 0.6, 0.8, 0.75}, then, based on Eq. (7), γ (5) = 1, γ (4) = 0.922, γ (3) = 0.84, γ (2) = and γ (5) = Using Eq. (6), H f (P 0, P 1 ) = From Eqs. (6) and (7), we can find that the history trust factor develops over time, and only positive experiences can lead to an increase in its value Availability-based trust factor In P2P environments, some of the peers acting as service providers can appear and disappear at any time of the day. These peers can change their services at any time according to their own interests. Therefore, one very important task in the P2P computing areas is to discover the most available peers (resources) meeting the requirements of other peers. The availability-based trust factor is used to evaluate the peer real-time behavior. Hence, this trust factor is a short-term peer behavior, and it should be more sensitive to new evidence. In particular, this trust factor must be more sensitive and responsive to the changes in peer behaviors. Generally speaking, availability-based trust factor is an evaluation value for real-time measurement indicators [17,22,3]. These real-time measurement indicators include date transfer rate, data throughput, service time, responding time, establish-connection delay, data transfer delay, release-connection delay, and so on. Three key indicators of availability were measured, namely, data transfer rate, data throughput, and service time (Fig. 2) [17,22,3]. In a previous work [17,35,16,9], monitoring agents (software sensors) were developed to acquire the indicator value of availability for grid computing systems. However, these software agents can also be used to monitor peer indicator value of availability for P2P systems. At a time-slot τ, supposing that n measurement samples {ξ k (1), ξ k (2),..., ξ k (Γ )} were obtained for the k th indicator of availability. Generally, before fusing calculation of these samples, each sample should be standardized to eliminate deviation caused by fusing results by each indicator item s characteristic unit and value domain. For each sample ξ k (τ), τ [1, Γ ], the mean ξ k (τ) and standard deviation (Sξ k (τ)) are calculated. These are denoted as follows: ξ k (τ) = 1 Γ ξ k (τ) (8) Γ t=1 S(ξ k (τ)) = 1 Γ Γ (ξ k (τ) ξ k (τ)). (9) t=1 The standardized value e k (τ) is then calculated, denoted as follows: e k (τ) = ξ k(τ) ξ k (τ). (10) S(ξ k (τ)) Lastly, the samples can be compressed into the value domain [0, 1]. Using the extremum standardization equation, the expression is defined as: b k ( τ) = e k (τ) max(ξ k (τ)) max(ξ k (τ)) min(ξ k (τ)) (11) where max(ξ k (τ)) and min(ξ k (τ)) are, respectively, the maximum and minimum values of {ξ k (1), ξ k (2),..., ξ k (Γ )}. Each sample of the k th indicator of availability is expressed within [0, 1], and increases along the positive direction. The bigger is the sample, the better it becomes. Definition 3. In the model presented here, the simple moving average method is used to calculate the availability-based trust factor: A f (P i, P j ) = M k=1 τ=1 Γ (b k ( τ)/γ ) y (12) where y is the total number of indicators of availability. Eq. (12) shows that the availability-based trust factor is calculated from the most recent time-stamp τ. Therefore, it is a short-term trust factor, and is more sensitive to new experiences. This makes the proposed model have a strong power to timely handle the changes in peer behaviors.

