Fault Tolerance for Real-Time Systems: Analysis and Optimization of Roll-back Recovery with Checkpointing

Increasing soft error rates in recent semiconductor technologies enforce the usage of fault tolerance. While fault tolerance enables correct operation in the presence of soft errors, it usually introduces a time overhead. The time overhead is particularly important for a group of computer systems referred to as real-time systems (RTSs) where correct operation is defined as producing the correct result of a computation while satisfying given time constraints (deadlines). Depending on the consequences when the deadlines are violated, RTSs are classified into soft and hard RTSs. While violating deadlines in soft RTSs usually results in some performance degradation, violating deadlines in hard RTSs results in catastrophic consequences. To determine if deadlines are met, RTSs are analyzed with respect to average execution time (AET) and worst case execution time (WCET), where AET is used for soft RTSs, and WCET is used for hard RTSs. When fault tolerance is employed in both soft and hard RTSs, the time overhead caused due to usage of fault tolerance may be the reason that deadlines in RTSs are violated. Therefore, there is a need to optimize the usage of fault tolerance in RTSs. To enable correct operation of RTSs in the presence of soft errors, in this thesis we consider a fault tolerance technique, Roll-back Recovery with Checkpointing (RRC), that efficiently copes with soft errors. The major drawback of RRC is that it introduces a time overhead which depends on the number of checkpoints that are used in RRC. Depending on how the checkpoints are distributed throughout the execution of the job, we consider the two checkpointing schemes: equidistant checkpointing, where the checkpoints are evenly distributed, and non-equidistant checkpointing, where the checkpoints are not evenly distributed. The goal of this thesis is to provide an optimization framework for RRC when used in RTSs while considering different optimization objectives which are important for RTSs. The purpose of such an optimization framework is to assist the designer of an RTS during the early design stage, when the designer needs to explore different fault tolerance techniques, and choose a particular fault tolerance technique that meets the specification requirements for the RTS that is to be implemented. By using the optimization framework presented in this thesis, the designer of an RTS can acquire knowledge if RRC is a suitable fault tolerance technique for the RTS which needs to be implemented. The proposed optimization framework includes the following optimization objectives. For soft RTSs, we consider optimization of RRC with respect to AET. For the case of equidistant checkpointing, the optimization framework provides the optimal number of checkpoints resulting in the minimal AET. For non-equidistant checkpointing, the optimization framework provides two adaptive techniques that estimate the probability of errors and adjust the checkpointing scheme (the number of checkpoints over time) with the goal to minimize the AET. While for soft RTSs analyses based on AET are sufficient, for hard RTSs it is more important to maximize the probability that deadlines are met. To evaluate to what extent a deadline is met, in this thesis we have used the statistical concept Level of Confidence (LoC). The LoC with respect to a given deadline defines the probability that a job (or a set of jobs) completes before the given deadline. As a metric, LoC is equally applicable for soft and hard RTSs. However, as an optimization objective LoC is used in hard RTSs. Therefore, for hard RTSs, we consider optimization of RRC with respect to LoC. For equidistant checkpointing, the optimization framework provides (1) for a single job, the optimal number of checkpoints resulting in the maximal LoC with respect to a given deadline, and (2) for a set of jobs running in a sequence and a global deadline, the optimization framework provides the number of checkpoints that should be assigned to each job such that the LoC with respect to the global deadline is maximized. For non-equidistant checkpointing, the optimization framework provides how a given number of checkpoints should be distributed such that the LoC with respect to a given deadline is maximized. Since the specification of an RTS may have a reliability requirement such that all deadlines need to be met with some probability, in this thesis we have introduced the concept Guaranteed Completion Time which refers to a completion time such that the probability that a job completes within this time is at least equal to a given reliability requirement. The optimization framework includes Guaranteed Completion Time as an optimization objective, and with respect to the Guaranteed Completion Time, the framework provides the optimal number of checkpoints, while assuming equidistant checkpointing, that results in the minimal Guaranteed Completion Time