This paper investigates the suboptimal problem of existing state-of-the-art routing protocols when they are applied to heterogeneous duty-cycled wireless sensor networks (WSNs). In particular, we discover that the selected optimal routes with the least cost based their routing metric may not always lead to the least transmission cost. The key reason is that the existing routing metrics used do not sufficiently capture packet transmission cost in heterogeneous duty-cycled WSNs. To address this issue, we propose a novel routing metric, namely expected transmission cost (ETC), which efficiently captures packet transmission cost in heterogeneous duty-cycled WSNs by estimating both expected rendezvous cost and communication cost. Based on ETC, we design an opportunistic routing protocol (EoR) which is proved to select optimal routes with the least packet transmission cost. Our experimental results show that EoR outperforms the stateof- the-art protocols in terms of energy efficiency, latency, and packet delivery ratio.
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