5 X. Li et al. / J. Parallel Distrib. Comput. 71 (2011) Fig. 3. Trusted path and feedback aggregation Feedback-based trust factor Feedback (also known as recommendation or reputation) provides an efficient and effective way to build reputation-based trust among peers in P2P environments. The trust model collects feedbacks from the third-part peers and aggregates them to yield the global reputation scores. After a peer completes a transaction, e.g., downloading a music file, the peer will provide his or her feedback for other peers to use in future transactions. Supposing that W = {W 1, W 2,..., W k,..., W M } is a set of FRs who have successfully provided their feedbacks for P j and T(W k, P j ) is the trustworthiness between W k and P j, then the feedback trust factor can be defined as follows: Definition 4. In the model presented here, the feedback trust factor between P i and P j is calculated by the following equation: M (ϖ (W k ) T(W k, P j )) k=1, M 0 F f (P i, P j ) = M (13) ϖ (W k ) k=1 0, M = 0 where ϖ (W k ) is the path function, which is used to assign weight to the credibility of W k. Because ϖ (W k ) should reflect the attenuation and transmission of the feedback trust factor, it is defined as following equation: level T(P ϖ (W k ) = m, P m+1 ), level > 0 (14) m=1 1, level = 0 where T(P m, P m+1 ) is P m s trustworthiness for the descendant node P m+1 along the direction of the trusted path. The level hops from an FR to the root of DTT (DTT is a logic data structure, and reflects a dynamic trust relationship between peers. The construction principle of DTT can be seen in a previous work [14,15]). As an example, consider the instance in Fig. 3. P 0 is the service provider, so it is the root of this DTT and its level = 0. P 1 and P 2 are the first-level nodes in this DTT, so their level = 1. According to Eq. (14), ϖ (P 1 ) = 0.5 and ϖ (P 1 ) = 0.7. P 3 is the second-level node, and its level equals 2. Using Eq. (14), we can get ϖ (P 3 ) = = 0.3. For P 9, it is the third-level node, and its trust weight ϖ (9) equals = In Fig. 3, P 14 is an SR and P 0 is an SP. Feedback nodes include P 3, P 9 and P 6. Assuming that T(P 3, P 14 ) = 0.7, T(P 9, P 14 ) = 0.8 and T(P 6, P 14 ) = 0.9, and from Eq. (14), ϖ (P 3 ) = 0.30, ϖ (P 9 ) = 0.24, and ϖ (P 6 ) = Using Eq. (13), F f (P 0, P 14 ) = Risk-based trust factor Risk is associated with almost every daily activity. For most people, it refers to the likelihood that in life s games of chance, an undesirable outcome will result. Risk is concerned with the deviation of one or more results of one or more future events from their expected value. Technically, the value of those results may be positive or negative. However, its general usage tends to focus only on the potential harm that may arise in a future event. Webster s dictionary 1, in fact, defines risk as possibility of loss or injury. Thus, risk is perceived almost entirely in negative terms. In the model presented here, the risk trust factor is used to evaluate risk before a P2P transaction occurs. Analyzing the risk involved in a transaction is important to decide whether or not to proceed with the transaction. Definition 5. In the model presented here, the risk-based trust factor is defined as: R f (P i, P j ) = 1 r(z) z + δ (15) where z, or the risk window, is the total number of the past interactions, r(z) is the total number of failing transactions in z, and δ is an adjustable positive. In Eq. (15), the risk window z is employed for the risk calculation. Only peer behavior inside the window is taken into consideration. With the window shifting forward, the risk value reflects the fresh statistics of the recent behaviors of the peer. The window size and adjustable positive constant play an important role in the risk calculation. The smaller is the window size, the more favorable the shorter-term assessment becomes. To reduce the risk, users can assign a low value to the adjustable constant δ. However, this will decrease the availability of the resources, because less risk for cooperation is requested and less peers are qualified to be cooperative. The trust system can define a trade-off between the risk and the resource availability by adjusting the adjustable constant δ. As an example, supposing that z = 10, r(z) = 2 and δ = 2, then according to Eq. (15), R f (P i, P j ) = Motivation-based trust factor According to human patterns of behavior, trustworthiness is high if a peer actively provides his or her service to other peers. 1

