arXiv:2611.07151v1 Announce Type: new Abstract: We study the age of information and peak age of information in status update systems with an arbitrary number of independent sources sharing a single server with generally distributed service times. We consider a general age-dependent self-preemptive policy in which an in-service update from source $c$ is preempted by a new same-source arrival with a probability $p_c(x)$ that depends on the elapsed service time $x$. This formulation subsumes the non-preemptive, fully self-preemptive, and probabilistically preemptive policies as special cases, and also accommodates threshold-based preemption. We develop a unified analytical framework based on non-homogeneous absorbing continuous-time Markov chains and semi-Markov chains to derive explicit expressions for the average age of information and peak age of information of each source under general per-source service-time distributions and age-dependent preemption rules. The framework applies to both single-source and multi-source systems and enables joint tuning of per-source preemption parameters. Numerical results for fifteen service-time distributions in the single-source setting reveal that the benefits of preemption depend strongly on the service-time hazard-rate structure, with threshold-based preemption providing its most notable additional gains over age-independent policies for distributions with unimodal hazard rates. For a dual-source system with lognormal service times, jointly tuned threshold-based preemption achieves lower sum average age of information and peak age of information than the considered age-independent policies, highlighting the importance of cross-source interactions in preemption decisions.