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This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

A reliable energy-efficient multi-level routing algorithm in wireless sensor networks is proposed. The proposed algorithm considers the residual energy, number of the neighbors and centrality of each node for cluster formation, which is critical for well-balanced energy dissipation of the network. In the algorithm, a knowledge-based inference approach using fuzzy Petri nets is employed to select cluster heads, and then the fuzzy reasoning mechanism is used to compute the degree of reliability in the route sprouting tree from cluster heads to the base station. Finally, the most reliable route among the cluster heads can be constructed. The algorithm not only balances the energy load of each node but also provides global reliability for the whole network. Simulation results demonstrate that the proposed algorithm effectively prolongs the network lifetime and reduces the energy consumption.

Wireless sensor networks (WSNs) have become a vibrant and exciting research and development area in recent years and can be used in many different applications, including battlefield surveillance, home security, smart spaces, environmental monitoring, and target tracking [

A wireless sensor network consists of a large number of tiny, low-powered, energy-constrained sensor nodes with sensing, data processing and wireless communication components. Sensor nodes in WSNs are small battery powered devices with limited energy resources, and their batteries cannot be recharged once the sensor nodes are deployed. Therefore, minimizing energy consumption is an important issue in the design of WSNs protocols. The energy is also the major consideration in designing the routing protocol. Cluster routing is an effective solution in reducing energy consumption, prolonging the lifetime of the networks and providing network scalability [

In recent years clustering routing technique has been widely investigated in the context of WSNs [

Our main contributions include

Fuzzy production rules are mapped into fuzzy Petri nets for representation of a network topology.

A cluster head selection mechanism is developed. This mechanism considers the residual energy, number of neighbors, and centrality of each node and uses fuzzy Petri nets for cluster heads selection.

Using fuzzy Petri nets and a reasoning mechanism, a reliable multi-hop routing algorithm, which creates routes among cluster heads, is developed.

The resulting reliable energy-efficient multi-level routing (REEMR) protocol is implemented and evaluated through simulations.

The remaining of the paper is organized as follows: In Section 2 we review the relevant work. In Section 3, background on fuzzy Petri nets for the representation of network topology is provided. In Section 4, the REEMR protocol, which includes a clustering algorithm and a reliable routing algorithm among cluster nodes, is presented. In Section 5, we evaluate the performance of REEMR protocol and compare it to several protocols. Finally, Section 6 concludes the paper.

The cluster routing technique involves sensor nodes in multi-hop communication within a cluster, and then the cluster head aggregates the data to decrease the number of transmitted messages to the base station.

Low-energy adaptive clustering hierarchy (LEACH) [

To overcome the limitations of LEACH, a fuzzy logic approach to cluster head election [

A generalized fuzzy logic based energy-aware routing [

Power-efficient gathering in sensor information systems (PEGASIS) [

In a distributed energy-efficient clustering algorithm (DEEC) [

Energy-efficient cluster formation protocol (EECF) [

Fuzzy Petri nets (FPN) [

_{1}, _{2}, . . ., _{n}

_{1}, _{2}, . . ., _{m}

^{∞} is the input function, a mapping from transitions to bags of places;

^{∞} is the output function, a mapping from places to transitions;

_{1}, _{2}, . . ., _{n}

Fuzzy Petri nets are different from ordinary Petri nets due to the features of fuzzy production rule systems that are different from discrete event systems [

The enabling and firing rules in FPN are given as follows:

A transition ^{•}

Enabled at marking

Fuzzy Petri nets may depict the fuzzy relationships between many propositions. Suppose a set _{1}, _{2}, . . ., _{n}_{j}_{k}

The fuzzy Petri net model for _{1} fires from its input place (_{1}) into an output place (_{2}). The certainty factor is 0.9. The truth degree value in the output place (_{2}) of _{1} is calculated as 0.72 (by 0.8× 0.9) when _{1} fires. According to the value, the node with higher residual energy may be elected as the cluster head.

A composite fuzzy production rule denotes its antecedent or consequence portion contains AND or OR connector. The composite fuzzy production rules can be classified into the following types:

_{j1} AND _{j2} AND . . . AND _{jn}_{k}_{j}

_{j}_{k1} AND _{k2} AND . . . AND _{kn}_{j}

_{j1} OR _{j2} OR . . . OR _{jn}_{k}_{j}

_{j}_{k1} OR _{k2} OR . . . OR _{kn}_{j}

In the following, the first three types of rules are mainly employed, and the different fuzzy variables are combined into a composite fuzzy production rule.

REEMR consists of a clustering algorithm and a reliable multi-hop routing algorithm, which are employed to divide sensor nodes into clusters and construct a reliable route for cluster heads, respectively.

To balance energy consumption of nodes, REEMR constructs clusters at each round similar to LEACH. To get a cluster head election chance, three fuzzy sets and different fuzzy production rules for knowledge representation are considered. The fuzzy variables that are used in the fuzzy production rules are defined as follows.

