## 3 Network Model and Problem Description
### Network Model  
We consider a WSN with a mobile sink \(M\) and \(N\) static sensor nodes deployed in a monitoring area, as shown in Figure 1. Each node has the same transmission radius \(R\). The sink periodically travels along a fixed path with a constant speed \(v_{M}\), and knows its own mobility pattern, which is uncontrollable.  
The sink path can be represented by a sequence of endpoints and turning points:  
\[P=(P_{0},P_{1},\,P_{2},...,P_{n}). \tag{1}\]Note that, if \(P\) is a round-trip path, the points sequentially accessed by the sink in one cycle are \(P_{0},P_{1},...,P_{n},...,P_{1},P_{0}\). If \(P\) is a cyclic path, those would be \(P_{0},P_{1},...,P_{n},P_{0}\). We use \(tp\) to denote the path type (i.e., round-trip or cyclic). Therefore, the sink mobility pattern including the sink path, the speed, and the path type can be characterized by a triple of (\(P\), \(v_{M}\), \(tp\)). Let \(\Omega(P)\) denote the direct communication region where the nodes' distances to the sink path \(P\) are less than the communication radius \(R\). Those nodes belonging to \(\Omega(P)\) are called _potential rendezvous nodes_ (RNs for short). We assume that each RN has enough storage space for buffering the received data. This is feasible as the development of the memory chip technology [33].  
When the sink is moving, it sends out Beacon messages in regular intervals to discover nearby nodes. Each node receiving the message updates the Beacon timestamp in its sink list. If the timestamp has not been updated for a period of time, the sink will be regarded as out of the communication range.  
Some other related assumptions are listed as follows:  
1. Location awareness: All nodes know their physical locations and exchange them with their neighboring nodes in the initial phase. The locations can be obtained by GPS modules outdoors. In indoor environments, many existing methods (e.g., range-based and fingerprint-based techniques) can also achieve satisfactory localization accuracy [44].
2. Unreliable links: The wireless communication is unreliable due to channel fading, interference, etc. The MAC (Media Access Control) layer measures the link quality by calculating the Packet Reception Ratio (PRR) [45]. To ensure the reliability of one-hop packet delivery, the ARQ (Automatic Repeat reQuest) mechanism is adopted, by which a packet encountering transmission failures will be retransmitted until being acknowledged. For instance, in CC2530, the receiver can acknowledge a packet with the software ACK [46].
3. Time synchronization: The clocks of sensor nodes are synchronized, which can be achieved by GPS modules or a practical time synchronization method in WSNs such as FTSP (Flooding Time Synchronization Protocol) [47] or Glossy [48].
4. Data transmission time: The wireless signal travels much faster than the mobile sink. Therefore, compared to the delay constraint and the travel time of the sink, the time for multi-hop transmissions and data uploading from RNs to the sink is negligible [14]. Furthermore, when the RN finds that its cached data cannot be delivered within the communication time with the sink, it will transfer the excess data to a delegation node that can be visited before the deadline (see Section 4.2).