M/M/1 Transient State Occupancy Probabilities Via the Discrete Fourier Transform

A procedure is given for the computation of the transient state occupancy probabilities of the
M/M/1
queue. The method makes use of the inverse discrete Fourier transform, computed by means of the fast Fourier transform. It avoids the direct evaluation of modified Bessel functions and sidesteps difficulties due to the computation of very large and very small intermediate quantities.