Residual Energy: The remaining energy of each node. The more residual energy the node has, the more data is processed and transmitted, and the longer lifetime of the node is.

Number of Neighbors: The number of neighbor nodes of each node. The number of neighbors affects in some way for proper cluster head election. It is more reasonable to select a cluster head in a region where the node has more neighbors.

Centrality: The sum of the distances between the node and its neighbors represents how central the node is to the cluster. The more central the node is to a cluster head, the more is the energy efficiency for it to transmit the data through the cluster head.

The node centrality is the sum of distances between a node and its neighbor nodes. The above fuzzy variables are input fuzzy variables for the fuzzy production rules, and the output variable is the node’s cluster head election chance. The trapezoid functions are employed as the membership functions corresponding to the fuzzy linguistic variables [

The fuzzy variable “residual energy” has three fuzzy sets—high, medium and low, and its membership function is shown in

The fuzzy variable “number of neighbors” has three fuzzy sets—many, medium and few. The possible fuzzy quantization of the range [

The fuzzy variable “centrality” has three fuzzy sets—far, medium and close, and its membership function is shown in

The outcome to represent the node’s cluster head election chance has five fuzzy sets—smallest, small, medium, large, and largest, and its membership function is shown in

These membership functions can be set according to the practical need. To calculate a chance to be a cluster head, a typical form of fuzzy production rules for cluster head election is exemplified as follows.

Since each input variable has 3 linguistic states, the total number of possible fuzzy inference rules is 3 × 3 × 3 = 27. According to the composite fuzzy production rule Type 1 in Section 3, a typical fuzzy Petri net model for the above fuzzy production rule is shown in _{1}, _{2}, _{3} are weights, and the node’s cluster head election chance is the output fuzzy variable. Assuming the truth degrees of the proposition “the residual energy is very high”, the proposition “the number of neighbors is few” and the proposition “the centrality is close” are 1, 1 and 0.9, respectively. Assuming the weights of the arcs are 0.6, 0.3 and 0.1, the threshold is 0.5, and the certainty factor is 0.9. When the transition _{4}) = (1 × 0.6 + 1 × 0.3 + 0.9 × 0.1) × 0.9 = 0.891.

From the fuzzy Petri net model, each node can get the fuzzy variable _{i}_{i}

If a sensor node does not receive the message ADV_Head before the time _{j}

The clustering algorithm:

_{i}_{i}

_{i}_{i}

_{i}

if (_{i}

_{i}

else if (_{i}_{j}

_{i}_{j}

_{i}_{j}

else if (_{i}

Among the _{i}_{l}

_{i}_{l}

endif

endwhile

After the clusters are formed, cluster heads aggregate the data traffic and forward it to the base station through a multi-hop route. Consequently, energy efficient and robust multi-hop routes among cluster heads should be constructed. As cluster heads change frequently, in this paper, we use fuzzy Petri nets and the reasoning mechanism to propose a reliable multi-hop routing among cluster heads.

In _{1} is 1.0.

Certainty factor and threshold value of every transition in the FPN model evaluate the reliability between each neighboring cluster head. The higher the certainty factor, the more reliable the link between two cluster heads. If the degree of reliability _{i}_{i}_{i}_{j}_{j}_{i}

According to _{1} needs to communicate with the base station _{10}, a reliable route needs to be constructed. This problem can be solved by developing a fuzzy reasoning algorithm based on fuzzy Petri net model. Assume that the truth degree of the cluster head _{1} is given. The places _{1} and _{10} are called the starting place and the goal place, respectively. If the truth degree of _{1} is greater than the corresponding threshold of its transition, it will flood a route request (RREQ) packet to its IRS. Otherwise, it will not flood the RREQ for the reason that this route is not reliable for a short time, which reduces the control overhead and provides a more reliable route. If a cluster head receives a RREQ packet from its neighbor and it is not the goal place, it will record the neighbor ID and forward the packet to all of its neighbors. Therefore, after a while, some relay cluster heads will receive at least one RREQ packet sent from the starting place. If the RREQ packets arrive at the goal place _{10}, _{10} chooses the route with the largest degree of reliability as its the most reliable route. Finally, _{10} will reply a Reply packet of the most reliable route to the starting place _{1}. The Reply control packet travels along the reverse path of the RREQ packet. Then multi-hop route among places is constructed.

The fuzzy reasoning algorithm can be expressed as a sprouting tree [_{k}_{k}

_{s}_{s}_{s}

_{j}

comptruth(_{s}

begin

if(IRS(_{s}

exit

else

for all _{k}_{s}

if _{s}

a transition is enabled,

create a new leaf node (_{k}_{k}

and create a new branch labelled _{s}_{s}

to (_{k}, α_{k}_{k}_{s}

if (_{k}_{j}

_{k}

else

suppose _{s}_{k}

call comptruth(_{s}

endif

endif

endfor

endif

end

The branch from _{s}_{j}_{j}_{1}), (_{j}_{2}), . . ., (_{j}_{l}_{l}_{1}, _{2}, . . ., _{l}_{j}

Consider the topology in _{1} broadcasts a RREQ packet to its neighbors _{2}, _{4}, and _{5}, until the base station receives the RREQ packet. The base station _{10} selects a reliable route using the fuzzy reasoning algorithm After performing the knowledge inference, a route sprouting tree can be illustrated in

REEMR is a distributed algorithm, where the nodes decide to be cluster heads according to the local neighbor nodes.