6 842 X. Li et al. / J. Parallel Distrib. Comput. 71 (2011) The value of feedback factor The value of feedback factor The value of α Fig. 4. The fitting curve of M f (P i, P j ) with changing parameter α The value of τ+μ The value of δ Fig. 5. The fitting curve of M f (P i, P j ) with changing parameters τ + µ and δ. Likewise, a peer with more interactions with other peers has a higher trustworthiness level. A new function called motivationbased trust factor is used to reflect these human patterns of behavior. Definition 6. In the model presented here, the motivation-based trust factor is defined as: 1 M f (P i, P j ) = (Ψ (τ + µ) + Ψ (δ)), τ + µ + δ < C 2 (16) 1, τ + µ + δ C where Ψ (x) = 1 1, δ is the total number of interaction x+α peers with P j, τ is the total number of P i s direct neighbors, and µ is the total number of P i s indirect neighbors. The motivationbased trust factor has a maximum if the value of τ + µ + δ is greater than a threshold value. The threshold value is defined as a positive constant C. The function Ψ (x) has the desirable property that allows the function to approach 1 quickly with increasing x (x could be any positive integer). The number α is an positive constant and can be tuned by the trust system accordingly. Fig. 4 shows the behavior of the fitting curve of M f (P i, P j ) with respect to the change in the adjustable constant α (assuming that δ = τ + µ = 100). Fig. 5 shows the behavior of the fitting curve of M f (P i, P j ) with respect to the change in δ and τ + µ (assuming that α = 0.2). From Figs. 4 and 5, the motivation-based trust factor is larger if τ + µ and δ are higher. As an example, supposing that δ = 5, τ + µ = 15 and α = 0.2, then from Eq. (16), M f (P i, P j ) equals Fusion calculation of the overall trustworthiness The WMA OWA algorithms combine an OWA operator and a WMA model [31,7,32,10,27,8,30,29,1], which not only consider the degree of influence between different data, but also focus on dynamical weighting problems. The decision makers simply need to change the weights of the input data dynamically based on the aggregation situation. The system provides fusion computing results to the decision makers. Thus, in the model presented here, WMA OWA algorithms are used to weight these trust factors. The WMA model with multiplying factors can give different weights to different data points. Mathematically, the WMA model is the convolution of the data points with a moving average function. In statistics, the WMA model is a type of finite impulse response filter used to analyze a set of data points by creating a series of averages of different subsets of the full data set. Definition 7. In technical analysis, the WMA model has the specific meaning of weights that change arithmetically. It is defined as: F(U) = n ω i U i (17) i=1 where F(U) is the fusion function for series U, i is the number of data items used to calculate the weighted average, U i is the actual data item, and ω i is the weight assigned to U i (with ωi = 1). The five trust factors are obtained: D = (H f (P i, P j ), A f (P i, P j ), R f (P i, P j ), M f (P i, P j ), F f (P i, P j )). Conceptually, if let U = D, Eq. (2) becomes a WMA model. The OWA operators provide a parameterized class of mean type aggregation operators [31,7,32]. Many notable mean operators such as the max, arithmetic average, median and min, are members of this class. They have been widely used in computational intelligence because of their ability to linguistically model the expressed aggregation instructions. Definition 8. Formally, an OWA operator of dimension n is a mapping F : R n R that has an associated collection of weights W = [ω 1, ω 2,..., ω n ] lying in the unit interval and summing to one and with: n F(p 1, p 2,..., p n ) = ω i p σ (i) (18) i=1 where p σ (i) is the i th highest value in the set {p 1, p 2,..., p n }. By choosing a value of W, different aggregation operators can be implemented. The OWA operator is a non-linear operator that results from the process of determining b j. An issue in the definition of the OWA operator is how to obtain the associated weighting vector W. Fuller proposed two ways to obtain it. The first approach is to use a kind of learning mechanism using some sample data, and the second approach is to try to give some semantics or meaning to the weights [7]. The weights of p σ (i) can be computed through the following equations [7]: w 1 [(n 1)λ + 1 nw 1 ] n = [(n 1)λ] n 1 [((n 1)λ n)w 1 + 1] (19) w n = ((n 1)λ n)w (n 1)λ + 1 nw 1 (20) w = n 1 t w (n t) 1 w (t 1) n. (21) In the above equations, the parameter λ can be treated as a tool for the trust system to determine the most important factor based on the set {p 1, p 2,..., p n }. According to [7], the optimal value of w i should satisfy Eq. (19). When w i is obtained, w n can be calculated using Eq. (20), and the other weights can be obtained from Eq. (21).

