THE COMPLETION-TIME OF PROGRAMS ON PROCESSORS SUBJECT TO FAILURE AND REPAIR

The objective of this paper is to describe a technique for computing t he distribution of the completion time of a program on a server subjec t to failure and repair. Several realistic aspects of the system are i ncluded in the model. The server behavior is modeled by a semi-Markov process in order to accommodate nonexponential repair-time distributio ns. More importantly, the effect on the job completion time of the wor k lost due to the occurrence of a server failure is modeled. We derive a closed-form expression for the Laplace-Stieltjes transform (LST) of the time to completion distribution of programs on such systems. We t hen describe an effective numerical procedure for computing the comple tion time distribution. We show how these results apply to the analysi s of different computer system structures and organizations of fault-t olerant systems. Finally, we use numerical solution methods to find th e distribution of time to completion on several systems.