IEEE TRANSACTIONS ON AUTOMATIC CONTROL Coverage and Energy Consumption Control in Mobile Heterogeneous Wireless Sensor Networks Xinbing Wang,Senior Member;IEEE,Sihui Han,Yibo Wu,and Xiao Wang Abstract-In this paper we investigate the coverage and parameter(s),e.g.the sensing range of sensors.By adjusting the energy consumption control in mobile heterogeneous wireless sensing range,designer can deploy WSNs with proper coverage sensor networks (WSNs).By term heterogeneous,we mean that capability.Often,quantifiable relation between coverage and sensors in the network have various sensing radius,which is an inherent property of many applied WSNs.Two sensor deployment the parameter(s)is established for better analysis.We can know schemes are considered -uniform and Poisson schemes.We study accurately from the results how the parameter(s)impact the the asymptotic coverage under uniform deployment scheme with network performance. i.i.d.and 1-dimensional random walk mobility model,respectively. We propose the equivalent sensing radius (ESR)for both cases Initially,stationary and flat WSNs received most attention in and derive the critical ESR correspondingly.Our results show the coverage study.By the term flat,we mean that sensors in that the network performance largely depends on ESR.By the network have identical sensing radius.In [21],Clouqueur controlling ESR,we can always promise the network achieve studied the sensor deployment strategy to improve the coverage full coverage,regardless of the total number of sensors or the performance of sensor network and proposed path exposure to sensing radius of a single senor under random mobility patterns, measure the performance.Shakkottai [22]took into account the which is a much easier and more general way to operate coverage control.Meanwhile,we can operate a tradeoff control between failure probability of sensors and obtained the necessary and coverage performance and energy consumption by adjusting ESR. sufficient conditions for a sensor grid to achieve asymptotic We demonstrate that 1-dimensional random walk mobility can full coverage.In [23].Liu defined three coverage performance decrease the sensing energy consumption under certain delay measures and characterized asymptotic behavior of these mea- tolerance,though requires larger ESR.Also,we characterize the role of heterogeneity in coverage and energy performance of WSNs sures.In [36]and [37],WSNs are also well studied and give under these two mobility models,and present the discrepancy of us great insights. the impact of heterogeneity under different models.Under the Poisson deployment scheme,we investigate dynamic k-coverage The 1-coverage studied in literature mentioned above is not of WSNs with 2-dimensional random walk mobility model.We satisfactory in many applications and high degree of coverage present the relation between network coverage and the sensing is consequently demanded (cf.[9]for the reasons to require range,which indicates how coverage varies according to sensing k-coverage rather than just 1-coverage).Kumar [9]studied capability.Both k-coverage at an instant and over a time interval asymptotic k-coverage in a mostly sleeping stationary sensor are explored and we derive the expectation of fraction of the network and found the coverage highly depend on the value whole operational region that is k-covered,which also identifies the coverage improvement brought by mobility. of the function (n is the number of sensors and p is the probability that a sensor is active).The sufficient value of Index Terms-Coverage control,mobility,heterogeneity,energy consumption control,scaling law. 藏me r to achieve full coverage.Another related topic is the approach I.INTRODUCTION to guarantee both coverage and connectivity of WSNs.In [10]. Wile ne ot erch moe wh gaion Bai and Xuan proposed deployment schemes to achieve full coverage and k-connectivity.And a new deployment-polygon on coverage is a fundamental one.The coverage of WSNs based methodology was introduced to prove the optimality of is of significance in many applications such as the security proposed deployment patterns. surveillance in estates,intrusion detection in battle-field or One common feature of the above papers is that they all military restricted zone,etc. study static WSNs.Sensor mobility is actually a concern in In this paper,we focus on the blanker coverage or area coverage study.Plenty of related works concentrate on refining coverage,which concentrates on the maximization of detection algorithm to reposition and control sensors to improve coverage rate of targets in the sensing field.The operational region is said [11][20][30].In this sense,mobility is exploited to reconfigure to be fully blanket covered if every single point in the region is the topology of the network.One commonly used approach sensed.The past decade has seen a surge of research activities for coverage control is developing Voronoi-based algorithm. on coverage.Normally,the coverage and energy consumption performance of WSNs are toned by one or several vital network In [32],Wang et al.proposed three movement protocols for sensors to fill the coverage hole based on the Voronoi approach. IThe early version of this paper appeared in the Proceedings of IEEE In [28],the authors optimized coverage performance with ICDCS'11 [31. sensors of limited mobility.In [35],the authors consideredIEEE TRANSACTIONS ON AUTOMATIC CONTROL 1 Coverage and Energy Consumption Control in Mobile Heterogeneous Wireless Sensor Networks Xinbing Wang, Senior