Information freshness and packet drop rate interplay in a two-user multi-access channel

In this work, we combine the two notions of timely delivery of information to study their interplay; namely, deadline-constrained packet delivery due to latency constraints and freshness of information. More specifically, we consider a two-user multiple access setup with random access, in which user 1 is a wireless device with a buffer and has external bursty traffic which is deadline-constrained, while user 2 monitors a sensor and transmits status updates to the destination. We provide analytical expressions for the throughput and drop probability of user 1. For user 2, we derive in closed form the age of information distribution, the average age of information (AoI), and the probability the AoI to be larger than a certain value for each time slot. The relations reveal a trade-off between the average AoI of user 2 and the drop rate of user 1: the lower the average AoI, the higher the drop rate, and vice versa. Simulations corroborate the validity of our theoretical results.