7 X. Li et al. / J. Parallel Distrib. Comput. 71 (2011) Following this, the OWA operator is used to calculate the weight vector W = (w 1, w 2,..., w 5 ). Algorithm 1. OWA-based Weight Vector Calculation (1) Input (λ, U); /* for different λ and n, we can get different OWA weight, λ is the situation parameter. */ (2) n = 5; (3) if λ < 0.5 then λ = 1 λ; endif (4) if λ 0.5 then Calculate w 1 according to Eq. (19); Calculate w m according to Eq. (20); for t = 2 to (m 1) do Calculate w t according to Eq. (21); endfor endif (5) Output weight vector W = (w 1, w 2,..., w 5 ). 5. Evaluation and comparison of performance From Liang and Shi s production technique [12], a simulator is used to test the feasibility of the proposed model based on Netlogo [26]. Netlogo is implemented by the JAVA language, and it is particularly well-suited for modeling complex systems that are continuously developing over time. Modelers can give instructions to hundreds or thousands of agents who are running independently. This makes it possible to explore the connection between the micro-level behavior of peers and the macro-level patterns that emerge from the interaction of many peers. Using Netlogo, a friendly GUI-based user interface is developed to control the simulation. Different parameters can be easily tuned to form different configurations. For comparison purposes, the other two well-known trust models, Peer Trust model [28] and Satsiou s model [23] are also implemented in the simulator Simulator settings (1) The roles of peers in simulator. In the simulator, the roles of peers as FRs can be one of four types: honest FR (HFR), malicious FR (MFR), exaggeration FR (EFR), and collusive FR (CFR). HFRs always give correct feedback, and MFRs always give the opposite opinion to others. EFRs exaggerate their rating by an exaggerating factor ε, which has a value of 0.5 in this simulation. EFRs send out the feedback T + ε (T 0.5) = T (T 0.5). CFRs send out 1 for the peers in the collusive group, and 0 for the peers outside the group. To make the simulator more versatile, the approach in Ref. [11] is adopted to classify SPs. Four kinds of role are introduced in the simulation: good, low-grade, no-response, and Byzantine. Good SPs always provide good services. The last three qualities are related to the bad SPs (BSPs), and their corresponding services lead to the decrease in the trustworthiness. The percentage of BSPs can be 20% BSPs, which simulates a relative stable community, or 70% BSPs, which simulates a high dynamic community with many dynamic peers. For the percentage of HFRs, two choices are made, namely, 20% and 80%. For 20% of HFRs, the community is a terrible one, with 80% of BFRs; 80% of HFRs denotes a relative good community with fewer bad FRs (20%). BSPs change their quality of service in a specific interval (I SP ). Decreasing the value of I SP can make an SP change its quality faster. P B is the percentage of BSPs in the P2P system. If P B = 30%, then there will be N P P B = 900 BSPs in the whole network, and the rest are good SPs. That is, the number of good SPs is N P (1 P d ) = Table 2 The parameters and their possible values in the simulation. Description Possible values I SP Interval of dynamics 3,12,30 N P Total number of peers 3000 P B % of bad SPs 20%, 70% P H % of honest FRs 20%, 80% Q R Quality as FR HFR, MFR, EFR, CFR Q S Quality as SP Bad, Dynamic, Good W Weights in [28,23] 0.3, 0.5, 0.7, 0.9 λ Parameter in Algorithm 1. [0.5, 1] h Allowed max history records(eq. (15)) 10 τ Adjustable positive constant(eq. (16)) 2 Table 3 The trust factors used by the three trust models. Trust model Trust decision factors Range 2-dimensions trust factor in [28,23] Multi-dimensions trust factor in our model Self-experience trust I [0, 1] information Rating trust information R [0, 1] The historical trust factors H f [0, 1] The availability trust factors A f [0, 1] The feedback trust factor F f [0, 1] The risk trust factors R f [0, 