Considering a wireless sensor network whose nodes are distributed randomly over a given area, a probability model for the network lifetime is provided. Using this model and assuming that packet generation follows a Poisson distribution, an analytical expression for the complementary cumulative density function (ccdf) of the lifetime is obtained. Using this ccdf, one can accurately find the probability that the network achieves a given lifetime. It is also shown that when the number of sensors, $N$, is large, with an error exponentially decaying with $N$, one can predict whether or not a certain lifetime can be achieved. The results of this work are obtained for both multi-hop and single-hop wireless sensor networks and are verified with computer simulation. The approaches of this paper are shown to be applicable to other packet generation models and the effect of the area shape is also investigated.
Wireless sensor networks (WSNs) are consisted of a set of cheap and usually battery-powered devices, called sensors. Sensor limited power usually necessitates a compromise between lifetime and other parameters such as the data rate or the quality of the received signal in the sink. It is usually impracticable to replace the sensors batteries after their operation period. Hence, estimating the network lifetime according to the initial energy in sensors is essential for network design. According to such lifetime estimation, one can choose the network parameters such as node density, data rate and initial energy of the sensors to achieve the desired lifetime.
Lifetime analysis has been studied in the literature based on different definitions such as the number of dead nodes in the network, network coverage and network connectivity [1]- [6]. Authors in [1] derive an upper bound on the network lifetime considering the spatial behavior of the data source. To achieve this goal, they first consider a simplified version where the data source is a specific point, and the source is connected to the sink with a straight line consisting of relaying sensors. They derive the optimum length of a hop and consequently the number of hops in the path to minimize the total energy consumed for the data delivery. Then, they remove the assumption of a source concentrated on a point and assume that the source is distributed over an area.
In [2], the results of [1] are extended to the networks whose nodes may perform different tasks of sensing, relaying and aggregating. The results of [1] are also extended to multiplesink networks in [3].
Work reported in [4] studies the network lifetime for a cell based network. It is assumed that N nodes are deployed over a hypercube. For the aim of energy conserving, the area is divided to n hypercubes (cells). Using occupancy theory [7], the distribution of the minimum number of sensors within each cell is investigated when N, n → ∞. Then, authors study the lifetime for the case when network remains almost surely connected. Using the number of sensors in each cell, the network lifetime is lower bounded based on the given lifetime of each sensor.
A lifetime study based on the area coverage is presented in [5]. It is assumed that the nodes have a circular sensing region and are distributed over a squared area. Using the stochastic geometry, theory of coverage process, and assuming the size of the area goes to infinity, an expression for the node density is derived to guarantee a k-coverage in the area. It is shown that using the proposed density, the network lifetime is upper bounded by kT where T is the given lifetime of each sensor. Although the upper bound is derived for an asymptotic situation when the area goes to infinity, it is shown through simulation that the derived bound is also reasonable for networks over a finite area.
Authors in [6] divide linear or circular networks to some bins where each bin contains a deterministically assigned number of nodes. The nodes within each bin, however, are deployed randomly. Also, the lifetime is defined as the time when a hole occurs in the routing scheme (i.e. death of a bin). Assuming a fixed transmission power for each packet and using the theory of stochastic processes, authors have found the probability distribution function (pdf) of the network lifetime. In addition, they propose a method to assign the number of nodes within each bin in order to maximize the network lifetime.
It is worthy to note that other studies in the literature are performed on the lifetime, e.g. [8]- [12]. However, the most related ones to this work are those that we discussed earlier.
In this paper, we find the probability of reaching a certain lifetime for randomly distributed networks based on the power dissipation model of the sensors. More specifically, unlike [4], [5], we do not assume that the lifetime of a sensor is given in order to find the network lifetime. Instead, we find the lifetime of a sensor (as a random variable) based on its power dissipation and packet generation model. Also, our analysis does not assume an infinite area and infinite number of sensors. In comparison to [6], we consider totally randomly deployed networks over more variant area shapes. In addition, both fixed and adjustable transmission power are studied in this work. Also, the definition of lifetime in our work is more general and can include the case studied in [6] (to be discussed in Section IV).
Considering the randomness in packet generation and sensor deployment in the area, the lifetime of a network is a random variable. For a lifetime analysis of the network, it is needed to have a knowledge of the lifetime of each individual sensor. In this work, instead of assuming that the lifetime of each sensor is given beforehand, we first perform a lifetime analysis at the sensor level. To this end, we model the lifetime of a sensor as a random variable and find its distribution b
This content is AI-processed based on open access ArXiv data.