## 5 Experimental Results  
Assume that \(N_{s}\) sensors are uniformly distributed over a square region in two-dimensional space. Parameters for the random waiting timer, number of sensors, and ratio of transmitting range \(R\) to the side length \(l\) of the square, _R/l_, are investigated to provide a simulation-based study of the proposed schemes. for the DASA scheme, the parameters (detailed in Section 3.3) for the experiments are given by \(C=100\), \(\lambda=10\), \(\alpha=0.5\), and \(\beta=1.5\). The first set of experiments illustrates two examples of generating a sensing round with the CASA approach and the DASA approach, respectively. According to the procedures of the CASA approach, as shown in Figure 6, the clusterhead selects a 2-hop cluster member and a relay node, say sensors 46 and 21, to initiate the round generation. For approximately minimizing the overlap of sensing coverage, sensors having no connectivity with sensor 46 may be selected as the round group member. By following the data gathering strategy in Section 3.2, sensors 46, 25, and 30 are chosen to form a sensing round. In Figure 7, based on the settings of the DASA approach, a 2-hop cluster member with a shorter random waiting timer, say sensor 73, broadcasts a message to its neighbors and a 1-hop cluster member, say sensor 11, broadcasts a message to claim its being a relay node for sensor 73. When receiving the broadcasting messages, the neighboring sensors extend their waiting times to reduce the sensing area redundancy and further prepare for being the round group members in the following sensing rounds. Thus, with the data gathering strategy as described in Section 3.3, sensors 73, 46, and 30 form a sensing round. Observe that, as shown in Figures 6 and 7, the proposed approaches avoid heavy sensing redundancy and maintain sufficient sensing coverage. Given a cluster topology, the second set of experiment studies the impact of parameter settings on  
Figure 6: An example of generating a sensing round with the CASA approach. network performance. With varying the number of sensors \(N_{S}\), Figure 8 shows the number of sensing rounds \(N_{RG}\) versus \(\alpha\) for \(\beta=1\) (left) and \(N_{RG}\) versus \(\alpha\) for \(\beta=1.5\) (right). Given a value of the parameter \(\beta\), the number of sensing rounds \(N_{RG}\) decreases with increasing value of the parameter \(\alpha\), which implies that the operation of updating the waiting time when receiving the round ID broadcast from the neighboring sensors may rearrange the sensing schedule and decrease \(N_{RG}\). Similarly, Figure 9 depicts the number of sensing rounds \(N_{RG}\) versus \(\beta\) with \(\alpha=0\) (left) and \(N_{RG}\) versus \(\beta\) with \(\alpha=0.5\) (right). Given \(\alpha=0\) (i.e. without applying the update formula), the number of sensing rounds \(N_{RG}\) increases slightly with increasing value of the parameter \(\beta\). This is because the setting of the parameter \(\beta\) may allow nearby sensors to work on different rounds such that the sensing redundancy may be suppressed. On the other hand, by applying the update formula (e.g. \(\alpha=0.5\)), the parameter \(\alpha\) may be a dominant factor affecting the number of sensing rounds \(N_{RG}\) since this mechanism allows the sensors to observe the behaviors of their nearby sensors and make adjustments in their waiting times. Therefore, the update operation of the waiting time described in (4) may play a critical role in scheduling management. Furthermore, in order to describe the interaction between the parameter settings and the network performance, Figures 10 and 11 illustrate the average coverage and average sensing overlap per round versus \(\alpha\) with \(\beta=1.0\) (left) and with \(\beta=1.5\) (right), respectively. Observe that in Figure 10, given \(\beta\) the average coverage per round increases with increasing value of \(\alpha\).