A key assumption of past duty cycle scheduling works is that they assume all sensor nodes are already deployed randomly around targets. As mentioned in Chapter
1, this does not guarantee sufficient number of sensor nodes around each target to ensure energy neutral operation. Moreover, unnecessary deployment of sensor nodes increases network cost. To this end, determining the locations to place sensor nodes before deriving a duty cycle is important.
The forthcoming sections review past works on the node placement problem. Specifically, it starts with the works in non-rechargeable, aka, conventional, WSNs. It then outlines the node placement works that consider the energy harvesting ca- pability of sensor nodes.
2.2.1
Conventional WSNs
As highlighted in Chapter 1, sensor nodes in conventional WSNs have no ability to replenish their energy supply. Therefore, the goal of these works is to minimize the deployment cost given a network lifetime, or to maximize network lifetime with limited number of sensor nodes. More examples can be found in [37].
Patel et al. [60] propose to place sensor nodes to meet one of four objectives: minimum number of nodes, minimum deployment cost, minimum energy consumed or maximum lifetime. They formulate each of the objectives as a ILP. A common constraint is to ensure all targets are monitored at a given coverage level. In the objectives for minimizing number of nodes, deployment cost and minimum energy consumed, the constraints include coverage, connectivity and a desired network lifetime. In particular, in order to minimize deployment cost, they consider different nodes: sensing only nodes, relays and base station; each with different deployment cost. Moreover, they aim to minimize the consumed energy by minimizing the number of relay nodes. Lastly, they maximize network lifetime, given the number of sensor nodes, subject to coverage and flow conservation constraints.
Cheng et al. [61] first propose a non-linear program with an objective to max- imize network lifetime subject to a fixed number of sensor nodes, coverage, energy and connectivity constraints. They then consider a scenario where sensor nodes with depleted energy can be replaced. They propose a function to calculate the cost of replacing an individual sensor node corresponding to its capability such as sensing, relaying and sink. They then revise the non-linear program with an objective to minimize the total cost of replacing sensor nodes.
Liu et al. [62] propose an approximation algorithm to minimize network cost, given a required network lifetime. Their algorithm also ensures coverage and network connectivity. Specifically, they first determine the locations to place sensing and relaying nodes for each target. They then remove redundant sensor nodes after all targets have a path connecting the base station/sink. They prove their algorithm
requires at most max{2l − m + 2, 3} times more sensor nodes than the optimal solution, where m is the number of targets and l is the targets within the sensing range of the base station.
The authors of [63] aim to place the minimum number of sensor nodes to ensure targets are detected with a given probability. They divide the sensing field into cells. Each cell provides a certain ‘coverage level’. The authors also define the ‘miss probability’ of a target to be its required event detection probability minus the ‘coverage level’ provided by sensor nodes covering it. They then provide a heuristic that places sensor nodes in cells with the highest miss probability until all sensor nodes have the required detection probability.
There are also works that consider placing heterogeneous sensor nodes. One aim is to minimize the total cost required to construct a WSN. The authors in [64] consider the various sensing capabilities of sensor nodes. These capabilities include monitoring temperature, sound, radioactivity and gas level. They also assume each target location has a specific sensing task. The objective is then to design an ap- proximation algorithm to minimize the total cost, e.g., the number of sensor nodes, whilst maintaining a given coverage level for each sensing task. They prove that their algorithm has a cost of at most 1.58 + times the optimal, where is a small value.
Wu et al. [65] aim to maximize the average detection probability in a sensing field by placing sensor nodes with different sensing capabilities or cost. They as- sume a sensor node with a large sensing range and higher detection quality to be more expensive. The design constraint is deployment budget. They show that such a problem is NP-complete and propose a genetic algorithm. This algorithm first calculates the coverage level provided by each type of sensor node at each location. After that, in order to achieve the required detection probability and budget, it uses operators such as crossover, mutation and translocation to determine the locations to place sensor nodes.
harvesting nodes. Consequently, once a node exhausts its energy, the resulting WSN is useless. Moreover, they do not consider deploying multiple sensor nodes in the same location. This is critical in energy harvesting WSNs due to varying recharging rates and duty cycling. To this end, the next section reviews node placement works that consider energy harvesting WSNs.
2.2.2
Energy Harvesting WSNs
In energy harvesting WSNs, existing works are focused on improving network cover- age or connectivity. Their objectives are to minimize sensor nodes subject to a given coverage level, or ensuring connectivity. Another research direction is to use radio frequency identification (RFID) technology, where a RFID reader/sensor node is used to recharge/monitor tags/targets. These works, however, have not considered equipping RFID reader/sensor nodes with energy harvesting capability, or indeed the readers/sensor nodes have an unlimited energy supply.
Eu et at. [66] consider placing solar energy harvesting sensor nodes to monitor a one-dimensional sensing space. For example, sensor nodes placed along a railway track to monitor vibration. The objective is to minimize the number of relaying nodes to forward data from one source node to one base station/sink. However, they do not consider complete targets coverage and energy neutral operation. Moreover, it is unclear how their solution can be extended to arbitrary sensing fields.
In [67] and [68], the authors consider targets placed uniformly in a sensing field, each of which is monitored by a set of sensing nodes. They also consider the random recharging rate at different locations. The objective is to place the minimum number of relay nodes to achieve network connectivity whilst ensuring relay nodes harvest large amounts of ambient energy. They prove the problem is NP-hard and propose a 12.4-approximation solution. This solution places relay nodes at locations with large amount of data to be forwarded and has a high energy harvesting rate. However, they assume sensor nodes are already deployed around targets. Moreover, they do
not consider deploying a sufficient number of sensor nodes to achieve energy neutral operation.
In RFID technologies, e.g., [69] and [70], they consider targets coverage with two objectives. The first one is to place RFID reader/recharging nodes to ensure tags/targets have a reliable energy source. Another one is to plan the trajectory of one or more mobile RFID reader/recharging nodes to replenish the energy of tags/monitor targets. However, as mentioned, these works do not consider energy harvesting capability of RFID readers/sensor nodes.