## Main Design of DERM
### Geographic Routing for EO-DRA
#### 4.2.1 Greedy Forwarding for EO-DRA  
We assume a packet originated from source node \(s\) is relayed to the current forwarding node \(i\). Based on the mobility pattern (\(P\), \(v_{M}\), \(tp\)), the recorded sink location at a certain time, the node can roughly compute the current sink location and further estimate the travel path \(L\) within the delay constraint \(D_{s}\). Note that the recorded location and its corresponding time are initialized with \(P_{init}\) and \(t_{init}\), respectively, and might be updated as introduced in Section 4.3. Then, the node chooses a best forwarding node at the current time from its neighbors. Considering both link qualities and locations of nodes, we introduce a comprehensive routing metric named the remaining ETX (\(rETX\)), which can be estimated as:  
\[rETX_{ij}=ETX_{ij}+\left\lceil\frac{dist(j,L)}{Avg\widetilde{Pro(h_{i}+1)}} \right\rceil\cdot Avg\widetilde{ETX}(h_{i}+1),\quad(h_{i}\geq 0), \tag{4}\]  
where \(rETX_{ij}\) represents the expected remaining ETX of the packet at node \(i\) when choosing neighboring node \(j\) as the next-hop forwarder. \(ETX_{ij}\) can be calculated as the reciprocal of the PRR between nodes \(i\) and \(j\). \(dist(j,L)\) is the shortest distance from node \(j\) to the polyline \(L\). \(h_{i}\) is the hop count from the source to the current node \(i\). \(Avg\widetilde{Pro(h_{i}+1)}\) and \(Avg\widetilde{ETX}(h_{i}+1)\) denote the estimated average single-hop packet progress and ETX of the first \(h_{i}+1\) hops, respectively. The single-hop packet progress (SPP) towards \(L\) when the packet is forwarded from \(i\) to \(j\) is defined as  
\[Pro_{ij}=dist(i,L)-dist(j,L). \tag{5}\]  
We first calculate the actual average SPP and ETX of the elapsed \(h_{i}\) hops [40]:  
\[AvgPro(h_{i})=\frac{(h_{i}-1)\cdot AvgPro(h_{i}-1)+Pro(h_{i})}{h_{i}},\quad(h _{i}\geq 1), \tag{6}\]  
\[AvgETX(h_{i})=\frac{(h_{i}-1)\cdot AvgETX(h_{i}-1)+ETX(h_{i})}{h_{i}},\quad (h_{i}\geq 1), \tag{7}\]  
where \(Pro(h_{i})\) and \(ETX(h_{i})\) represent the actual SPP and ETX of the \(h_{i}th\) hop forwarding, respectively. \(AvgPro(0)\) and \(AvgETX(0)\) at the source node can be set as zero because they are useless in our computation. Then, we have  
\[Avg\widetilde{Pro(h_{i}+1)}=\frac{h_{i}\cdot AvgPro(h_{i})+Pro\widetilde{(h_{ i}+1)}}{h_{i}+1},\quad(h_{i}\geq 0), \tag{8}\]  
\[Avg\widetilde{ETX}(h_{i}+1)=\frac{h_{i}\cdot AvgETX(h_{i})+ETX\widetilde{(h _{i}+1)}}{h_{i}+1},\quad(h_{i}\geq 0), \tag{9}\]where \(\mathit{Pro}(\widetilde{h_{i}+1})\) and \(\widetilde{ETX(h_{i}+1)}\) are the expected SPP and ETX of the \((h_{i}+1)th\) hop forwarding, and can be estimated as the average of SPPs and ETXs of all \(i\)'s neighbors with a positive progress, respectively. Therefore, we deduce the best forwarder \(j\) satisfying following conditions:  
\[\left\{ \begin{array}{l}\min\limits_{j\in N(i)}\ rETX_{ij},\\ s.t.\ Pro_{ij}>0,\end{array} \right. \tag{10}\]  
where \(N(i)\) denotes the neighboring node set of \(i\). Based on the new metric, the packet will be forwarded towards the destination region in an efficient way. If the packet arrives at an RN located in the destination region, it will be buffered until being collected by the sink. Moreover, if the RN finds that its buffered data cannot be uploaded to the mobile sink within the limited communication time, it will delegate the excess data to a neighboring RN that has spare communication time and can be visited within the delay constraint. If no such an RN can be found, the data will be transferred along the adjacent route (constructed in Section 4.4) to seek a delegation node. We take Figure 3 as an example to illustrate the forwarding process. The source node \(s\) has a data packet required to be delivered within the delay constraint \(D_{s}\). It looks up the target sink in its sink list, and estimates that \(M\) will travel from current location \(A\) to location \(C\) within the delay constraint. Thus, the travel path \(L\) is polyline \((A,B,C)\).