Peak Age of Information in Slotted ALOHA Networks
Sepehr Asvadi, Farid Ashtiani
Abstract
In this paper, we concentrate on the peak age of information (PAoI) in a discrete-time slotted ALOHA network comprised of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\boldsymbol {M}$ </tex-math></inline-formula> buffer-less nodes, capable of keeping just one packet at each slot. In this network, a collision happens whenever at least two nodes transmit their packets simultaneously. Thus, there is some interaction among queues, and the transmission delay of a packet might prolong more than one slot. The packets are generated at each node stochastically and independently. The nodes follow the preemptive queueing policy. In this network, we propose a trellis-based model to analyze packet system time and derive the exact average PAoI of symmetric and asymmetric slotted ALOHA networks. We confirm our analysis by simulation results in different conditions. By exploiting numerical results, we optimize the average PAoI of the symmetric slotted ALOHA network, find the PAoI-constrained regions, and compare the PAoI of slotted ALOHA networks with and without retransmission of the failed packets.