Higher-powered relay nodes have been proposed as cluster heads in hierarchical sensor networks to increase the network connectivity, coverage and lifetime. Determining an appropriate placement scheme of the relay nodes that ensures adequate coverage and connectivity, while using a minimum number of relay nodes, is an important design problem and a significant amount of work has been done in this area in recent years. However, most of the existing placement strategies typically assume only stationary nodes, where data of each relay nodes (received from the underlying sensor nodes in its cluster) are routed to the base station(s), using either single-hop or multi-hop routing schemes. Recently, the use of mobile data collectors (MDC) has been shown to improve the network performance in a variety of sensor network applications. In this paper, we consider a hierarchical relay node based network, where a mobile data collector moves along a fixed trajectory, collects data from each relay node and delivers them to the base station. Such a model reduces the energy dissipation of the relay nodes by relieving them of the burden of transmitting data over longer distances, thereby increasing the overall lifetime of the network. The issue is to find the minimum number of relay nodes, along with their locations such that all network requirements are satisfied. We present an integrated integer linear program (ILP) formulation that takes into consideration the sensor data rates, the relay nodes buffer size and the speed of the MDC, and determines an optimal relay node placement scheme, which ensures that there is no data loss due to relay node buffer overflow and the energy dissipation does not exceed a specified level.
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