1] The motivation trust factors M f [0, 1] P H is the percentage of HFRs. If P H = 80%, then there are N P P H = 2400 HFRs in the P2P network, and the remaining N P (1 P H ) FRs are bad FRs. Finally, time-step is the running steps of the simulation. Instead of using the physical running time, the notion of time-step, which is introduced in Netlogo, is used to calculate the simulation time. Within each time-step, a peer finishes all the activities, including service requests, service providing, trustworthiness update, and rating dissemination. All the parameters discussed above and their possible values used in the simulator are summarized in Table 2. (2) Computing of the trust factors in simulator. The trust factors used by the three trust models are summarized in Table 3. For the Peer Trust model [28] and the Satsiou model [23], two trust factors, namely, self-experience trust information (first-hand trust information) and rating trust information (or second-hand trust information), are necessary to calculate the trustworthiness. Self-experience trust information is similar to the historical trust factor, and rating trust information is similar to the feedback trust factor in the model presented here. Therefore, the Peer Trust and Satiou models are called 2-dimensional trust models with two trust factors. In the simulator, the following equation is used to compute for the trustworthiness of the 2- dimensional trust models [12]: T(P i, P j ) = W I + (1 W) R (22) where I is the self-experience trustworthiness, R is the rating trustworthiness, and W is the weight of I (correspondingly, 1 W is the weight of R). In the simulator, I and R are computed according to related algorithms in Refs. [28,23]. In addition, W [0, 1] and it is randomly configured by users, so that it can be set as 0.3, 0.7, 0.8, and so on. From the introduction, our model includes five trust factors. In the simulator, T(P i, P j ) is computed using the following equation: T(P i, P j ) = 5 w k D k (P i, P j ) (23) k=1 where D k (P i, P j ) is one of the five trust factors H f (P i, P j ), A f (P i, P j ), F f (P i, P j ), R f (P i, P j ), and M f (P i, P j ), adn w k is the weight of the k th trust factors, which is automatically computed by the OWA algorithm.

8 844 X. Li et al. / J. Parallel Distrib. Comput. 71 (2011) Table 4 The trust factors used by the trust model. Model Scenario w 1 w 2 w 3 w 4 w 5 Our trust model P P P P Dynamic computed by Algorithm 1. P1.A P1.B P2.A P2.B P3.A P3.B P4.A P4.B Netlogo can compute four trust factors according to the expressions described in Section 4, including H f (P i, P j ), F f (P i, P j ), R f (P i, P j ), and M f (P i, P j ). For A f (P i, P j ), actual measured data are needed, so it is difficult to simulate using Netlogo. In the simulator, its calculation method is simplified as follows: 0.9, A f (P i, P j ) = for good SP 0, for bad SP. (24) In Eq. (24), the expression of A f (P i, P j ) is slightly modified from the original mechanism proposed in Section 4.2. However, its basic idea is similar to that presented in Section 4.2, i.e., a good SP has high resource availability, and a bad SP does not provide the sharing resource completely Performance evaluation All trust models should have good accuracy in trustworthiness evaluation, which can give the model a strong capability to resist malicious network behavior. As seen in the first set of experiments, the mean absolute deviation (MAD) is used to evaluate the accuracy of the proposed model [2,24]. et β(t) = (25) t where e t is the evaluation error at time-stamp t, and e t = A t+1 F t. A t is an actual value calculated by Netlogo at t, and F t is the forecast value calculated by Netlogo before t. t is the total running time-stamp of Netlogo. β(t) is an indicator of accuracy in the trust evaluation. It is checked to determine if the error is within an acceptable control limit. The value improves as it approaches zero. An experiment of interest is