Violation Probability of Age of Information in a Multi-Source Status Update System

In the ever more real-time applications in Internet of Things (IoT), age of information (AoI) is usually applied to analyze system timeliness. The violation probability and distribution of AoI are sometimes alternatives to the average AoI since they are more practical for stricter timeliness requirements, especially when the AoI fluctuates greatly. This paper investigates the timeliness of a real-time IoT based multi-source system, which is abstracted as a multi-source M/M/1/1 bufferless preemptive queue. The violation probability and probability density function of the per-stream AoI are derived in closed form. It is proved that the violation probability and stability of per-stream AoI monotonically decrease with the arrival rate of the corresponding source. Numerical results verify the correctness of theoretical analyses.