The Internet of Things (IoT) paradigm, has opened up the possibility of using the ubiquity of small devices to route information without the necessity of being connected to a Wide Area Network (WAN). Use cases of IoT devices sending updates that are routed and delivered by other IoT devices have been proposed in the literature. In this paper we focus on receivers only interested in the freshest updates from the sending device. In particular, the dynamic network created by routing/gossiping through small devices creates the possibility of delivering updates out of order. Thus, the entire process can be studied well through a queueing system with infinitely many servers, all serving updates with a random service time. Age of Information (AoI) was proposed as the main metric to measure information freshness. We study the amount of time that the AoI is over a certain threshold at the receiver end as a Quality of Service (QoS) measure, called update outage probability. Particularly, given the recent interest in the literature for time domain analysis of the AoI, we obtain the exact expressions for the AoI, peak AoI (pAoI), effective service time and effective departure time distributions for an M/M/$\infty$ queuing system from a time domain perspective, and study the interdependence between the various parameters involved in order to satisfy a given statistical constraint on timeliness.