  We consider a situation that multiple monitoring applications (each with a
different sensor-monitor pair) compete for a common service resource such as a
communication link. Each sensor reports the latest state of its own
time-varying information source to its corresponding monitor, incurring
queueing and processing delays at the shared resource. The primary performance
metric of interest is the age of information (AoI) of each sensor-monitor pair,
which is defined as the elapsed time from the generation of the information
currently displayed on the monitor. Although the multi-source first-come
first-served (FCFS) M/GI/1 queue is one of the most fundamental model to
describe such competing sensors, its exact analysis has been an open problem
for years. In this paper, we show that the Laplace-Stieltjes transform (LST) of
the stationary distribution of the AoI in this model, as well as the mean AoI,
is given by a simple explicit formula, utilizing the double Laplace transform
of the transient workload in the M/GI/1 queue.
