  In this paper, energy efficiency of hybrid automatic repeat request (HARQ)
schemes with statistical queuing constraints is studied for both constant-rate
and random Markov arrivals by characterizing the minimum energy per bit and
wideband slope. The energy efficiency is investigated when either an outage
constraint is imposed and (the transmission rate is selected accordingly) or
the transmission rate is optimized to maximize the throughput. In both cases,
it is also assumed that there is a limitation on the number of retransmissions
due to deadline constraints. Under these assumptions, closed-form expressions
are obtained for the minimum energy per bit and wideband slope for HARQ with
chase combining (CC). Through numerical results, the performances of HARQ-CC
and HARQ with incremental redundancy (IR) are compared. Moreover, the impact of
source variations/burstiness, deadline constraints, outage probability, queuing
constraints on the energy efficiency is analyzed.
