Considering that practical wireless sensor networks are mostly built upon energy-constrained sensor nodes, network lifetime becomes a key deployment factor for sustainability of such networks initiating an attempt for prolonging the lifetime. Adopting a new multi-mode switching protocol for sensor nodes between active and sleep states, in this study, the authors propose a new mathematical method using an embedded simulation-based computing of an energy-efficient strategy performance metric to maintain resiliency of the network against side effects appearing in duty-cycling protocols. Here, the authors use a Monte Carlo simulation to estimate network reliability. Then the proposed mathematical model enables us to build a decision for optimised performance upon trade-offs between consumed energy, reliability, coverage intensity and endto-end delays by locating a network's operational points. The authors show the trade-off operational significance of the model against the percentage of sleeping probability via some design factors including figure of merit. † Sleep probability p s, † Node density σ, † Number of neighbour nodes n − 1=πr 2 σ, † The non-empty probability (the node's queue is non-empty) in which lead to packet transmission is τ. According to our previous work [16], the wireless channel at any moment is in one of the following states: † idle state (S i), † collision state (S c), † successful transmission state (S s). Fig. 1 Sample graph to show two-terminal reliability computation www.ietdl.org