## 3 Reducing Transmission Overhead without Compromising Throughput
### LARep Design
#### 3.2.4 Phase 4: Message Replication Phases  
In order to present the replication mechanisms of our proposed LASnF replication technique in this section, we adopt the terminologies \"spray phase\" and \"focus phase\" from SnF [43]. In the spray phase, message replication varies with current network conditions, while in the focus phase, only messages that meet a given criterion are replicated. **Spray Phase. ** Whenever two nodes encounter each other, each one attempts to replicate a message for which the other presents a higher forwarding utility. According to Definition 2, the message may first enter the spray phase. Definition 2 (Replication in the spray phase): Any message, \(m\), that satisfies the condition \((quotaControl_{m}+w_{m})<1\) (cf. Equation (8)) is replicated and forwarded to an encountered node, irrespective of the node's forwarding utility, where \(homeWorkDist\) is the Euclidean distance between the home and work locations of the node in custody of the message. \[quotaControl_{m}=\frac{homeWorkDist}{srcDstDist_{m}} \tag{8}\]  
The \(homeWorkDist\) property ensures that the value of \(quotaControl_{m}\) is higher for nodes that often travel longer distances. This allows the equation to indicate how far away the destination node is located with respect to spatial locality. By considering spatial locality in node movement, messages carried by a node that often travels longer distances exit the spray phase sooner, since there is a higher chance of encountering nodes with much better forwarding utilities. With the \(srcDstDist_{m}\) property,the value of \(quotaControl_{m}\) decreases the farther apart the message custodian and destination node are located, while \(w_{m}\) in Definition 2 increases with more copies of \(m\) in the network. This way, while \(m\)'s current replication quota (i.e., the number of copies yet to be generated) increases with the distance between the custodian and destination, and reduces according to the progress the message has made in the network. This is because the property \(w_{m}\) not only indicates the number of \(m\)'s replicas currently available in the network, but also the cumulative forwarding utilities of the nodes that may be currently carrying the message. This allows for a more flexible quota in the spray phase that varies according to the forwarding utilities of encountered nodes. **Focus Phase. ** When the condition for the spray phase is not met (i.e., if \(quotaControl_{m}\geq 1\)), the message enters the focus phase. Messages in the focus phase are replicated based on the criterion given in Definition 3. **Definition 3 (Replication in the focus phase). **_A node \(i\) forwards to another node \(j\) one copy of a message \(m\) destined to node \(d_{m}\), if an only if \(\left[U_{j}(d_{m})>(U_{i}(d_{m})+quotaControl_{m})\right]\wedge\left[U_{j}(d_{m })>maxU_{i}(d_{m})\right]\), where \(maxU_{i}(d_{m})\) is a property in the message header that is updated to the maximum forwarding utility among the nodes that have been forwarded a copy of \(m\) in the focus phase._  
Instead of transferring \(m\) to node \(j\) when \(U_{j}(d_{m})>U_{i}(d_{m})\), including \(quotaControl_{m}\) relatively relaxes the condition for messages whose source and destination nodes are farther apart. In other words, the larger the distance between the source and destination nodes of a message, the more copies are likely to be generated, and vice versa. The second condition, \(U_{j}(d_{m})>maxU_{i}(d_{m})\), ensures that the message is replicated to nodes with increasing forwarding utilities, hence, further reducing excessive replication. Note that unlike Spray and Focus where messages that have been transferred in the focus phase are deleted from the sender's buffer, LASnF retains a copy, which may be replicated to other nodes if the proposed forwarding conditions are met. Hence, when the source and destination nodes are farther apart, more copies tend to be generated. Otherwise, a copy is generated only when a node with much higher forwarding utility is encountered.