When sensors are overly deployed, one may want to put some sensors into sleep mode to reduce the level of coverage. One may further reduce the transmission power of sensors to reduce the network connectivity. As far as we know, the combination of these mechanisms has not been studied in the literature. In this subsection, we
explore these two possibilities based on the foundations developed in Section 3.
The basic idea is as follows. Suppose that we are given a sensor network that is kinit-covered and kinit-connected (this can be decided by Theorem 4 and the protocol in Section 4.1 ). If such levels of coverage and connectivity are beyond our expecta-tion, we propose a protocol to modify the network to ks-covered and kc-connected such that kinit ≥ ks ≥ kc ≥ 1. First, in Section 4.2.1, we present a sleep protocol to reduce the network to ks-LDPC (which means ks-covered and ks-connected) by putting some sensors into sleep mode. Then, in Section 4.2.2, a power control pro-tocol is presented to reduce the network to kc-LDPC. This results in a ks-covered, kc-connected network because reducing the transmission power of a sensor will not affect its sensing range.
4.2.1 The Sleep Protocol
In this protocol, each sensor only needs to know the locations and sensing regions of its two-hop neighbors that are in the active state. Suppose that the network is kinit-LDPC. The purpose of this protocol is to put some sensors into the sleep mode such that the network is at least ks-LDPC, where kinit ≥ ks. For each sensor Sx
that intends to go to sleep, it will execute the following procedure:
1. For each sy that is a direct neighbor of sxsuch that sx and sy have overlapping in their sensing regions, let p(sx, sy) be the perimeter of sy’s sensing range that is covered by sx’s sensing range. Sensor sxthen calculates the level of coverage of p(sx, sy). If the level of coverage is at least ks+1, then sx is a candidate.
2. If sx is a candidate for each sy which is a direct neighbor of sx, then sx is eligible to go to the sleep mode. Then sx sends a SLEEP message to each of its neighbors and waits for their responses by setting up a timer T .
3. Each sy which is a neighbor of sx can reply a GRANT-SLEEP message to sx
if it has no pending grant currently. Otherwise, a REJECT-SLEEP message is replied. Note that to avoid erroneously putting too many sensors into sleep and to maintain synchronization, a sensor can have at most one pending grant at one time. Specifically, a GRANT-SLEEP message is clear from the pending status once a CONFIRM/WITHDRAW message is received (see step 4 below).
Figure 4.1: An example of the Sleep Protocol. Sensor sx is a candidate with respect to sensor sy.
4. If sx can collect a GRANT-SLEEP message from each of its neighbors, sx
broadcasts a CONFIRM message to its neighbors and then goes to sleep. If any REJECT-SLEEP message is received or the timer T expires, sxbroadcasts a WITHDRAW message to its neighbors.
Note that in the above step 1, sx needs to know all direct neighbors of sensor sy. Since sx and sy are direct neighbors, these sensors are sx’s two-hop neighbors.
Fig. 4.1 shows an example of the above protocol. If sx intends to go to sleep, it will check the perimeter p(sx, sy) (shown in thick line). Since p(sx, sy) is also covered by sz and sw. If the target coverage is ks=1, then sx is a candidate with respect to sy. Also note that the timer T is necessary because we assume an unreliable broadcast.
4.2.2 The Power Control Protocol
The power control protocol is aim to reduce the transmission power of sensors to save energy. Since this operation does not affect the sensing unit(s), the sensing capability of sensors (and thus the level of coverage of the network) is not reduced.
Suppose that the network is ks-LDPC. The purpose of this protocol is to reduce some sensors’ transmission power to make the network at least kc-LDPC, where ks
≥ kc. This results in a ks-covered, kc-connected network.
This protocol assumes that each sensor knows the information of its two-hop neighbors. For sensor sx which intends to reduce its transmission powers, it executes the following procedure:
1. Let sy be the direct neighbor of sx that is farthest from sx. Sensor sx then
REJECT
Figure 4.2: A power control protocol example.
computes the perimeter coverage of the segments p(sx, sy) and p(sy, sx). If both segments are at least (kc + 1)-LDPC, sx is allowed to conduct power control. Then sx sends a DISCONNECT message to sy.
2. On receipt of sx’s disconnecting request, if sy has no pending disconnecting request currently, sy can reply a GRANT-DISC message to sx. Otherwise, a REJECT-DISC is replied. Note that a DISCONNECT message is clear from the pending status once a GRANT-DISC /REJECT-DISC message is received.
3. If a GRANT-DISC message is received, sx can reduce its transmission power such that only its second farthest direct neighbor is covered and go back to step 1 to try to further reduce its transmission power. Otherwise, a REJECT-DISC message will stop sx from reducing its transmission power.
Note that in the above protocol, sensor sy may not be able to reduce its trans-mission power even if sx successfully receives sy’s granting message. This is because sy may need to maintain connectivity with other neighbors that are farther away than sx.
Fig. 4.2 shows an example. Initially, the network is 2-covered and 2-connected
(i.e., kinit=2). We only consider sensor sx and its two neighbors sy and sz. We will disconnect the communication link between sx and its farthest direct neighbor, sy, by power control. First, sx examines its intersection with sy. Both segments p(sx, sy) and p(sy, sx) are 2-LDPC, so sx sends a DISCONNECT message to sy, which will agree by replying a GRANT-DISC message. Then sx can reduce its transmission power to the level that can reach the next farthest neighbor sz. Next, sx examines its intersection with sz. Both segments p(sx, sz) and p(sz, sx) are 2-LDPC, so sx sends a DISCONNECT message to sz. Suppose that sz has a pending disconnecting request currently, it will reply a REJECT-DISC message to sx. Then sxstops its procedure. Note that in the above scenario, symay not necessarily reduce its transmission power even if it grants sx’s request to reduce power. For example, sy may not be able to reduce its power because sw wants to remain connected with sy. In order to maintain connectivity with sw, sy can still reach sx. This results in an asymmetric link between sx and sy (i.e., the transmission power of sx cannot reach sy, but the transmission power of sy can reach sx). Therefore, only sx can benefit from the transmission power.