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The authors study the design of heterogeneous two-tier wireless sensor networks (WSNs), where one tier of nodes is more robust and computationally intensive than the other tier. The authors find the ratios of densities of nodes in each tier to maximise coverage and network lifetime. By employing coverage processes and optimisation theory, the authors show that any topology of WSN derived from random deployments can result in maximum coverage for the given node density and power constraints by satisfying a set of conditions. The authors show that network design in heterogeneous WSNs plays a key role in determining key network performance parameters such as network lifetime. The authors discover a functional relationship between the redundancy, density of nodes in each tier for active coverage and the network lifetime. This relationship is much less pronounced in the absence of heterogeneity. The results of this work can be applied to network design of multi-tier networks and for studying the optimal duty cycles for power saving states for nodes in each tier.