  We study age-agnostic scheduling in a non-preemptive status update system
with two sources sending time-stamped information packets at random instances
to a common monitor through a single server. The server is equipped with a
waiting room holding the freshest packet from each source called "single-buffer
per-source queueing". The server is assumed to be work-conserving and when the
waiting room has two waiting packets (one from each source), a probabilistic
scheduling policy is applied so as to provide Age of Information (AoI)
differentiation for the two sources of interest. Assuming Poisson packet
arrivals and exponentially distributed service times, the exact distributions
of AoI and also Peak AoI (PAoI) for each source are first obtained.
Subsequently, this analytical tool is used to numerically obtain the optimum
probabilistic scheduling policy so as to minimize the weighted average AoI/PAoI
by means of which differentiation can be achieved between the two sources. In
addition, a pair of heuristic age-agnostic schedulers are proposed on the basis
of heavy-traffic analysis and comparatively evaluated in a wide variety of
scenarios, and guidelines are provided for scheduling and AoI differentiation
in status update systems with two sources.
