Delay and Energy Constrained Random Access Transport Capacity

In this paper, we consider a delay and energy constrained wireless ad hoc network with node density of λ_n, where a packet should be delivered to the destination within D(λ_n) seconds using at most E(λ_n) energy in joules while satisfying the target outage probability. The performance metric for analyzing the network is the delay and energy constrained random access transport capacity (DE-RATC), i.e., $C_ϵ(D(λ_n), E(λ_n), which quantifies the maximum end-to-end distance weighted rate per unit area of a delay and energy constrained network using a random access protocol. It is shown that a slotted ALOHA protocol is order-optimal under any delay and energy constraints if equipped with additional features such as power control, multi-hop control, interference control, and rate control, and the delay and energy constraints can be divided into three regions according to the relation between the physical quantities due to the constraints and those due to the node density and network size. The three regions are the non-constrained (NC) region, where the DE-RATC is given by Θ(√λ_n/logλ_n); the delay-constrained (DC) region, where the DE-RATC depends only on the delay constraint as Θ(D(λ_n); and the non-achievable (NA) region where a packet delivery under the given constraints is impossible. Also, it is shown that an arbitrary tradeoff between the rate of each source node and the number of source nodes can be achieved while keeping the optimal capacity scaling as long as λ_s=Ω√λ_n/logλ_n, Dλ_n))).