  Delay-reliability (D-R), and throughput-delay-reliability (T-D-R) tradeoffs
in an ad hoc network are derived for single hop and multi-hop transmission with
automatic repeat request (ARQ) on each hop. The delay constraint is modeled by
assuming that each packet is allowed at most $D$ retransmissions end-to-end,
and the reliability is defined as the probability that the packet is
successfully decoded in at most $D$ retransmissions. The throughput of the ad
hoc network is characterized by the transmission capacity, which is defined to
be the maximum allowable density of transmitting nodes satisfying a per
transmitter receiver rate, and an outage probability constraint, multiplied
with the rate of transmission and the success probability. Given an end-to-end
retransmission constraint of $D$, the optimal allocation of the number of
retransmissions allowed at each hop is derived that maximizes a lower bound on
the transmission capacity. Optimizing over the number of hops, single hop
transmission is shown to be optimal for maximizing a lower bound on the
transmission capacity in the sparse network regime.
