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Wireless sensor networks require energy-efficient data transmission because the sensor nodes have limited power. A cluster-based routing method is more energy-efficient than a flat routing method as it can only send specific data for user requirements and aggregate similar data by dividing a network into a local cluster. However, previous clustering algorithms have some problems in that the transmission radius of sensor nodes is not realistic and multi-hop based communication is not used both inside and outside local clusters. As energy consumption based on clustering is dependent on the number of clusters, we need to know how many clusters are best. Thus, we propose an optimal number of cluster-heads based on multi-hop routing in wireless sensor networks. We observe that a local cluster made by a cluster-head influences the energy consumption of sensor nodes. We determined an equation for the number of packets to send and relay, and calculated the energy consumption of sensor networks using it. Through the process of calculating the energy consumption, we can obtain the optimal number of cluster-heads in wireless sensor networks.

Wireless sensor networks (WSNs) are organized by wireless nodes for monitoring the existing conditions in a specific area. Sensor nodes consists of three basic devices: a sensor that observes changes in the surroundings, a processor that handles the sensing data, and a wireless transmitter/receiver set that sends processed data to a base station (BS) that collects, analyzes and sends the sensing data to an external network [

The cluster-head is in charge of transmitting sensing data from its own local cluster, as well as collecting and compressing multiple data before sending them to a sink node. They consume more energy than other sensor nodes as a result of these additional tasks. Therefore, it is desirable that all sensor nodes should take on the role of a cluster-head, equally and randomly. Based on the number of cluster-heads, the size of a local cluster may change. It is important to construct adaptive clusters because the number of cluster-heads has an effect on the energy consumption of the cluster-head and the sending of member nodes’ data. As more cluster-heads become available and the smaller the size of a local cluster, the smaller the amount of packets required to be sent will be. With additional cluster-heads, however, there is an increase in the number of packets needed for cluster-heads to communicate to a sink or base station, therefore increasing the energy consumption as a result of clustering. In this paper, we determine the energy variation rate of whole sensor networks based on the energy consumption of a local cluster (intra-cluster) and between local clusters (inter-cluster) using equations. Further, based on this result, we propose an optimal number of cluster-heads in wireless sensor networks based on multi-hop routing.

A typical application that sensor node networks support is the monitoring of some remote environment. Since individual nodes’ data in a sensor network are often correlated, the end user does not require all the redundant data, but rather some high-level fraction of the data that accurately describes the events occurring in the environment. To achieve this, LEACH [

This paper is based on the following assumptions: all sensor nodes can communicate with other nodes in a possible communication radius, R [

The radio model for a sensor node’s energy consumption assumes that all of the nodes maintain a minimum level of successful communication. There are different energy calculations between transmitting and receiving data. Generally, a radio model defines the energy consumption of a transmitter-receiver as _{elec} J/bit_{amp} J/bit

_{Tx}

In _{R}

The clustering energy consumption of sensor networks is divided into two categories: intra energy generated in a local cluster and inter energy generated when a cluster-head sends the aggregated data to a sink. In each category, the total energy consumption of the networks, _{cluster}_{ch}_{member}

For calculation, we assume the sensor networks are organized as follows: the size of the network is A × A. Sensor nodes are equally distributed over the networks. For simplicity, a cluster-head is located in middle of a local cluster as shown in

The total number of cluster-heads in a network is defined as m, therefore the area of the sensor networks is the same as the total area of local clusters which can be calculated as a^{2}π × m = A^{2}. From this, we can figure out the radius of a local cluster, ‘a’, as:

The number of nodes in a local cluster can be expressed as N/m. As shown in ^{th} ring represents the distance at the farthest nodes, ‘a’. Additionally, it represents hop counts between the cluster-head and the farthest nodes. So, nodes’ hop counts in the n^{th} ring can be described as a/R. We know the average number of sensor nodes with n^{th} hop counts as compared to the area of a local cluster within the area, which is to subtract the area of the (n−1)^{th} ring from the area of the n^{th} ring [^{th}_{avg_node}, the average number of nodes with n^{th} hop counts is:

The average number of nodes with (n−1)^{th} hop counts, (n−1)^{th}_{avg_node} is:

