Distribution of the Peak Age of Information in a Random Access Relay Network

In this paper, we focus on peak age of information (PAoI) in a random access relay network comprised of a source, a relay, and a destination. The source transmits stochastic status update packets towards the destination which monitors the status to issue prompt control commands. The transmission is done directly or through a relay. The source and relay send their packets subject to slotted Aloha protocol. Then, it is possible to encounter a collision, leading to more staled packets at the destination, i.e., more age of information. We propose two management policies in the case of collision based on prioritizing the source packet or the relay packet, i.e., source prioritization (SP) or relay prioritization (RP) policies, respectively, to reduce the chance of next collisions. We propose an analytical model in order to derive the distribution (i.e., probability mass function) of PAoI in our network scenario. In this model, we trace the status of two typical packets consecutively received successfully by the destination. We will observe that phase-type distribution plays a key role in deriving the PAoI distribution. By obtaining numerical results we observe significant effect of random access relaying in improving PAoI in some conditions. Moreover, we deduce that though SP and RP lead to very close results for mean PAoI, the variances and tail probabilities may be very different. Simulations confirm our analytical approach in different conditions.