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

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. If a new update arrives when the service is busy, it is dropped in the first model; and it preempts the current update in the second model. 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 dropping, we also derive a second upper bound by utilizing stochastic ordering if the interarrival times have decreasing mean residual life (DMRL) and service times have new better than use in expectation (NBUE) property.