## 2 Message Replication in OppNets for Sensed Data Collection
### Impact of High Degrees of Spatial Locality
Knowledge about \(N\), the total number of nodes in the network, is required to compute: UMVUE's total number of message replicas existing in the network; and \(L\), the replication quota for fixed-quota replication techniques. UMVUE estimates \(N\) by counting unique IDs of encountered nodes. Unfortunately, this may be too costly for resource constrained nodes as it requires large storage and frequent lookup operations. Also, it may take long for this method to converge, especially in networks comprising of disjointed communities. Furthermore, UMVUE relies on the assumption that nodes are assigned IDs of the same pattern. In Smart City scenarios however, node IDs may not be of the same pattern, considering that they may be from different communities, regions or sub-networks. [PERSON] et al. [72] show that in an independent and identically distributed (IID) uniform mobility, the value of \(L\) for a required expected delay can be determined as a function of only \(N\). The authors propose a method of determining \(N\) through inter-contact time statistics, that is, if nodes are assumed to perform independent random walks. This method converges faster than ID-counting, since the only requirement, which is sufficient inter-contact time samples, may come from nearby nodes. However, nodes do not show location preference under IID uniform mobility and these estimations have not been investigated under a more realistic mobility model such as WDM. WDM increases reality by introducing spatial locality in node movement, which allows nodes to reveal different levels of location preference. Higher chances of message loss  
With different number of message copies and varying amounts of progress made in the network, the order in which they are transmitted and dropped needs to conform to their priority. Although many strategies for determining these orders exist, desirable results are realized only when they are in accordance with the message replication technique. Hence, some message replication techniques (e.g., [PERSON] et al. [49] and [PERSON] et al. [55]) are complemented with buffer management policies, which often consist of rules for queuing messages, dropping messages or both. In order to create room in node buffers, most replication techniques utilize the first-in-first-out (FIFO) dropping policy in which the message that was received first is dropped first, while others drop messages with higher hop  
Figure 8: Average difference between the sending nodes’ and receiving nodes’ forwarding utilities for messages traversing 0, 1, 2 and 3 regions, under (**a**) low (**b**) medium and (**c**) high degree of spatial locality, with PRoPHET using fixed-quota replication (L = 8). count (e.g., [PERSON] et al. [49]) or less remaining TTL (e.g., [PERSON] et al. [55]). The idea is that there is a higher probability of having more copies of such messages in the network and dropping them is unlikely to impact significantly on their delivery. However, in Smart City scenarios where user movement exhibits high degrees of spatial locality, dropping such messages may have significant impact on throughput. Since fewer nodes travel across multiple local districts [62] (i.e., regions), related messages are likely to be delivered through more number of hops and may need to stay longer in node buffers (cf. Figure 9). Hence, with the existing dropping policies, messages traversing longer distances tend to be dropped before arriving their destination. Sub-optimal message copies  
The results in Figure 10 indicate that a fixed quota may cause some messages to be under-replicated (i.e., generating less copies than required) and others over-replicated (i.e., generating more copies than necessary) under high degrees of spatial locality. Depending on the location of source and destination nodes, some messages may require more quota to guarantee delivery, while others may require less [28].