  We study the power spectral density of continuous time Markov chains and
explicit its relationship with the eigenstructure of the infinitesimal
generator. This result helps us understand the dynamics of the number of
customers for a M/M/1 queuing process in the heavy traffic regime.Closed-form
relations for the power law scalings associated to the eigenspectrum of the
M/M/1 queue generator are obtained, providing a detailed description of the
power spectral density structure, which is shown to exhibit a $1/f^{3/2}$
noise.We confirm this result by numerical simulation.We also show that a
continuous time random walk on a ring exhibits very similar behavior.It is
remarkable than a complex behavior such as $1/f$ noise can emerge from the
M/M/1 queue, which is the ''simplest'' queuing model.
