Age of Information in Multi-Source Updating Systems: An M/G/1 Vacation Queueing Model

Concurrent with the rise of real-time wireless systems enabled by the Internet of Things, the age of information (AoI) has been widely perceived as a crucial destination-centric performance metric to quantify the timeliness of data delivery. This paper deals with the analysis of information freshness in a multi-source M/G/1 queueing system with utilization of idle server time, referred to as server vacation, in an effective manner. In particular, the status update packets in our model are generated independently by a finite set of source nodes and according to a Poisson process, while their service time follows a general random variable. Using stochastic decomposition and the Laplace-Stieltjes transform, we derive the average AoI (AAoI) expression for the multi-source M/G/1 queueing model with generally-distributed vacation time in closed form. Our numerical simulations validate the accuracy of the derived AAoI expression and assess the impact of different parameters on the system performance.