  Energy efficiency and transmission delay are very important parameters for
wireless multi-hop networks. Previous works that study energy efficiency and
delay are based on the assumption of reliable links. However, the unreliability
of the channel is inevitable in wireless multi-hop networks. This paper
investigates the trade-off between the energy consumption and the end-to-end
delay of multi-hop communications in a wireless network using an unreliable
link model. It provides a closed form expression of the lower bound on the
energy-delay trade-off for different channel models (AWGN, Raleigh flat fading
and Nakagami block-fading) in a linear network. These analytical results are
also verified in 2-dimensional Poisson networks using simulations. The main
contribution of this work is the use of a probabilistic link model to define
the energy efficiency of the system and capture the energy-delay trade-offs.
Hence, it provides a more realistic lower bound on both the energy efficiency
and the energy-delay trade-off since it does not restrict the study to the set
of perfect links as proposed in earlier works.
