Theoretical analysis of the lifetime and energy hole in cluster based wireless sensor networks

Abstract

Cluster based wireless sensor networks have been widely used due to the good performance. However, in so many cluster based protocols, because of the complexity of the problem, theoretical analysis and optimization remain difficult to develop. This paper studies the performance optimization of four protocols theoretically. They are LEACH (Low Energy Adaptive Clustering Hierarchy), MLEACH (Multi-hop LEACH), HEED (Hybrid Energy-Efficient Distributed Clustering Approach), and UCR (Unequal Cluster based Routing). The maximum FIRST node DIED TIME (FDT) and the maximum ALL node DIED TIME (ADT) are obtained for the first time in this paper, as well as the optimal parameters which maximize the network lifetime. Different from previous analysis of network lifetime, this paper analyzes the node energy consumption in different regions through the differential analysis method. Thus, the optimal parameters which maximize the lifetime can be obtained and the detailed energy consumption in different regions at different time can be also obtained. Moreover, we can obtain the time and space evolution of the network, from a steady state (without any death) to a non-steady state (with some death of nodes), and then to the final situation (all nodes die). Therefore, we are fully aware of the network status from spatial and temporal analysis. Additionally, the correctness of the theoretical analysis in this paper is proved by the Omnet++ experiment results. This conclusion can be an effective guideline for the deployment and optimization of cluster based networks.

Introduction

Generally, in wireless sensor networks, the sensor nodes cannot be replaced or recharged after deployed, while most applications have pre-specified lifetime requirements. For instance, the required lifetime for effective network monitoring is longer than 9 months in applications in Refs. [1], [21]. Therefore, it is of great significance for the research of sensor network lifetime.

The lifetime has different definitions in different research fields. It is defined in Refs. [10], [7] as the time when first node dies (First Die Time, FDT). Xue and Ganz [31] defines it as the time when all nodes die. In Refs. [7], [31], it is defined as the time when the amount of dead nodes reaches a specified percentage ($k\%$ Die Time, KDT), thus the time when $k=100$ is ADT and the half die time (HDT) is the time when $k=50$. Besides, in Refs. [10], [31], lifetime is defined as the network partition time (parted time, PT).

Under the condition of multiple hops, sensor nodes close to the sink have larger energy consumption because they are burdened with heavier relay traffic, and these areas are named as hotspots [10]. Nodes at the hotspots tend to die early when they deplete their energy, leading to what is called energy hole [10]. Then the nodes close to the dead nodes are required to forward the outer data, and it can further accelerate the death rate of the nodes in the region. This phenomenon is called “the Funnel Effect” [10]. Consequently, the network ends soon or becomes nonfunctioning.

We regard the research of lifetime has equal importance as that of energy hole. Actually, FDT is the time when energy hole comes into being. As energy hole goes on, it comes to the time called PT when the sink is partitioned from the network by energy hole. Finally, no more data can be delivered to the sink, which is called ADT. While the weakest region is where most energy is consumed, it is also the place where energy hole occurs [9], the size of energy hole is the same as that of the weakest region. Therefore, we can claim that the research of energy hole size as well as when and where energy hole will occur are the research of the dynamic evolution from time and space. The research on energy hole from time can help us to evaluate whether lifetime meet application requirements, so that we can maximize the lifetime by optimizing network parameters. At the same time, the research from space can help us deploy the sensor nodes that have larger initial energy or take measures to decrease the energy consumption at hotspot, and then we can get considerable increase in lifetime with a smaller cost. It is clear that how to calculate the distribution of energy hole and its evolution process from time present a guideline for network designing and planning, the energy hole can be avoided by optimizing network parameters, which is of great importance for the improvement on the network lifetime.

However, it is a challenging task to optimize the lifetime for cluster based sensor networks. First, there are many factors that impact the network lifetime and energy hole. For instance, the data gathering protocol, the cluster radius, the data gathering and aggregation rate, and various physical parameters in cluster based networks. These parameters act on or influence each other, making the theoretical analysis extremely difficult. Second, in cluster based networks, the protocol itself is quite complex and nodes work as cluster head in an alternate way with different probabilities, leading to a complex theoretical analysis of the network lifetime. Finally, there are so many cluster based network protocols which cannot enumerate, and each protocol uses different data gathering mechanisms. Thus, to determine a theoretical upper bound of the network lifetime for these protocols is extremely difficult. Therefore, Refs. [31] pointed out that it was very difficult to analyze the cluster based network lifetime in theoretical aspects.

The main objective of this paper is not to put forward a new protocol for cluster based networks, or to improve an existing clustering protocol to prolong network lifetime. Instead, it aims to theoretically explore internal factors that impact the lifetime of cluster based sensor networks, which gives the spatial and temporal characteristics of energy hole as well as the upper bound of network lifetime. The purpose of this is based on the following points. First, theoretical analysis of the network lifetime upper bound enables us to achieve the expected lifetime before deploying the network, not depending on the experience. Second, theoretical analysis of the network lifetime upper bound enables us to know the main factors that affect the network lifetime, providing the best network parameters selection method to obtain the maximum network lifetime and improve network efficiency. Finally, according to the analysis results of the energy hole’s time–space characteristics, we can be fully aware of the weakness [9] of the network in advance and deploy the sensor nodes that have larger energy (such as increase node density, deploy larger initial energy) in order to greatly improve the network lifetime with a smaller cost.

Compared with previous studies, this paper’s main contributions are follows.

(1) Researchers have found that near the sink, there is a hotspot of high energy consumption, easily leading to energy hole. However, the concept of “near the sink” is too vague and cannot be used to guide the network design and optimization. To the best of our knowledge, there is little research on the exact location and the occurrence time and the duration of energy hole. In this paper, we accurately obtained them, as well as the factors that affect lifetime through theoretical analysis, which can effectively guide the design and optimization of sensor networks.

(2) Although there are some research on the analysis of network lifetime [32], [13], [33], this paper is different from them. This paper attempts to establish a theoretical analysis to get the size, time and location of the energy hole, as well as the network lifetime under a given data gathering protocol. In this paper, the network protocols are generalized into four categories, and almost all the current cluster based network protocols can be classified into these four. This paper analyzes the four categories and gives theoretical analysis results of the network lifetime and energy hole, so this research has a broader significance for theoretical guidance.

(3) Many meaningful conclusions are obtained in this paper. Cluster radius $r$ which makes FDT reaches the maximum, does not necessarily achieve the maximum ADT, and vice versa. This shows that a suitable cluster radius $r$ should be based on the needs of application. In the multi-hop network LEACH, FDT is about half of the ADT, which shows that the network loses some functionality when the first node dies, but there is a long period of non-steady state before it finally comes to the end. The minimum residual energy of the network does not necessarily mean the maximum lifetime and vice versa. The simple method of reducing the energy consumption level or balancing energy consumption is not very good, which indicates that it is necessary to consider both the energy consumption level per unit and the energy balancing strategy at the same time. They are given in the list at the end of this paper.

This paper is structured as follows. Section 2 presents the related research of sensor network. Section 3 is the description of the structure of cluster based network model mentioned in this paper and its problem. Data transmission features, characteristics of energy consumption and network lifetime analysis of LEACH will be discussed in Section 4. Section 5 discusses the maximum network lifetime and energy hole of the multi-hop LEACH. Section 6 discusses the maximum network lifetime and the optimization of HEED. The analysis results of the UCR network lifetime upper bound are given in Section 7. Section 8 is about the theoretical and experimental analysis results. Section 9 presents the conclusions and further research of this paper.