Member, IEEE, Sihui Han, Yibo Wu, and Xiao Wang Abstract—In this paper 1 , we investigate the coverage and energy consumption control in mobile heterogeneous wireless sensor networks (WSNs). By term heterogeneous, we mean that sensors in the network have various sensing radius, which is an inherent property of many applied WSNs. Two sensor deployment schemes are considered –uniform and Poisson schemes. We study the asymptotic coverage under uniform deployment scheme with i.i.d. and 1-dimensional random walk mobility model, respectively. We propose the equivalent sensing radius (ESR) for both cases and derive the critical ESR correspondingly. Our results show that the network performance largely depends on ESR. By controlling ESR, we can always promise the network achieve full coverage, regardless of the total number of sensors or the sensing radius of a single senor under random mobility patterns, which is a much easier and more general way to operate coverage control. Meanwhile, we can operate a tradeoff control between coverage performance and energy consumption by adjusting ESR. We demonstrate that 1-dimensional random walk mobility can decrease the sensing energy consumption under certain delay tolerance, though requires larger ESR. Also, we characterize the role of heterogeneity in coverage and energy performance of WSNs under these two mobility models, and present the discrepancy of the impact of heterogeneity under different models. Under the Poisson deployment scheme, we investigate dynamic k-coverage of WSNs with 2-dimensional random walk mobility model. We present the relation between network coverage and the sensing range, which indicates how coverage varies according to sensing capability. Both k-coverage at an instant and over a time interval are explored and we derive the expectation of fraction of the whole operational region that is k-covered, which also identifies the coverage improvement brought by mobility. Index Terms—Coverage control, mobility, heterogeneity, energy consumption control, scaling law. I. INTRODUCTION WIRELESS Sensor Networks (WSNs) have inspired a wide range of research, among which investigation on coverage is a fundamental one. The coverage of WSNs is of significance in many applications such as the security surveillance in estates, intrusion detection in battle-field or military restricted zone, etc. In this paper, we focus on the blanket coverage or area coverage, which concentrates on the maximization of detection rate of targets in the sensing field. The operational region is said to be fully blanket covered if every single point in the region is sensed. The past decade has seen a surge of research activities on coverage. Normally, the coverage and energy consumption performance of WSNs are toned by one or several vital network 1The early version of this paper appeared in the Proceedings of IEEE ICDCS’11 [3]. parameter(s), e.g. the sensing range of sensors. By adjusting the sensing range, designer can deploy WSNs with proper coverage capability. Often, quantifiable relation between coverage and the parameter(s) is established for better analysis. We can know accurately from the results how the parameter(s) impact the network performance. Initially, stationary and flat WSNs received most attention in the coverage study. By the term flat, we mean that sensors in the network have identical sensing radius. In [21], Clouqueur studied the sensor deployment strategy to improve the coverage performance of sensor network and proposed path exposure to measure the performance. Shakkottai [22] took into account the failure probability of sensors and obtained the necessary and sufficient conditions for a sensor grid to achieve asymptotic full coverage. In [23], Liu defined three coverage performance measures and characterized asymptotic behavior of these mea￾sures. In [36] and [37], WSNs are also well studied and give us great insights. The 1-coverage studied in literature mentioned above is not satisfactory in many applications and high degree of coverage is consequently demanded (cf. [9] for the reasons to require k-coverage rather than just 1-coverage). Kumar [9] studied asymptotic k-coverage in a mostly sleeping stationary sensor network and found the coverage highly depend on the value of the function npπr2 log(np) (n is the number of sensors and p is the probability that a sensor is active). The sufficient value of npπr2 log(np) to ensure full coverage was derived under three different deployment model. Hence, the WSNs can take proper value of r to achieve full coverage. Another related topic is the approach to guarantee both coverage and connectivity of WSNs. In [10], Bai and Xuan proposed deployment schemes to achieve full coverage and k-connectivity. And a new deployment-polygon based methodology was introduced to prove the optimality of proposed deployment patterns. One common feature of the above papers is that they all study static WSNs. Sensor mobility is actually a concern in coverage study. Plenty of related works concentrate on refining algorithm to reposition and control sensors to improve coverage [11][20][30]. In this sense, mobility is exploited to reconfigure the topology of the network. One commonly used approach for coverage control is developing Voronoi-based algorithm. In [32], Wang et al. proposed three movement protocols for sensors to fill the coverage hole based on the Voronoi approach. In [28], the authors optimized coverage performance with sensors of limited mobility. In [35], the authors considered