On the numerical solution of transient probabilities of a state-dependent multiserver queue

Abstract

The transient system size probabilities for a multiserver queueing model in which the arrival rate increases if there are fewer units in the system and steadily decreases to zero for larger number of units is obtained by writing the Laplace transform of these probabilities as a continued fraction and finding the inversion through the properties of tridiagonal matrices. The effectiveness of this procedure is illustrated through tables and graphs for the above queueing model and its busy period.

Keywords:

• Continued fractions
• tridiagonal matrices
• eigen values

C.R. Classification:

• D.4.8
• G.m
• G.1.2