ON THE NUMERICAL-SOLUTION OF TRANSIENT PROBABILITIES OF QUADRATIC BIRTH AND DEATH PROCESSES

The transient system size probabilities for birth and death processes with quadratic birth and death rates are obtained by writing the Lapla ce transform of these probabilities as a continued fraction and findin g the inversion through the properties of tridiagonal matrices. The ef fectiveness of this procedure is illustrated through tables and graphs , for an infinite capacity as well as for a finite capacity birth and death processes.