Matrix-geometric and Recursive Algorithm Solution of a Two-stage Unreliable How Line

Abstract

A two stage flow line finite inventory bank and stages that can fail on completion of a task is equivalent to a C₂/C₂/1/N queueing model in which the arrival process is switched off once N customers wait for service. After transformation of the state equations, two alternative solution procedures are developed, one based on the matrix geometric algorithm and the other based on a recursive algorithm. A comparison of the two algorithms shows that there is no difference in the bank size at which numerical instability occurs, but the recursive algorithm is about eight times faster.