# 3D Void Handling Geographic P2P-RPL for Indoor Multi-Hop IR-UWB Networks
## 2 Related Works
### Greedy Forwarding and Void Handling Point-to-Point RPL in 3D Indoor Environments
Define \(d(uv)\) as the distance between nodes \(u\) and \(v\). Let \(n\) be the neighbor with the shortest distance to \(d\) out of \((N(c)\cap R(c)^{\complement})\). if\(d(nd)<d(cd)\)then  Send a unicast packet to \(n\). \(c\longleftarrow n\) else  Send a broadcast packet to \(N(c)\). \(c\longleftarrow N(c)\)  end if  end while  end while
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Figure 5: GVA-P2P-RPL. (**a**) The network node connectivity, where the gray nodes are void nodes that have no neighbor node closer to the destination than themselves. From (**b–g**), P2P-DIO messages are greedily forwarded when possible and locally broadcast when void nodes are encountered. The solid arrows are greedily forwarded P2P-DIO messages, and solid dashed arrows are locally broadcast P2P-DIO messages. (**e**) The final P2P route chosen by the destination as the solid arrows. P2P-RPL uses the standard trickle timer algorithm [8] to effectively flood P2P-DIO messages throughout the network. Because all network nodes participate in the route discovery, P2P-RPL generally reaches the destination quickly. In GVA-P2P-RPL, only a few nodes in the whole network participate in the route discovery, which reduces the routing overheads but results in longer route discovery time. The purpose of the standard trickle algorithm is to effectively suppress redundant message transmissions [21]. P2P-RPL requires such a suppression mechanism to be strictly in action because all nodes participate in the route discovery. In 3D environments, the number of participating nodes in P2P-RPL increases as the dimensionality is expanded from 2D. Compared to P2P-RPL, GVA-P2P-RPL significantly reduces redundant messages, especially when P2P-DIO messages are greedily forwarded. In such cases, the suppression mechanism is unnecessary, as no contention exists. Using this advantage, we present the adaptive trickle timer (ATT) in 3D GVA-P2P-RPL, which uses a shorter minimum trickle timer interval \(I_{min}\) parameter value by adaptively changing the listen-only periods to reduce the long route discovery time. The DODAG configuration option [9] field, a RPL control message option that distributes configuration information of the current DODAG, is modified to piggyback a halved \(I_{min}\) value in implementation. With ATT, GVA-P2P-RPL completes its route discovery procedure much faster than P2P-RPL without the need for additional nodes. The shortened listen-only periods provide better P2P-DIO message collision avoidance among one-hop neighbors, too. Figures 6 and 7 show how ATT shortens the route discovery time and provides collision avoidance effects compared to P2P-RPL. P2P-RPL, using the standard trickle algorithm, reaches the destination \(d\) when node \(n_{9}\) first transmits its P2P-DIO message as shown in Figure 7. P2P-RPL more likely faces P2P-DIO message collisions as a large number of nodes participate in contentions and listen-only periods are relatively long. GVA-P2P-RPL, using the same standard trickle algorithm, reaches the destination also when node \(n_{9}\) first transmits its P2P-DIO message as shown in Figure 8. The P2P-DIO message transmission of node \(n_{9}\) takes more time in the latter case because P2P-RPL utilizes all network nodes in the route discovery process. Therefore, P2P-RPL has a far better chance of propagating P2P-DIO messages earlier than GVA-P2P-RPL with the standard trickle algorithm. To reduce such delays, GVA-P2P-RPL with ATT in Figure 9 has a shorter \(I_{min}\) parameter value and adaptively shortens its listen-only periods, leading to a higher probability of passing P2P-DIO messages earlier than before. All simulations and example cases in this paper use a half-length \(I_{min}\) value in ATT, compared to the standard trickle. The detailed algorithm of ATT is shown in Algorithm 2. With this approach, GVA-P2P-RPL reaches the destination when node \(n_{9}\) first transmits its P2P-DIO message, and hence the route discovery completes faster than P2P-RPL.