The Completion Time of Programs on Processors Subject to Failure and Repair

The objective of this paper is to describe a technique for computing the distribution of the completion time of a program on a server subject to failure and repair. Several realistic aspects of the system are included in the model. The server behavior is modeled by a semi-Markov process in order to accommodate nonexponential repair-time distributions. More importantly, the effect on the job completion time of the work 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 then describe an effective numerical procedure for computing the completion time distribution. We show how these results apply to the analysis of different computer system structures and organizations of fault-tolerant systems. Finally, we use numerical solution methods to find the distribution of time to completion on several systems.