## 3 System Model Analysis
### Computing Task Processing Model  
To reduce the computational time, another BS, i.e., node \(b_{j},\forall\mathsf{j}\in\mathcal{B}\), is required to complete the task in collaboration and in parallel. Thus, a task partition policy is needed to select proper BSs to complete the service. The task must be intelligently computed into sub-tasks in parallel. The BS, i.e., node \(\mathsf{b_{i}},\forall\mathsf{i}\in\mathcal{B}\), maintains a portion of the task and transmits the rest of the task to the nearest BS, i.e., node \(b_{j},\forall\mathsf{j}\in\mathcal{B}\). Hence, node \(b_{i}\) and \(b_{j}\) compute the task in parallel. After completing the task, node \(\mathsf{b_{i}}\) transmits the result to the previous BS, node \(b_{i}\), and node \(\mathsf{b_{i}}\) combines these results and transmits the combined result to the SN node, \(n_{N}\). The cooperative computing decision is also considered between BSs and represented by \(V_{b(T_{s})}\). If \(V_{b(T_{s})}=0\), the \(b_{j},\forall\mathsf{j}\in\mathcal{B}\) will not cooperate with the desired \(b_{j},\forall\mathsf{i}\in\mathcal{B}\). Otherwise, if \(V_{b(T_{s})}=1\), the BSs will cooperate with each other. As the ship (considered BS node \(b_{j}\)) moves from one place to another, it might be out of the communication range of node SN. If the BS moves out of the transmission range of node SN, node SN broadcasts a message to another BS node, \(b_{j}\), in the coalition, and then the node \(b_{j}\) restarts to seek an alliance by broadcasting its information to other BSs. The information contains the identity of the node \(b_{j}\). When a BS node, \(b_{k},\mathsf{k}\in\mathcal{B}\), and \(\mathsf{k}\
eq\mathsf{i}\
eq\mathsf{j}\) receive the identity and find that it is closest to the node \(b_{j}\), then node \(b_{k}\) transmits the information with its own identity to node \(b_{j}\), and the two nodes, \(b_{j}\) and \(b_{k}\), form an alliance. The task is divided and allocated to the two BS nodes, and the computation result is transmitted to the SN node, then the SN node stops broadcasting the message to its BS node. Here, we assume a threshold time interval to reduce the service time in our proposed model. After the  
Figure 1: Network model for cooperative communication. threshold time expires, the SN node stops broadcasting without waiting for the feedback from node \(b_{i}\). At this time, if the SN node receives the feedback from node \(b_{k},\text{k}\in\mathcal{B}\), and the SN rebroadcasts the offloading task to the BS node \(b_{k},\text{k}\in\mathcal{B}\) in its coalition. The BS needs to divide the task intelligently into sub-components. The sub-components are divided in such a way that a minimum amount of time is needed to finish the total task. For instance, the computational tasks offloaded within a \(T_{s}\) are divided into two sub-components, one for node \(b_{i},\text{i}\in\mathcal{B}\) and one for node \(b_{j},\text{j}\in\mathcal{B}\), respectively. We denote node \(b_{i}\), \(\text{i}\in\mathcal{B}\) as the receiver BS and node \(b_{j},\text{j}\in\mathcal{B}\) as the cooperative BS. The divided portions of the computational task are denoted by \(T_{t_{i}}\) and \(T_{t_{j}}\), respectively. Hence, \(A_{t}=A_{t_{i}}+A_{t_{j}}\). Thus, we have the following cases if \(V_{b(T_{s})}=1\) and \(V_{n(T_{s})}=1\), respectively. 1. \(A_{t}=A_{t_{i}}\) and \(A_{t_{j}}=0\): In this case, the computational task is only offloaded to node \(b_{i},\text{i}\in\mathcal{B}\) in a \(T_{s}\). Hence, node \(b_{i},\text{i}\in\mathcal{B}\) is both received and a cooperative BS. 2. \(A_{t_{i}}>0\) and \(A_{t_{j}}>0\): In this case, the computational task is offloaded to both received and cooperative BSs. The node \(b_{i},\text{i}\in\mathcal{B}\) and node \(b_{j},\text{j}\in\mathcal{B}\) process the divided components of the task in parallel. The combined result is delivered from node \(b_{i},\text{i}\in\mathcal{B}\) to the SN node which offloaded the task. 3.