Age of Information in G/G/1/1 Systems

Abstract

We consider a single server communication setting where the interarrival times of data updates at the source node and the service times to the destination node are arbitrarily distributed. We consider two service discipline models. In the first model, if a new update arrives when the service is busy, it is blocked, in the second model, a new update preempts the current update in service. For both models, we derive exact expressions for the age of information metric with no restriction on the distributions of interarrival and service times. In addition, we derive upper bounds that are easier to calculate than the exact expressions. In the case with blocking, we also derive a second upper bound by utilizing stochastic ordering if the interarrival and service times have log-concave distribution.