Industrial wireless sensor networks (IWSNs) are required to provide highly reliable and real-time transmission. Moreover, for connected K-neighborhood (CKN) sleep scheduling-based duty-cycled IWSNs in which the network lifetime of IWSNs can be prolonged, the two-phase geographic greedy forwarding (TPGF) geographic routing algorithm has attracted attention due to its unique transmission features: multi path, shortest path, and hole bypassing. However, the performance of TPGF in CKN-based duty-cycled IWSNs with radio irregularity is not well investigated in the literature. In this paper, we first evaluate the impact of radio irregularity on CKN-based duty-cycled IWSNs. Furthermore, we investigate the routing performance of TPGF in CKN-based duty-cycled IWSNs with radio irregularity, in terms of the number of explored routing paths as well as the lengths of the average and shortest routing paths. Particularly, we establish the upper bound on the number of explored routing paths. The upper bound is slightly relaxed with radio irregularity compared with without radio irregularity; however, it is bounded by the number of average 1-hop neighbors in always-on IWSNs. With extensive simulations, we observe that the cross-layer optimized version of TPGF (i.e., TPFGPlus) finds reliable transmission paths with low end-to-end delay, even in CKN-based duty-cycled IWSNs with radio irregularity.
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