Age of Information in Internet of Vehicles: A Discrete-Time Multisource Queueing Model

This work studies information freshness of a V2I status updating link in IoV. The status updating link is modeled as a multi-source Ber/Geo/1/1 non-preemptive or preemptive queue. We focus on statistical characteristics of the age of information (AoI) and peak AoI (PAoI). To fully track the AoI evolutions under non-preemptive and preemptive policies, Markov three-dimensional age process (3DAP) and two-dimensional age process (2DAP) are respectively introduced. Their first element is the AoI process; The second one stands for if an update of the concerned source is in transmission and its current age; The third element of 3DAP denotes if an update of another source is in transmission. An analytical approach for studying the AoIs and PAoIs in discrete-time multi-source systems is presented. By studying the state transitions, balance equations, and stationary distributions of 3DAP and 2DAP, analytical expressions of the distributions and averages of AoIs and PAoIs under both queueing policies are derived. Moreover, the optimal probabilistic update selection mechanism (PUSM) that maximizes overall freshness is derived in closed-form for the two-source case. Numerical results validate effectiveness of the theoretical analyses and reveal usefulness of the retransmission. It is found that in terms of improving the overall freshness, the PUSM should be designed to make effective update generation probabilities of sources as close as possible.