PROOF. At the beginning of each round, every node first broadcasts a message ADV_E to calculate the centrality and the number of its neighbor, and the maximal total ADV_E overhead is

PROOF. For a place _{i}

In REEMR, the nodes with higher residual energy, more neighbor nodes and less centrality are more likely to be elected as cluster heads. The node whose degree of reliability is less than the corresponding threshold of transition will not flood any data. Therefore the route is reliable and is not easily broken.

We conducted several experiments to evaluate the performance of REEMR protocol and compare it to other protocols.

We assume

All the sensor nodes are stationary after the sensors are deployed.

All the sensor nodes are time synchronous.

All the sensor nodes are homogeneous and power limited, and they have exclusive identification.

All the sensor nodes are equipped with power control capabilities to vary their transmitted power.

The communication link is symmetrical. The nodes can estimate the distance between the transmitter and receiver by the received signal strength indication (RSSI).

We assume a radio hardware energy dissipation model, similar to those used in [_{elec}_{fs}d^{2} or _{mp}d^{4}, depends on the distance to the receiver and the acceptable bit-error rate.

In WSNs, the cluster heads need to aggregate and fuse the data, and the energy for data aggregation parameter is set as _{DF}

To illustrate the performance of the proposed algorithm, the simulations are performed in Matlab. Each round consists of a clustering phase, multi-hop routing phase and data transmission phase. In the clustering phase, a set of cluster heads is elected and the remaining nodes become cluster members. In multi-hop routing phase, multi-hop route is set up. In the data transmission phase, each cluster member node sends a fixed amount of data to its cluster head, and each cluster head aggregates the received data and then transmits to the base station by multi-hop routing.

We firstly consider a wireless sensor network with

The cluster formations of LEACH and REEMR in the same round are shown in

The network lifetime is the most important performance metric for WSNs. In [

As LEACH randomly chooses the cluster heads and their distribution is not uniform, some cluster heads may have too many cluster member nodes. Therefore, these cluster heads may consume much energy and die too soon. MOECS considers multiple parameters such as the distance of a node to the cluster head and residual energy to select cluster heads, which help sensor nodes achieve balanced energy dissipation to prolong the network lifetime. CHEF considers the energy and local distance to choose the optimal cluster heads, which are uniformly deployed in the networks. Consequently CHEF further prolongs the lifetime of the networks than LEACH. In PEGASIS, the distance of the neighbor nodes is less than that of the cluster members and the cluster heads in LEACH, and its head only receives the data of two nodes. Consequently, PEGASIS achieves higher performance than LEACH.

The residual energy of the network also provides an estimate of the network lifetime.

Routing algorithms have been well considered as one of the effective solutions to enhance energy efficiency and scalability of wireless sensor networks. In this paper, a reliable energy-efficient multi-level routing algorithm for wireless sensor networks is proposed, which considers residual energy, number of neighbors and centrality for cluster formation which are critical for well-balanced energy dissipation of the network. REEMR employs fuzzy Petri nets to choose cluster heads and construct multi-hop routing among cluster heads by fuzzy reasoning algorithm.

Simulation results demonstrate that REEMR achieves significant energy savings and prolongs network lifetime when compared to LEACH, MOECS, CHEF and PEGASIS. Multiple parameters involved in the cluster formation process for REEMR help sensor nodes dissipate their energy at a much more balanced rate as compared to other protocols.

This work is supported by the Aero Science Foundation of China under Grants No. 20100796004 and Doctor Startup Foundation of Air Force Engineering University.

An example fuzzy Petri nets model for network knowledge representation.

Fuzzy Petri nets representation of type 1 rules.

Fuzzy Petri nets representation of type 2 rules.

Fuzzy Petri nets representation of type 3 rules.

Membership functions of the fuzzy variables.

An example fuzzy Petri nets model for a cluster head election rule.

Topology of cluster heads.

FPN model of topology of cluster heads.

The sprouting tree.

Cluster formation of LEACH.

Cluster formation of REEMR.

The network lifetime in rounds for random topology.

Mean residual energy of LEACH, MOECS, CHEF, PEGASIS, and REEMR.

Total number of data messages received at the base station.

Simulation parameters.

Initial energy per node | 2 J |

_{elec} |
50 nJ/bit |

_{fs} |
10 pJ/(bit·^{2}) |

_{mp} |
0.0013 pJ/(bit·^{4}) |

_{0} |
87 m |

_{DF} |
5 nJ/(bit· signal) |

Size of a data packet | 500 bits |