PERFORMABILITY MEASURE FOR ACYCLIC MARKOVIAN MODELS

Continuous-time Markov processes with a finite-state space are general ly considered to model degradable fault-tolerant computer systems. The finite space is partitioned as (Ui=1Bi)-B-m, where B-i stands for the set of states which corresponds to the configuration where the system has a performance level (or reward rate) equal to r(i). The performab ility Y-t is defined as the accumulated reward over a mission time [O, t]. In this paper, a renewal equation is established for the performa bility measure and solved for both ''standard'' and uniform acyclic mo dels. Two closed form expressions for the performability measure are d erived for the two types of models. Furthermore, an algorithm with a l ow polynomial computational complexity is presented and applied to a d egradable computer system.