Reliability analysis for a data flow in event-driven wireless sensor networks using a multiple sending transmission approach
© Wang et al.; licensee Springer. 2013
Received: 12 August 2013
Accepted: 23 October 2013
Published: 5 December 2013
Reliability analysis is an important issue in wireless sensor networks (WSNs). This paper aims to study the reliability of a data flow in event-driven wireless sensor networks with multiple sending transmission approach without acknowledgments. Initially, an event-driven wireless sensor network model is described in terms of limited node battery energy and shadowed fading channels. Then, in order to analyze the network reliability, the wireless link reliability and the node energy availability are investigated, respectively. Furthermore, the analytical expressions of the instantaneous network reliability and the mean time to failure (MTTF) are derived. Finally, the simulation results validate the correctness and accuracy of the analytical results.
KeywordsWireless sensor networks Network reliability Multiple sending MTTF
Recent advances in micro-electro-mechanical systems, digital electronics, and wireless communications have led to the emergence of wireless sensor networks (WSNs). A WSN consists of a number of wireless sensor nodes. Each sensor node is a device, equipped with multiple on-board sensing elements, wireless transmitter/receiver modules, computational and power supply elements. Usually, it is characterized by its small size and limited computational and communication capabilities with limited energy supplied by a battery. Indeed, they are deployed in an area of interest to collect data from the environment, process sensed data, and take action accordingly. Typical applications of the WSNs include battlefield surveillance, environmental monitoring, biological detection, smart spaces, and industrial diagnostics[3, 4]. Due to the superiority in monitoring spatial phenomena, the WSNs have drawn a lot of attention both in academia and industry.
In the past few years, intensive researches for WSNs have been conducted in many aspects, such as localization, synchronization[6, 7], deployment, and communication protocol. However, it should be emphasized that comparing with other wireless networks, WSNs are more prone to failure due to energy depletion, hardware failure, communication link errors, and so on. Obviously, how to measure the impacts from such network failure is one important issue for practical design and operations, which motivates the research on reliability analysis for WSNs.
So far, reliability analysis has been intensively studied in many traditional wireless communication networks. Chen and Lyu analyzed the end-to-end expected instantaneous reliability for wireless common object request broker architecture (CORBA) networks. Cook and Ramirez-Marquez analyzed the two-terminal reliability for mobile ad hoc networks. They[12, 13] also employed Monte Carlo (MC) simulation method to evaluate the reliability of mobile and cluster ad hoc networks, respectively. Dominiak et al. analyzed the terminal-pair (two-terminal) reliability for IEEE 802.16 mesh networks. Liu et al. proposed a more general region failure model to assess the reliability of wireless mesh networks affected from a region failure. Egeland and Engelstad analyzed the k-terminal reliability for both planned and random wireless mesh networks. However, due to the non-repairable nodes and the limited node battery energy in WSNs, the traditional reliability evaluation methods are not applicable for WSNs. It has actually been reported that the energy constraint is the main factor preventing the full exploitation of WSN technology. So far, only a few researches can be found for the reliability of WSNs in the open literature. AboElFotoh et al. proposed a reliability measure under the assumption that the transmitter/receiver ranges of all sensor nodes are all the same. Obviously, such assumption violates that fact that the real transmitter/receiver ranges usually change with practical wireless link conditions and traffic loads. Shazly et al. further proposed a three-state node reliability model for WSNs reliability analysis. Cheng et al. developed the predictability of collective timeliness for hard network lifetime environments through the worst-case energy consumption analysis. However, the proposed model cannot reflect the relation between the data transmissions and energy consumptions.
This paper will try to analyze the reliability of a data flow in event-driven WSNs with multiple sending transmission approach without acknowledgments. Considering the effects from wireless links, traffic loads, energy consumptions, and node failures, a more rigorous system model is described for a data flow in event-driven WSNs. Based on the proposed system model, wireless link reliability and node energy availability are analyzed respectively. Then, the instantaneous network reliability and the mean time to failure (MTTF) of the data flow in event-driven WSNs are derived.