examining how trust is changed to consider the cases in which some factors are missing, such as feedback factor or motivation factor, and so on. Table 4 gives the scenario parameters of this simulation. To clearly illustrate the simulation results, a normal configuration with 3000 peers is developed as the baseline for comparison. A small portion of the baseline consists of bad peers, i.e., P B = 20%. Thus there are % = 600 dynamic peers in this configuration. The percentage of honest FRs is set to 80%. This percentage of HFRs reflects that the community is a relative good community (i.e., with fewer bad FRs). In Table 4, P1 makes a description of which only two trust factors are considered in trust evaluation. In scenario A of P1 (P1.A), the historical trust factor and feedback trust factor are considered, and the weight of each factor is 0.5. In P1.B, only the historical trust factor and availability-based trust factor are considered, and the weight of each factor is 0.5. By the same token, P2 makes a description of which only three trust factors are considered in trust evaluation, and P3 makes a description of which four trust factors are considered. P4 make a description of which all five trust factors are considered. In P4.A, each of the five weights is 0.2. In P4.B, the weights are computed by Algorithm 1. Fig. 6 draws the experimental result of β(t) with different trust factors. Clearly, the number of trust factors has a direct impact on Fig. 6. Simulation results with different numbers of trust factors. Table 5 The results under different values of the situation parameter λ. λ = 0.5 λ = 0.6 λ = 0.7 λ = 0.8 λ = 0.9 λ = 1.0 β(t) the accuracy of the trust model. In Fig. 6, if the simulator uses the trust model with all five trust factors, then the value of β(t) is the smallest one among eight scenario parameters. With such a rich set of trust factors, superior accuracy of trust evaluation can be achieved. From an application point of view, the computing process of the multiple trust factors needs more overhead, which will affect the overall performance of the trust system. However, in view of the significant improvement in the security and credibility of the P2P system, a small additional overhead can be negligible Comparison of accuracy Based on the experimental results arising from different values of the situation parameter λ in Algorithm 1, the experimental environment is a more stable community, in which only small part of the peers are malicious (MFR + EFR + CFR = 20%), and 80% of SPs always provide stable service. Table 5 summarizes the experimental results, which are obtained under a relatively stable community. At λ = 0.6, β(t) has the optimum value. Therefore, in the later experiments, λ is set to 0.6 as the basic value for the situation parameter. Fig. 7 is the experimental result under a relatively stable environment. In the simulation, the total percentage of malicious FRs is 20%, and the total percentage of BSPs is also 20%, which indicates that the community is a relatively good community (i.e, with fewer malicious peers). From Fig. 7, all three models have relatively stable performance within 2000 time-steps, even if their β(t) are changed from 0.13 to This reflects that the three models play well when facing the few number of malicious peers. Under real network environments, most peers are good. Therefore, from a practical point of view, all three models can meet the application requirements. Fig. 8 shows the comparison of the results of β(t) under a malicious community. In the simulation, the total percentage of malicious FRs is 50%, and the total percentage of BSPs is 80%, which indicates that the community is a terrible environment. Fig. 8 shows that, in a malicious environment, our trust model still has robust service capability, and its β(t) is equal to From Figs. 7 and 8, the trust model presented here shows a more stable performance than the other two models, as we expected.

