Spatiotemporal Analysis for Age of Information in Random Access Networks\n under Last-Come First-Serve with Replacement Protocol

We investigate the age-of-information (AoI) in the context of random access\nnetworks, in which transmitters need to send a sequence of information packets\nto the intended receivers over a shared spectrum. Due to interference, the\ndynamics at the link pairs will interact with each other over both space and\ntime, and the effects of these spatiotemporal interactions on the AoI are not\nwell understood. In this paper, we straddle queueing theory and stochastic\ngeometry to establish an analytical framework, that accounts for the interplay\nbetween the temporal traffic attributes and spatial network topology, for such\na study. Specifically, we derive accurate and tractable expressions to quantify\nthe network average AoI as well as the outage probability of peak AoI. Besides,\nwe develop a decentralized channel access policy that exploits the local\nobservation at each node to make transmission decisions that minimize the AoI.\nOur analysis reveals that when the packet transmissions are scheduled in a\nlast-come first-serve (LCFS) order, whereas the newly incoming packets can\nreplace the undelivered ones, depending on the deployment density, there may or\nmay not exist a tradeoff on the packet arrival rate that minimizes the network\naverage AoI. Moreover, the slotted ALOHA protocol is shown to be instrumental\nin reducing the AoI when the packet arrival rates are high, yet it cannot\ncontribute to decreasing the AoI in the regime of infrequent packet arrivals.\nThe numerical results also confirm the efficacy of the proposed scheme, where\nthe gain is particularly pronounced when the network grows in size because our\nmethod is able to adapt the channel access probabilities with the change of\nambient environment.\n