  We consider a priority queueing system where a single processor serves k
classes of packets that are generated randomly following Poisson processes. Our
objective is to compute the expected Peak Age of Information (PAoI) under
various scenarios. In particular, we consider two situations where the buffer
size at each queue is one and infinite, and in the infinite buffer size case we
consider First Come First Serve (FCFS) and Last Come First Serve (LCFS) as
service disciplines. For the system with buffer size one at each queue, we
derive PAoI exactly for the case of exponential service time and bounds (which
are excellent approximations) for the case of general service time, with small
k. For the system with infinite buffer size, we provide closed-form expressions
of PAoI for both FCFS and LCFS where service time is general and k could be
large. Using those results we investigated the effect of ordering of priorities
and service disciplines for the various scenarios. We perform extensive
numerical studies to validate our results and develop insights.