9 X. Li et al. / J. Parallel Distrib. Comput. 71 (2011) Mean Absolute Deviation, MAD Successful Service Percent (%) HFR=80%, MFR=10%, EFR=5%, CFR=5% SRF=0.2, SDF=0.2, DPP= Fig. 7. Comparison of β(t) values in a relatively stable community. 80 Fig. 9. Simulation results under an idle and stable environment Mean Absolute Deviation, MAD Successful Service Percent (%) HFR=80%, MFR=10%, EFR=5%, CFR=5% SRF=0.8, SDF=0.2, DPP=0.2 Fig. 10. Simulation results under a busy and stable environment. Fig. 8. Comparison of β(t) values in a malicious community Comparison of adaptability In general, the dynamics of P2P networks are caused by (1) peer dynamism, i.e., all peers can randomly join or leave the networks; (2) SP dynamism, i.e., an SP can dynamically change its identity between good service and bad service; and (3) service dynamism. In a busy P2P system, there are more service requests than in an idle system. In the simulator, three parameters are used to show the dynamics of the simulated P2P system [12]: (1) Service requesting frequency (SRF [0, 1]). After a random time for each peer, it sends out a service request to an SP. The higher is the SRF, the more service requests are sent out. (2) Service dynamic factor (SDF). After a random time (20 time-stamps in the simulation), an SP oscillates to provide either good or bad service. (3) Dynamic peer percentage (DPP). This indicates the number (DPP P D ) of peers that are unstable. Any peer is free to leave or join the system at any moment. A high successful service percentage (SSP) reflects that the system has good adaptability. Thus, we use SSP to evaluate the adaptability of these trust models. Assuming that G( t) is the total number of good services counted by the simulator in period t, and S( t) is the total number of service requests in t, SSP ϕ( t) is defined as: t G( )t t=1 ϕ( t) = 100%. (26) t S( t) t=1 In the experiments, the configurations are set as HFR = 80%, MFR = 10%, EFR = 5% and CFR = 5%, which is in accordance to a real P2P system. In a real P2P system, most peers are honest (HFR = 80%), thus only a small part of the peers are malicious. According to the four network environments, the related problems are discussed: (1) idle and stable environment, (2) busy and stable environment, (3) idle and high dynamic environment, (4) highly busy and dynamic environment. First, the case of an idle and stable environment, where the dynamic factors are SRF = 0.2, SDF = 0.2 and DPP = 0.2, is observed. Fig. 9 shows that in this case, the three models exhibit good robustness in providing successful service, in which the values of ϕ( t) exceed 90%. However, the ϕ( t) of the proposed model is slightly higher than that of the Peer Trust and Satsiou models. Fig. 10 shows the simulation results under a busy but stable environment, where the dynamic factors are SRF = 0.8, SDF = 0.2, and DPP = 0.2. In this network environment, the ϕ( t) of Peer Trust decreased by 8%, and that of the Satsiou model

10 846 X. Li et al. / J. Parallel Distrib. Comput. 71 (2011) Successful Service Percent (%) Successful Service Percent (%) SRF=0.2, SDF=0.8, DPP=0.8 HFR=80%, MFR=10%, EFR=5%, CFR=5% Fig. 11. Simulation results under an idle and dynamic environment. HFR=80%, MFR=10%, EFR=5%, CFR=5% SRF=0.8, SDF=0.8, DPP=0.8 Fig. 12. Simulation results under a busy and dynamic environment. declined by 2%. The decrease in the ϕ( t) value in the proposed model is less than 1%, which reflects that it is more robust than the other two models under a busy and stable environment. To study the adaptability under a highly dynamic environment, the service dynamic factor (SDF) and dynamic peer percentage (DPP) are set to 0.8 in the next group of simulations. Fig. 11 shows that in an idle and high dynamic environment, where SRF = 0.2, SDF = 0.8, and DPP = 0.8, the proposed model still has the highest adaptability, and its ϕ( t) reaches 95%. However, with the increase in DPP and SDF, the adaptability for the Peer Trust and Satsiou models significantly decrease. This decrease is clear for Peer Trust, in which the ϕ( t) sharply dropped to below 85%. When SRF = 0.8, the P2P network is not only a busy system, but also a highly dynamic one. Fig. 12 plots the simulation results under this environment, where SRF = 0.8, SDF = 0.8, and DPP = 0.8. In the simulation, the performance of each model has an obvious decrease. However, compared with Peer Trust and Satsiou models, the model presented here still has higher adaptability under such a highly dynamic environment. From a comparison of these results, the trust model in this study is found to have a more robust adaptability both in the stable network community and in the dynamic network community. The main reason for this difference is that in the Peer Trust and Satsiou models, subjective methods were used to weight the trust factors. These do not capture the complexity and adaptability of the trust evaluation process. Consequently, they may result in misinformation and preclude an accurate evaluation of trustworthiness. The model presented here uses innovative WMA OWA combinatorial algorithms to weight the multiple trust factors. They overcome the limitation of the weight assignment in the other two models. Therefore, the effect of the adaptive weighting method on the accuracy of the trust evaluation represents a substantial improvement of the trust evaluation. As a whole, the results of this model, used with multiple trust factors, are much better than those models with simple trust factors. 