Reliability analysis for chain topology wireless sensor networks with multiple-sending transmission scheme

Jie Cai 0 Xiaoyu Song 1 Jinyuan Wang 2 Ming Gu 0 0 Key Laboratory for Information System Security of Ministry of Education, School of Software, Tsinghua University , 100084 Beijing, China 1 Department of ECE, Portland State University , Portland, OR 97207, USA 2 National Mobile Communications Research Laboratory, Southeast University , 210096 Nanjing, China Reliability analysis is a key problem in wireless sensor networks (WSNs). The primary contribution of this paper is an in-depth study of the reliability of a chain topology wireless sensor network with multiple-sending scheme. We study the wireless link reliability for the fading channels. The node energy availability for the source and relay nodes is investigated in terms of the limited node energy. The instantaneous network reliability and the mean time to failure are derived. Finally, the initial node energy allocation scheme is proposed to balance the lifetime of each sensor node, thus reducing the total energy consumption. The simulation results substantiate the correctness of the theoretical results. 1 Introduction A wireless sensor network (WSN) consists of a large number of low-cost sensor nodes [1] distributed in large geographic area. It senses the interested events, generates packets, and transmits packets to the sink node or the access point via wireless communication. Each node is equipped with sensing, communication, computational, and energy supply modules. Considering the size and the cost, sensor nodes are devices with limited resources, particularly communication capability and battery energy [2]. However, due to the superiority in monitoring the spatial phenomena, the wireless sensor network is adopted in many applications, such as military applications, environment monitoring, biological detection, and smart home. Generally, wireless sensor nodes may often be deployed in a harsh and inhospitable physical environment [3]. Therefore, the packet loss rate in wireless sensor network is much higher than other networks due to the influence of the environment, energy depletion, and hardware failure. Nevertheless, many safety-critical applications are proposed recently, for example, structural health monitoring [4], clinical monitoring [5], etc. The missing of urgent packets in these applications may cause severe property loss and casualties which are often unacceptable [6]. Hence, the reliable transmission is essential for applications of wireless sensor network. In order to guarantee the practicality of applications, how to measure the reliability of the wireless sensor network is an important issue which motivates us to investigate the reliability analysis for such networks. Recently, the reliability analysis has drawn significant attention for wireless network. There exist many intensive studies about reliability analysis for traditional wireless communication network. Chen [7] evaluated the endto-end expected reliability and its corresponding mean time to failure (MTTF) in different wireless communication schemes for wireless CORBA networks. Cook [8] discussed the two-terminal reliability analysis using the random waypoint mobility model for a mobile ad hoc wireless network. Snow [9] analyzed the reliability, availability, and survivability for a typical cellular or personal communication service network. Bai [10] analyzed the reliability of DSRC wireless communication for vehicle safety applications through experiment based on real-world experimental data. Egeland [11] analyzed the k-terminal reliability and network availability for planned and random wireless mesh networks. However, the reliability analysis for wireless sensor network is quite different due to the non-repairable sensor node and limited battery energy. It is reported in [12] that the energy constraint is the main factor preventing from the full exploitation of wireless sensor network technology. So far, there are a few research works about reliability analysis for wireless sensor network. In [13], the author first conducted actual experiments to characterize link reliability measures in an actual sensor network setting and then investigated how link-level re-transmission and multi-path routing might improve the reliability of wireless sensor network. However, the influence of environment to link reliability between two neighboring node was not involved. Cheng [14] proposed the high energy first clustering algorithm to address network lifetime predictability by the worst case energy consumption analysis. But the designed reference model cannot illuminate the relations between the data transmission and energy consumption. Wang [15] studied the reliability for an event-driven wireless sensor network which only the source node is able to sense events and generate packets. In this paper, we analyze the reliability of chain topology wireless sensor networks where the source and relay nodes can sense events and generate packets using the multiple-sending scheme. Considering the impact from the channel fading and node failure caused by the battery energy depletion, the wireless link reliability and node energy availability are analyzed, respectively. Then, the instantaneous network reliability and the MTTF of WSNs are derived. In order to reduce the total energy consumption, the energy-saving initial node energy allocation scheme is proposed to balance the lifetime of sensor nodes. The remainder of the paper is organized as follows: The next section derives the expression of wireless link reliability with a composite channel model which is represented as a mixture of the path loss and the shadow fading. In Section 3, the node energy availability for the source and relay nodes, the instantaneous network reliability, and the MTTF of WSNs are discussed. Furthermore, the allocation of initial energy for each node is investigated for energy saving. Numerical results are presented in Section 4. The conclusions are drawn in Section 5. 2 Wireless link reliability We focus on a chain topology wireless sensor network shown in Figure 1 which includes a source node, N relay nodes, and a sink node. The source and relay nodes generate packets by sensing events and transmit the locally generated packets to the next sensor node via the wireless channel. Relay nodes receive packets from the previous sensor node and retransmit them. Except for the sink node, all other nodes are powered by batteries. There exist two transmission schemes to improve the reliability between neighboring nodes in recent research papers: the multiple-sending-based transmission scheme and the acknowledgement-based transmission scheme. The multiple-sending-based transmission scheme can eliminate the ACK control mechanism and reduce the latency of the data delivery as described in [3]; it has similar performance with the acknowledgement-based scheme when the environment of network is not good. We adopt the multiple-sending-based scheme in this paper. Let the source node and (...truncated)