1 Impact of Heterogeneity on Coverage and Broadcast Reachability in Wireless Sensor Networks Yun Wang, Xiaodong Wang, Dharma P. Agrawal and Ali A. Minai OBR Center of Distributed and Mobile Computing, Department of Electrial and Computer Engineering and Computer Science, University of Cincinnati, Cincinnati, OH, 45221-0030 Email: {wany6, wangxd, dpa, aminai }@email.uc.edu Telephone:(513) 556–3437 Abstract— While most existing research efforts in the area of wireless sensor networks have focused on networks with identical nodes, deploying sensors with different capabilities has become a feasible choice. In this paper, we focus on sensor networks with two types of nodes that differ in their capabilities, and discuss the effects of heterogeneity of sensing and transmission ranges on the network coverage and broadcast reachability. Our work characterizes how the introduction of a few sensor nodes with bet- ter capabilities can reduce the number of total required sensors without sacrificing the coverage and the broadcast reachability. Analytical results are validated via simulations. Our work can be extended to more complicated heterogenous wireless sensor networks with more than two types of sensors, while homogenous networks can also be seen as a special case of heterogeneous wireless sensor networks where the two types of sensors are the same. This work can serve as a guideline for designing large-scale sensor networks cost-effectively. Index Terms—Coverage, Heterogeneity, Homogeneity, Reach- ability, Wireless Sensor Networks. I. I NTRODUCTION A wireless sensor network (WSN) is a collection of small, cheap and low powered sensor nodes which can dynamically form a network without any underlying infrastructure support [1], [2]. As sensor nodes are emerging as a key tool to gather information from diverse physical phenomena, a number of applications such as habitat monitoring, health caring, battle- field surveillance and enemy tracking have been proposed and discussed [2]. Most existing research focus on the homoge- neous WSN where all the sensors are identical in terms of sensing, communication, computation, and power capabilities [3] [4], and homogeneous architecture is easy to model and resilient to individual sensor failures. However, the presence of a few more powerful sensors can improve the network reliability and stability with marginal or no increase in the cost of network deployment [5]. This makes the heterogeneous WSN increasingly important, and the research in this area is highly desirable. Recently, researchers [4], [6], [5] in sensor networks have proposed to deploy sensor nodes with different capabilities as part of the same network. Intuitively, the introduction of some sensor nodes with greater capabilities can help enhance the overall network performance. However, questions of where, how many, and what types of heterogeneous resources to deploy remain largely unexplored [5]. This raises the issue of quantifying the effects of deploying heterogeneous sensor nodes on quality of service of the whole network. One of the fundamental problems in sensor networks is sensing coverage. In general, it answers the questions about the quality of service (surveillance) that can be provided by a particular sensor network [7] [8]. To be specific, it reflects how well a sensor network is monitored or tracked by the sensors [9]. The coverage is defined as the probability that any target point in the sensed area is within the sensing range of any nearby sensors. Here, we focus our work on the case that a number of sensor nodes, deployed in a field to detect certain intrusion activities. An example of such a scenario may be seismic or acoustic sensors deployed in a battle field to detect enemy intrusion [9]. It should be noted that the introduction of sensor nodes with longer transmission range might complicate the operation of the network with the introduction of asymmetric links, since a node with longer transmission range might reach another node with shorter transmission range, but the node with shorter transmission range might not be able to reach the node with longer transmission range. Previous works on the connectivity have only considered bi-directional links for both homogenous range assignment [10], and heterogenous range assignment [11]. In this paper, we focus on the network broadcast reachability, which is defined as the probability that a packet broadcast from a sensor with longer transmission range can reach all the other sensors in the network, if we assume perfect scheduling and no collision at the MAC layer. Broadcast reachability has practical implications in broadcast, where a symmetric link is not required. Intuitively, hetero- geneity leads to a more significant improvement in broadcast reachability than in connectivity, where connectivity is defined as the probability that a packet broadcast from any sensor can reach all the other sensors in the network. By abstracting large scale sensor networks into graphs, important properties of the WSNs can be investigated. In this paper, we focus on sensor networks comprising two types of nodes that differ in their sensing and transmission ranges. It is no doubt that sensors with more complex detector or signal processing units can have better sensing capabilities. Thus, in our work, we model a better sensing capability