On the transient behavior of a finite birth-death process with an application

The transient distribution of the number in the system and the distribution of the length of a busy period for a finite birth and death process is derived by solving the system of linear equations of Laplace-Transforms and finding the inversions through the properties of tridiagonal symmetric matrices. It is proved that the distributions of a busy period is hyperexponential. The steady-state solution of the number of customers in the system is …