Age of Information in Random Access Channels

In applications of remote sensing, estimation, and control, timely communication is critical but not always ensured by high-rate communication. This work proposes decentralized age-efficient transmission policies for random access channels with
$M$
transmitters. We propose the notion of
age-gain
of a packet to quantify how much the packet will reduce the instantaneous age of information at the receiver side upon successful delivery. We then utilize this notion to propose a transmission policy in which transmitters act in a decentralized manner based on the age-gain of their available packets. In particular, each transmitter sends its latest packet only if its corresponding age-gain is beyond a certain threshold which could be computed adaptively using the collision feedback or found as a fixed value analytically in advance. Both methods improve age of information significantly compared to the state of the art. In the limit of large
$M$
, we prove that when the arrival rate is small (below
$\frac {1}{eM}$
), slotted ALOHA-type algorithms are order optimal. As the arrival rate increases beyond
$\frac {1}{eM}$
, while age increases under slotted ALOHA, it decreases significantly under the proposed age-based policies. For arrival rates
$\theta $
,
$\theta =\frac {1}{o(M)}$
, the proposed algorithms provide a multiplicative gain of at least two compared to the minimum age under slotted ALOHA (minimum over all arrival rates). We conclude that it is beneficial to increase the sampling rate (and hence the arrival rate) and transmit packets selectively based on their age-gain. This is surprising and contrary to common practice where the arrival rate is optimized to attain the minimum AoI. We further extend our results to other random access technologies such as Carrier-sense multiple access (CSMA).