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A key metric to express the timeliness of status updates in latency-sensitivenetworked systems is the age of information (AoI), i.e., the time elapsed sincethe generation of the last received informative status message. This metricallows studying a number of applications including updates of sensory andcontrol information in cyber-physical systems and vehicular networks as wellas, job and resource allocation in cloud clusters. State-of-the-art approachesto analyzing the AoI rely on queueing models that are composed of one or manyqueuing systems endowed with service order, e.g., FIFO, LIFO, orlast-generated-first-out order. A major difficulty arising in these analysismethods is capturing the AoI under message reordering when the delivery isnon-preemptive and non-FIFO, i.e., when messages can overtake each other andthe reception of informative messages may obsolete some messages that areunderway. In this paper, we derive an exact formulation for the distribution ofAoI in non-preemptive, non-FIFO systems where the main ingredients of ouranalysis are Palm calculus and time inversion. Owing to the rationality of theLaplace-Stieltjes transforms that are used in our approach, we obtaincomputable exact expressions for the distribution of AoI.

A Palm Calculus Approach to the Distribution of the Age of Information