# Cooperative Data Collection Mechanism Using Multiple Mobile Sinks in Wireless Sensor Networks
## 3 Network Environment and Problem Formulation
### Network Environment  
Given a monitoring region \(\mathbb{R}\), this paper considers a mobile wireless sensor network that consists of a set of \(n\) sensor nodes \(S=\{s_{1},s_{2},s_{3},\cdots,s_{n}\}\) randomly deployed in \(\mathbb{R}\). There are \(k+1\) mobile sinks \(M=\{m_{0},m_{1},\cdots,m_{k}\}\) aiming at collecting data from all sensor nodes. The \(k\) mobile sinks, including \(m_{1},\ldots,\ m_{k}\), aim to collect data from all sensors in their own local area while the \(m_{0}\) treated as the global mobile sink aims to collect data from the \(k\) mobile sinks. The global mobile sink \(m_{0}\) is initially arranged at the location of static sink. The function of static sink is to upload the data to the Internet for further processing. Assume that the communication ranges of all mobile sinks and sensor nodes are identical. Each mobile sink has rich power or is supported with an energy harvesting system. In addition, the paper assumes that all mobile sinks are aware of the locations of all sensor nodes and their own location information. Among the \(k\) mobile sinks, there is a leader, denoted by \(m_{ leader}\), which is in charge of executing the proposed data collection mechanism and broadcasting the results to all mobile sinks.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Studies**} & **Number of** & **Path** & **Data Collection** & **Mobile Sinks** \\  & **Mobile Sink** & **Construction** & **Latency** & **Cooperation** \\ \hline
[14] & single & O & long & \(\times\) \\
[15] & single & O & long & \(\times\) \\
[16] & multiple & O & short & \(\times\) \\
[17] & multiple & \(\times\) & long & O \\
[18] & multiple & \(\times\) & short & \(\times\) \\
[19] & multiple & \(\times\) & short & \(\times\) \\
[20] & multiple & O & short & O \\ The proposed CDCA & multiple & O & short & O \\ \hline \hline \end{tabular}
\end{table}
Table 1: Comparison between the proposed CDCA and existing mechanisms.  
All sensor nodes periodically generate one data packet in every time period \(t\) and the packet must be delivered to the sink. This paper aims to develop a data collection mechanism which partitions the sensors into \(k\) disjoint sets \(T=T_{1}\), \(T_{2},\ldots,T_{k}\) and assigns \(i\)-th set \(T_{i}\) to mobile sink \(m_{i}\). Since the mobile sink \(m_{i}\) aims to collect data from all sensor nodes in \(T_{i}\), it establishes a tour passing through all sensors in \(T_{i}\). However, for some large-scale applications, it is time consuming for data collection, which might lead to the problem of buffer overflow. To prevent from this situation, the leader should select some sensors and only visit them in \(T_{i}\). Let \(P_{i}=\left\{p_{i,1},p_{i,2},p_{i,3},\cdots,p_{i,k_{i}}\right\}\) be the set of \(k_{i}\) selected CPs in \(T_{i}\). In each round, the mobile sink \(m_{i}\) will visit each \(p_{i,j}\) and collect data from each \(p_{i,j}\) and then return to the root of \(T_{i}\). Let \(\hat{\pi}_{i}\) represent the path passing through all CPs \(p_{i,j}\) in \(T_{i}\) and the path length of \(\pi_{i}\) is \(|\pi_{i}|\). In the next subsection, the problem formulation of this paper will be presented.  
Figure 1 illustrates an example of several CPs and five mobile sink in a rectangular region. In Figure 1, the red circles represent the static sink whereas the black circles denote the selected CPs. The sensor nodes have been partitioned into five groups, and each group organizes a path by \(m_{i}\). In each path, every mobile sink \(m_{i}\) moves along the established path, which passes through all CPs in \(T_{i}\) to collect data. The global mobile sink \(m_{0}\) will leave from the static sink, move along the constructed path and collect all data stored in root \(T_{i}\). Then the global mobile sink \(m_{0}\) goes back to the static sink.