When nodes with n^{th} hop counts send data packets to nodes with (n−1)^{th} hop counts, the number of relay packets can be determined by dividing ^{th} hop counts in a local cluster, the average number of relay packets, _{n_Intra},

In an intra-cluster, a node’s energy consumption is divided into two types: transmission energy of own sensing data and relay energy of neighbor’s sensing data. Therefore, the average energy consumption of nodes with n^{th} hop counts, _{mem_intra}, is to add packet transmission energy, _{Trans}_{Relay}

The average number of packets which a cluster-head receives from member nodes is N/m. The energy consumption of cluster heads for aggregate packets is _{agg}_{Trans}_{ch}

Generally, a sink node is located close to the sensor network. The distance between a cluster-head and a sink is from one hop R to n^{th} node’s distance added to one hop R,

As the number of relay packets is also increased in proportion to s, in inter-clusters, the average number of relay packets, _{n_Inter}

In an inter-cluster, as the CHs can only send the packet to a sink node, we just find the relay packet energy. To achieve this, during inter-cluster transmission, the average energy consumption between a cluster-head and a sink, _{mem_inter}

Based on the clustering energy equations, we can find the average energy consumption of member nodes, _{member}

For network configuration, we assume the following network topology, as described in

We set up the size of the networks to be 100 m × 100 m, with a possible node communication radius, R, set at 5 meters. To prevent an isolated node, the number of network nodes is 400. The sensor node’s initial energy is 1 J (Joule) and the data packets of a node are 525 bytes between a cluster-head and member node, and a sink and a cluster-head. As described previously, a sink node is located outside of the sensor networks with the distance between a sink and the networks defined as R. For constant energy, we set up the transmission/receiving energy, _{elec}_{amp}^{2}. The aggregation energy per a packet, _{f}_{agg}

In an intra-cluster scenario, if there is a single cluster-head, as illustrated in

The reason for this is that the average distance between a cluster-head and member nodes is decreased. In the case of cluster-heads being more than 27% of the networks, a local cluster does not generate the relay packets, as the distance between a cluster-head and member nodes is a < R. On the other hand, the packets which a cluster-head collects from member nodes are fixed, regardless of changing the number of cluster-heads, because the total aggregated data from nodes is always 400, as seen in

In an inter-cluster, with an increase of cluster-heads, there is an increase of relay packets between a cluster-head and a sink. As illustrated in

In

In previous clustering algorithms for WSNs, they did not consider the practical transmission radius of sensor nodes for communicating with nodes in and out of clusters. All sensor nodes, however, should use the multi-hop method as they have a restricted communication radius. In multi-hop based communication, communication messages or packets in the WSNs are increased in proportion to the distance between nodes. Also, clustering algorithms are affected by the distance. In any clustering algorithm, packet delivery distance is an important issue and is influenced by the number of clusters. All this is related to energy consumption in WSNs. We need to know how many clusters are best in WSNs. Thus we propose the optimal number of cluster-heads based on changing the number of cluster-heads and the associated consumed energy. To prove this, we calculated the energy change in the total network consumption using the number of relay packets in intra-cluster and inter-cluster transmission. We found the change ratio of a cluster-head’s energy, the change ratio of intra-cluster energy, and the change ratio of inter-cluster energy based on a sensor energy model and relay packets by experiments. Therefore, we determined that a change in the number of cluster-heads affects the consumed energy of a sensor network and were thus able to determine the optimal number of cluster-heads a sensor network requires.

This work is financially supported by the Ministry of Education, Science and Technology (MEST), the Ministry of Knowledge Economy (MKE) through the fostering project of HUNIC.

Calculation model for clustering,

Intra-Cluster.

Inter-Cluster.

Energy consumption and node alive.

System parameter for network configuration.

Network size | 100 × 100 (100 m^{2}) |

Sensor nodes | 400 |

Radius of sensor nodes | 5 m |

Data packet | 525 bytes |

_{elec} |
50 nJ/bit |

_{amp} |
10 pJ/bit/m^{2} |

_{f} |
0.021 mJ |

Initial Energy | 1 J |