ABSTRACT
The homogeneous equation is discussed with application to the differentialdifference equation for the transient behavior of the number in the system of an M/M/1 queue. The solution is obtained in the form of a Laplace transform for which an approximate inversion is constructed for the probability that the system is empty and which is applicable over the entire range The operational method of Boole is presented as an alternative procedure for the solution of the homogeneous equation.
