Throughput-Delay-Reliability Tradeoff with ARQ in Wireless Ad Hoc Networks

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, where the transmission capacity is defined to be the maximum density of spatial transmissions that can be simultaneously supported in an ad hoc network under quality of service (QoS) constraints (maximum retransmissions and reliability). The transmission capacity captures the T-D-R tradeoff as it incorporates the dependence between the throughput, the maximum delay, and the reliability. 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.