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Many embedded systems consist of a mix of hard and soft real-time tasks where the interarrival times of the tasks, particularly soft real-time tasks, are not xed. 5). This leads to a system whose workload changes over time and the workload of the tasks can occasionally be so high that the system starts missing deadlines. We say that the system has a transient overload, in which the system needs to gracefully degrade the performance of the system. 2 Notations and Assumptions A summary of notations used in this thesis is given in Appendix A.

32 Preliminaries The three rules above order operations such that a recording of them is serializable [19, 104]. Unfortunately, this algorithm can be subject to deadlocks, which means that two or more transactions cannot continue their execution because they are waiting for locks to be released, but the locks are never being released since they are held by transactions involved in the waiting. An example clari es the reasoning. 3. Transaction τ1 holds a write-lock on x and requests a read-lock (for instance) on y.

The value of a version is denoted vdj . , the similarity relation is re exive. Furthermore, if a value of data item di , vdi , is similar to another value of data item di , vdi , then vdi is assumed to be similar to vdi . This is a natural way to reason about similar values. If value 50 is similar to value 55, it would be strange if value 55 is not similar to value 50. Thus, the relation similarity is symmetric. 4 is re exive, symmetric and transitive, but a similarity relation does not need to be transitive.

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