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Dempster Shafer theory is a mathematical theory of evidence used to combine different pieces of information to calculate the probability of an event. It is a generalization of the Bayesian theory of subjective probability.
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to as its behavior Bij and is a binary value: {cooperate, don t cooperate}. Node i uses Tij to make a decision as follows: Bij = cooperate don t cooperate Tij Bij Tij < Bij (13.4)
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Discussions. Like CONFIDANT, RFSN also treats misbehaving and faulty nodes the same way. The rationale is that a node that is uncooperative has to be excluded irrespective of the cause of uncooperative behavior. In RFSN, nodes are allowed to exchange only good reputation information. Also, in RFSN, only direct reputation information is propagated. This prevents the information from looping back to the initiating node. However, this increases the memory overhead slightly since a separate data structure has to be maintained for direct reputation. 13.6.5 DRBTS DRBTS stands for distributed reputation and trust-based beacon trust system. This model was proposed by Srinivasan, Teitelbaum, and Wu recently to solve a special case in location-beacon sensor networks. DRBTS is a distributed model that makes use of both rst-hand and second-hand information. It has two types of nodes: beacon node (BN) and sensor node (SN). It is symmetric from the BN perspective but asymmetric from the SN perspective. This is because beacon nodes are capable of determining their location and must pass this information to the sensor nodes. The dif culty is that without knowledge of their own location, a sensor node has no way of telling if a beacon node is lying to it. DRBTS enables sensor nodes to exclude location information from malicious beacon nodes on the y by using a simple majority principle. DRBTS addresses the malicious misbehavior of beacon nodes. Information Gathering. In DRBTS, information gathering is addressed from two different perspectives: the sensor node perspective and the beacon node perspective. From a beacon node perspective, DRBTS uses a watchdog for neighborhood watch. When an SN sends a broadcast asking for location information, each BN will respond with its location and the reputation values for each of its neighbors. The watchdog packet overhears the responses of the neighboring beacon nodes. It then determines its location using the reported location of each BN in turn, and then it compares the value against its true location. If the difference is within a certain margin of error, then the corresponding BN is considered benign, and its reputation increases. If the difference is greater than the margin of error, then that BN is considered malicious and its reputation is decreased. From a sensor node perspective, there is no rsthand information gathered by sensor nodes through direct observations. They rely completely on the second-hand information passed to them from nearby beacon nodes during the location request stage.
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DRBTS also includes a method by which BNs can send out location requests disguised as SNs, in case of low network activity. However, unlike CONFIDANT, DRBTS does not differentiate rst-hand information into personal experience and direct observation. Information Sharing. DRBTS does make use of second-hand information to update the reputation of its neighboring nodes. However, information sharing is only with respect to BNs. SNs do not share any information since they do not collect any by virtue of their own observation of their neighborhood. In DRBTS, nodes are allowed to share both positive and negative reputation information. This is allowed to ensure a quick learning time. Information Modeling. Let BN j respond to a SN s request. Then BN i, in the range of j updates its reputation entry of j using the direct observation as follows. RNew = 1 RCurrent + (1 1 ) ki ki (13.5)
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where = 1 if the location was deemed to be truthful and = 0 otherwise, and 1 is a weight factor. To use second-hand information, assume Bj is reporting about BN k to BN i. Now BN i rst performs a deviation test to check if the information provided by BN j is compatible. |RCurrent RCurrent | d ji ki (13.6)
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If the above test is positive, then information provided is considered to be compatible and the entry Rik is updated as follows. RNew = 2 RCurrent + (1 2 ) RCurrent j,i j,i k,i (13.7)
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But, if the deviation test in equation 13.6 is negative, then j is considered to be lying and its reputation is updated as follows. RNew = 3 RCurrent j,k j,k (13.8)
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Equation (13.8) ensures that nodes that lie are punished so that such misbehavior can be discouraged. Decision Making. Decisions are made from the sensor node s perspective. After sending out a location request, an SN waits until a predetermined timeout. A BN has to reply before the timeout with its location information and its reputation ratings for its neighbors. Then, the SN, using the reputation ratings of all the responding BNs,
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