  This paper considers a communication system where a source sends
time-sensitive information to its destination. We assume that both arrival and
service processes of the messages are memoryless and the source has a single
server with no buffer. Besides, we consider that the service is interrupted by
an independent random process, which we model using the On-Off process. For
this setup, we study the age of information for two queueing disciplines: 1)
non-preemptive, where the messages arriving while the server is occupied are
discarded, and 2) preemptive, where the in-service messages are replaced with
newly arriving messages in the Off states. For these disciplines, we derive
closed-form expressions for the mean peak age and mean age.
