## 3 Dynamic Sensor Scheduling Algorithms
### Distributed Adaptive Scheduling Algorithm (DASA)  
The Setting of Waiting Timer  
The distributed method operates much like the CAWT [27] in utilizing a random timer. As the clusterhead broadcasts a message to start the scheduling assignment, sensor \(i\) initializes a random waiting timer with a value \(WT_{i}^{(0)}\):  
\[WT_{i}^{(0)}=\frac{1}{N_{hop}}\cdot T_{i}\cdot\beta^{N_{b}^{(i)}}, \tag{3}\]which is related to the cluster topology and the neighbor information. Note that \(T_{i}\) is a sample from the distribution \(C\)+\(\lambda\)\(\cdot\)\(U(0,1)\), where \(C\) and \(\lambda\) are positive numbers, which are used to specify the sampling range of the waiting time, and \(U(0,1)\) is a uniform distribution. \(N_{hop}\) is the number of hops from the clusterhead to the cluster member, \(N_{b}^{(i)}\) is the number of neighboring cluster members of sensor \(i\), \(\beta\) is a positive number with \(1<\beta\). The rationale for the settings in equation (3) is that, due to the overlap of sensing area in a cluster, the coverage overlap of a 1-hop cluster member is usually larger than that of a 2-hop cluster member. This suggests that a 2-hop cluster member may be a good candidate to initialize a round group. On the other hand, a 1-hop cluster member may choose to wait and join the round group later. Furthermore, a cluster member with more neighbors may have a lower priority to execute the sensing task since its sensing area may be covered by the nearby cluster members. If the random waiting timer expires (i.e. \(WT_{i}=0\)), then sensor \(i\) broadcasts a message proclaiming that it is a good candidate to be a group member, which also serves to notify its neighbors that it has a higher priority for the sensing task. For its neighboring sensor \(j\), the update formula of the random waiting timer may be given by:  
\[WT_{j}^{(k+1)}=(1+\alpha)\cdot WT_{j}^{(k)}, \tag{4}\]  
where \(WT_{j}^{(k)}\) is the waiting time of sensor \(j\) at time step \(k\) and \(0<\alpha\). The setting of \(\alpha\) can be attributed to the fact that the neighboring nodes receiving the broadcasting message increase their waiting timers such that they may work in different rounds and the sensing redundancy may be suppressed in each sensing round. Figure 2: The procedures of selecting a pair of distributed gateways in Scenario 1 (a) and Scenario 3 (b). The Scheduling Scheme  
The message for communication among the cluster members consists of: (1) the ID of the sending sensor, (2) the round ID of the sending sensor, and (3) the relay round ID of the selected relay sensor. At the beginning, the round ID and the relay round ID of each sensor is one and zero, respectively. Based on equation (3), 1-hop cluster members set longer waiting times compared with 2-hop cluster members. When a 2-hop timer expires, the 2-hop cluster member broadcasts a message with the initial round ID 1 and selects its 1-hop parent cluster member as a relay node from the cluster topology. Thus, the selected relay node records its relay round ID and will execute the data dissemination in that sensing round. Since a 1-hop cluster member can report the collected information to the clusterhead directly, relay nodes are not necessary in this case. In order to reduce the overlap of the coverage in each sensing round, the neighboring nodes receiving the broadcasting message update their waiting timers and increase their round IDs by 1 such that they may work in different rounds. In order to maintain the correct round ID information when receiving multiple messages among neighboring nodes, the ID updating strategy may be described as follows. Given a cluster member with round ID \(u\) and a message sent by a cluster member with round ID \(v\), the cluster member with round ID \(u\) may update its round ID by \(u=v+1\) if the round ID \(u\leq v\). Otherwise, the received message is ignored. Accordingly, an update criterion for the sensing node can be derived:  
\[\mathrm{Round}\ \mathrm{ID}\ \ u=\left\{