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In this section, we present our scheme for message replication in DTNs. We call the scheme as hybrid, as we are also considering the occasional presence of MANET like environments in our network, when for example, the pedestrians stay closer to each other for longer durations, or the nodes are communicating with road side base stations.

Suppose a node has a message " that is requested by node N. At a time instant Š, the node makes contact with a relay node . At this occasion, the node has to decide whether or not to replicate " on node in a hope that node might carry forward replica to node N. The node will replicate " on node , if and only if, node ’s utility value is greater than node ’s utility value for the replica " . The aforementioned utility value depends on: (a) the probability that a node will deliver message to destination before the life time expiry of message, and (b) the probability that the node will stay in contact with a message’s destination for a duration greater than time required to transfer the message. If node exhibits greater values of (a) and (b) as compared to the node , the replica will be transferred to node , and subsequently node will delete the replica from local buffer. Otherwise, after transferring replica to node , the node will retain local copy of replica. The motivation behind such approach is to remove the excessive replicas from the network to conserve storage by placing replicas on nodes that appear to be

Let _, be the time the message " has spent waiting in buffers since creation, and _‰ be the life time of message " . We denote to be a random variable representing the additional time that " might wait before reaching destination. Then, we define message’s utility as the probability that the message will be delivered to the destination N before the life time expiry [6.5], given as Q Y• _, 9 ; _‰€. This can also be represented as:

Q YŽ ; ‰ ,•. (6.1)

In (6.1), we need to find the probability that additional wait time of replica is less than remaining life time. As the message is transferred only during an opportunistic contact, the probability in (6.1) is same as the probability that the node will make a contact with node N, before the expiry of message. We call such probability as utility value of node for the current message:

Q, Y•‹ /Š0 ; ‰ ,€ . (6.2)

In the above equation, ‹ /Š0 is mean inter-contact time between nodes and N at time Š. The network nodes are cumulating their inter-contact time information in the form of bounded time-series data. Moreover, a few nodes (such as buses) are following partially scheduled mobility patterns. Therefore, we can apply exponential smoothing to forecast the value of inter- contact time between the node and node N, as given below:

‹ /Š0 /1 d0•†8_{∙ 3•0€ 9 5 d ∙ /1 d0}•† †8

•†8 7’

∙ Œ • € (6.3)

In the above equation, the parameter 0 ! d ! 1 is time-series smoothing constant, Œ • € is inter-contact time of node with N at time instant , 3•Š€ is the base value of recursion, and

‹ /Š0 is the forecasted inter-contact time node with N. As the mobile devices are limited in

Therefore, we set a limit on the maximum number of entries stored per node in the form of a sliding time window 1 ! ! ~, where the entry at Š ~ represents the latest meeting. The more recent entries within the range [1, ω€ must be given higher weightage than the others to ensure information freshness. Therefore, we assign progressively decreasing weights to the older entries, such that, as the entry becomes older it contributes less to the overall forecasting. The base case value of recursion 3•Š€ computed at time instant Š is given as:

3•0€ 1_{# ∙ 5 Œ} •Š €

:†8 7’

(6.4)

The above equation is the simple moving average of latest # entries of the inter-contact times Œ between and N. Let _R be the time required to transfer a message " when two nodes make contact. Assuming that neighbour node has sufficient buffer space, the message will be successfully transferred to neighbour if and only if the contact duration of sender and receiving neighbour is greater than the required message transfer time _R . Therefore, we compute the utility “_, Y• _R ; /Š0€, indicating the probability that the message will be transferred between node and N in contact duration . To compute the aforementioned probability, we need to find the estimated value of contact durations between nodes and N. By replacing with Œ in (6.3) and (6.4), we get the forecasted value of contact duration /Š0. Fig. 6.2 illustrates the flow of our replica placement scheme HSM.

As reflected from Fig. 6.2, the procedure attempts to remove the redundant copies of messages from nodes’ buffers, and attempts to allocate replicas on more appropriate nodes in terms of contact durations and inter-contact times with the destinations.