Analytically Modeling Unreliable Parallel Processing Systems with General Task Time Distributions

For many computing systems, failure is rare enough that it can be ignored or dealt with as an afterthought. In other systems, failure is so common that the recovery procedure can have a significant impact on the performance of the system. There are many different recovery schemes for tasks, however, they can be grouped into three broad categories: (1) Resume: When a task fails, it knows exactly where it stops and can continue at that point when allowed to resume (i.e., preemptive resume -prs); (2) Replace: When a task fails, then later when the processor continues, it begins with a brand new task (i.e., preemptive repeat different - prd); and, (3) Restart: When a task fails it loses all work done to that point and must start anew upon continuing later preemptive repeat identical - pri. In this paper, assuming a computing system is unreliable, we discuss how heavy-tail distributions can appear in an otherwise exponentially or non-exponentially distributed task stream. This is an important consideration since it is known that power-tails can lead to unstable systems. We then demonstrate how to obtain performance and dependability measures for a class of computing systems comprised ofP unreliable processors and a finite number of tasks, N.