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Lots of real-time applications over Internet of things (IoT)-based statusupdate systems have imperative demands on information freshness, which isusually evaluated by age of information (AoI). Compared to the average AoI andpeak AoI (PAoI), violation probabilities and distributions of AoI and PAoIcharacterize the timeliness in more details. This paper studies the timelinessof the IoT-based multi-source status update system. By modeling the system as amulti-source M/G/1/1 bufferless preemptive queue, general formulas of violationprobabilities and probability density functions (p.d.f.s) of AoI and PAoI arederived with a time-domain approach. For the case with negativeexponentiallydistributed service time, the violation probabilities and p.d.f.s are obtainedin closed form. Moreover, the maximal violation probabilities of AoI and PAoIare proposed to characterize the overall timeliness. To improve the overalltimeliness under the resource constraint of IoT-device, the arrival rateallocation scheme is used to minimize the maximal violation probabilities. Itis proved that the optimal arrival rates can be found by convex optimizationalgorithms. In addition, it is obtained that the minimum of maximal violationprobability of AoI (or PAoI) is achieved only if all violation probabilities ofAoI (or PAoI) are equal. Finally, numerical results verify the theoreticalanalysis and show the effectiveness of the arrival rate allocation scheme.

Violation Probabilities of AoI and PAoI and Optimal Arrival Rate Allocation for the IoT-based Multi-Source Status Update System