The remainder of this paper is organized as follows. The system model is introduced in Section 2. In Section 3, the expressions of the node energy availability and the instantaneous network reliability and MTTF of event-driven wireless networks are derived. Numerical results are presented in Section 4 before conclusions are drawn in Section 5.
2 System model
where k! is the factorial of k, and.
where is the transmit power of the n th relay node.
where γt is the target SNR.
3 Reliability analysis
In typical WSN applications, wireless sensor nodes are scattered in large geographical regions and it is not always possible to perform node maintenance after the network deployment. For this reason, all nodes have to adapt their behaviors to the environmental changes. This section will firstly analyze the wireless link reliability and the node energy availability, respectively. Then, the instantaneous network reliability and MTTF are evaluated for the data flow.
3.1 Wireless link reliability
where is the complentary error function.
3.2 Node energy availability
In the considered WSN, the sensor nodes are powered by low-voltage batteries. If the stored energy is depleted, the node is an energy-unavailable node and thus loses its functioning. Based on the energy stored in a node, the node energy availability for source node and relay nodes will be discussed in the following subsections.
3.2.1 Source node energy availability
where the function is the upper incomplete gamma function.
To reduce the computation complexity, we further analyze the probability in (19) and obtain Proposition 1.
Proof. See Appendix 1.
3.2.2 Relay node energy availability
where denotes the binomial coefficients, and.
where is the regularized incomplete beta function.
To reduce the computation complexity, we further analyze the probability in (25) and obtain Proposition 2.
Proof. See Appendix 3.
3.3 Instantaneous network reliability
4 Numerical results
In this section, both the Monte Carlo (MC) simulation results and theoretical results will be presented. Here, the accuracy of the derived expressions of wireless link reliability, the instantaneous network reliability, and MTTF will be verified, and the impacts of the number of relay nodes will be discussed.
Main simulation parameters
Intensity function for NHPP models
The initial energy of all nodes
Power required by sensing event per second
Power dissipation to run transmitter circuitry
Length of the linear region
2.5 × 105 bit/s
Power of background noise
4 × 10-14 W
Variance of shadow fading
Path loss exponent
LOS path loss at dref
Sensing the environment and sending the sensed information to a sink node are two primary jobs of a WSN. These jobs are required to be done with greater reliability because some major decisions depend on the information collected from WSNs. However, sensors are typically powered through batteries in WSNs and it has been reported that the energy constraint is the main factor preventing the full exploitation of WSN technology. So, reliability evaluation is a critical step for the design of the WSNs. Based on energy-based reliability model, this paper investigates the system performance in an event-driven wireless sensor network with a multiple sending approach without acknowledgments. A system model is established including sensor energy consumption model and the wireless link model. Then the wireless link reliability, node energy availability, instantaneous network, and MTTF are investigated in this paper. However, the node energy availability expression and the system instantaneous reliability expression are not in closed form, thereby making calculation cumbersome. To bypass this problem, two propositions are developed which make it possible to calculate the node energy availability and the system instantaneous reliability easier. The simulation results show that the analytical expressions are accurate enough. Furthermore, the results are useful in designing a WSN to obtain good network performance. For future work, the reliability analysis of a data flow in event-driven WSN with acknowledgment-based transmission scheme and the reliability evaluation of the WSNs with a random node distribution will be investigated.
Proof of proposition 1
Proposition 1 is proved.
Derivation of the probability distribution of random variable D n (t)
The probability distribution of random variable D n (t) will be deduced in this appendix.
Proof of proposition 2
Thus, Proposition 2 is proved.
This work is supported by National 863 High Technology Development Project (no. 2013AA013601), Key Special Project of National Science and Technology (no. 2013ZX03003006), National Nature Science Foundation of China (nos. 61372106, 61102068, 61172077, and 61223001), Research Fund of National Mobile Communications Research Laboratory, Southeast University (no. 2013A04), Program Sponsored for Scientific Innovation Research of College Graduate in Jiangsu Province (no. CXZZ13_0098), Research Fund for the Doctoral Program of Higher Education (no. 20113218120017), and Open Research Fund of National Mobile Communications Research Laboratory, Southeast University (no. 2012D14).
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