AoI in Source-Aware Preemptive M/G/1/1 Queueing Systems: Moment Generating Function

We consider a multi-source status update system consisting of multiple independent sources, one server, and one sink. The packets of the sources are generated according to Poisson processes and served according to a generally distributed service time. We consider a system with no waiting buffer and model it as a multi-source M/G/1/1 queueing model. We introduce a source-aware preemptive packet management policy and subsequently derive the moment generating functions (MGFs) of the age of information (AoI) and peak AoI of each source. According to the policy, when a packet arrives, the possible packet of the same source in the system is replaced by the fresh packet. Simulation results show the performance of the packet management policy.