6. Conclusion and future work P2P computing or networking is a distributed application architecture that partitions tasks or work loads between peers. Peers are equally privileged, equipotent participants in the application. To encourage resource sharing among peers and combat malicious peer behavior, trust management is essential for peers to assess the trustworthiness of others and to interact selectively with more reputable ones. Without an efficient trust management facility, peers will have little incentive to contribute their computing or bandwidth resources. The peers may hesitate to interact with unknown peers due to the concern of receiving corrupted or poisoned files or being exploited by malware. This paper proposed an innovative P2P trust model with multiple trust factors based on WMA OWA combination algorithms. The contributions beyond existing approaches are: (1) multiple factors are incorporated to reflect the complexity of trust; (2) the properties (weights) of these factors are dynamically assigned by WMA OWA combination algorithms. This model surpasses the limitations of existing approaches, in which weights are assigned subjectively. We have shown that our model yields very good results in many typical cases, and the proposed mechanism is robust against various complicated environments. However, there are still some open issues as our future work. 1. First of all, we are looking for ways to make the approach more robust against malicious behavior, such as collusion among peers. We are also interested in combining trust management with intrusion detection to address concerns of sudden and malicious attacks. 2. Another open problem is how to accurately evaluate the trustworthiness of newly joined peers with only few feedback reports and how to motivate more users to submit their feedbacks to the trust evaluation model. The selection of an optimal configuration for many design parameters of our proposed solutions is also an important question to be studied in future. 3. 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Systems Man and Cybernetics 18 (1998) [32] R.R. Yager, Induced aggregation operators, Fuzzy Sets Syst. 137 (1) (2001) [33] Y. Zhang, Q. Ji, Active and dynamic information fusion for facial expression understanding from image sequences, IEEE Trans. Pattern Anal. 27 (5) (2005) [34] R. Zhou, K. Hwang, Powertrust: a robust and scalable reputation system for trusted peer-to-peer computing, IEEE Trans. Parallel Distrib. Syst. 18 (5) (2007) [35] Q. Zhu, X. Gui, Study on the method of active deployment of soft-sensors in grid monitoring system, Journal of Chinese Computer Systems 28 (9) (2007) Xiaoyong Li is an associate professor of computer science at Beijing University of Posts and Telecommunications. He received his Ph.D. Degree in computer science major from Xi an Jiaotong University in As the first author, he has published more than 40 journal papers and obtained five patents and three software copyrights. In 2009, he was awarded outstanding graduate in Shaanxi Province. His current research interests mainly include network computing and trusted systems. Now he is in charge of a project of the National Nature Science Foundation of China (No ), and a project of the Chinese Universities Scientific Fund under Grant No. BUPT 2009RC0201. Feng Zhou is a full professor of the School of Computer Science and Technology, Beijing University of Posts and Telecommunications, China. He is Director of the Center of Computer Architecture (CCR) at Beijing University of Posts and Telecommunications University. His research interests include mobile internet, embedded computing and communication protocols. He is the author and co-author of a large number of papers published in journals and conference proceedings. He is also a committee member of Information Storage Technology, China Computer Federation. Xudong Yang is a full professor of the School of Computer Science and Technology, Beijing University of Posts and Telecommunications, China. He is Vice Director of the Center of Computer Architecture (CCR) at Beijing University of Posts and Telecommunications University. His research interests include Internet of Things (IOT), mobile internet, and embedded computing. He has published more than 20 papers in international journals and conferences.