  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.
