Network configuration for optimal utilization efficiency of wireless sensor networks

Abstract

This paper addresses the problem of configuring wireless sensor networks (WSNs). Specifically, we seek answers to the following questions: how many sensors should be deployed, what is the optimal sensor placement, and which transmission structure should be employed. The design objective is utilization efficiency defined as network lifetime per unit deployment cost. We propose an optimal approach and an approximation approach with reduced complexity to network configuration. Numerical and simulation results demonstrate the near optimal performance of the approximation approach. We also study the impact of sensing range, channel path loss exponent, sensing power consumption, and event arrival rate on the optimal network configuration.

Introduction

Wireless sensor networks (WSNs) have captured considerable attention recently due to their enormous potential for both commercial and military applications. A WSN consists of a large number of low-cost, low-power, energy-constrained sensors with limited computation and communication capability. Sensors are responsible for monitoring certain phenomenon within their sensing ranges and reporting to gateway nodes where the end-user can access the data.

In WSNs, sensors can be deployed either randomly or deterministically. A random sensor placement [1] may be suitable for battlefields or hazardous areas while a deterministic sensor placement is feasible in friendly and accessible environments. In general, fewer sensors are required to perform the same task with a deterministic placement. A typical configuration for WSNs with deterministic sensor placement may include the following three aspects: the network size which chooses the total number of sensors to be deployed, the sensor placement which determines the location of each sensor in the desired area, and the transmission structure which specifies how data are relayed among sensors to the gateway node. As illustrated in Fig. 1, total N sensors are deployed along a straight line of length L. The sensor placement and the transmission structure are specified by d ≜ [d₁, … , d_N] and $\mathbb{P}\triangleq \{P_{i\text{,}j}{\}}_{i\text{,}j=1}^N$, respectively, where d_i denotes the distance between adjacent sensors and P_i,j the probability that sensor i transmits its data to sensor j.

In this paper, we address all three aspects of network configuration. The contribution of this paper is twofold. First, we introduce a performance measure of utilization efficiency defined as network lifetime per unit deployment cost. In general, both network lifetime and deployment cost increase with the network size. While deployment cost increases almost linearly with the number of sensors, the increasing rate of network lifetime diminishes when the network is large. Utilization efficiency captures the rate at which network lifetime increases with the network size. It can thus effectively address the tradeoff between network lifetime and deployment cost, providing balanced design guidelines for network configuration. Under the performance metric of utilization efficiency, we study the effect of sensing energy consumption and event arrival rate on the optimal network size. We find that a dense network is desirable when the event arrival rate is large. On the other hand, when the sensing energy consumption is relatively large, a sparse network is preferred.

Second, we formulate network configuration for optimal utilization efficiency as a multi-variate non-linear optimization problem by jointly optimizing sensor placement, transmission structure, and network size. The impact of sensing range and channel path loss exponent on sensor placement is studied. We find that sensors should be placed more compact and closer toward the gateway node when their sensing range is large and more uniformly when the channel path loss exponent is large. We also extend our results to a two-dimensional WSN with grid structures.

Sensor placement problem has been addressed in many network applications [2], [3], [4], [5], [6]. Different performance measures have been used to develop sensor placement schemes. For example, Dhillon and Chakrabarty [7] propose two algorithms to optimize sensor placement with a minimum number of sensors for effective coverage and surveillance purposes under the constraint of probabilistic sensor detections and terrain properties. Lin and Chiu [8] address the sensor placement problem for complete coverage under the constraint of cost limitation. Ganesan et al. [9] jointly optimize sensor placement and transmission structure in a one-dimensional data-gathering WSN. Their approach aims at minimizing the total power consumption under distortion constraints. Kar and Banerjee [10] address the optimal sensor placement to ensure connected coverage in WSNs. Sensor placement schemes that maximize network lifetime have also been addressed for different WSNs. For example, Dasgupta et al. [11] propose an algorithm to find the optimal placement and role assignment to maximize the lifetime of a WSN that consists of sensors and relay nodes. Hou et al. [12] address the energy provisioning and relay node placement in a two-tiered WSN. In [13], the placement of gateway nodes is studied to maximize the lifetime of a two-tiered WSN. In [14], a greedy sensor placement scheme is proposed to maximize the lifetime of a linear WSN.

The rest of the paper is organized as follows. In Section 2, we present a model of linear WSN and define network lifetime and utilization efficiency. In Section 3, the utilization efficiency of the linear WSN is analyzed and its asymptotic behavior is studied. In Section 4, we propose an optimal solution and an approximation solution with reduced complexity to network configuration. Section 5 extends the results to a two-dimensional WSN. Numerical and simulation results are provided in Section 6. Section 7 concludes the paper.