A job is to be run on a machine subject to random failures. Failures are not self-evident. They must be detected by explicit tests, or checks. Checks detect failures to avoid wasting time working with a defective machine. After each successful check one has the option of saving the work just completed. Then, when failures occur, only the work done since the last save must be repeated. Effective use of checks and saves requires a compromise, since these procedures are themselves time-consuming. Scheduling saves alone, when failures are evident as soon as they occur, is often called checkpointing. The novelty of the model studied here stems from not assuming that failures are self-evident. This compounds the usual checkpointing problem by requiring schedules of failure checks as well as saves. This paper gives schedules of checks and saves that minimize the expected total time required to complete a given job. The most general failure mechanism considered is a renewal process. The Poisson process receives special emphasis, as it leads to the simplest results. INFORMS Journal on Computing, ISSN 1091-9856, was published as ORSA Journal on Computing from 1989 to 1995 under ISSN 0899-1499.

This work is devoted to the analysis of page replacement algorithms under assumptions on the stochastic nature of the sequence of memory accesses. A detailed discussion of the authors' results, some of which were published in Russian, and their relations to other papers is given. The object of study of this paper is two families of page replacement algorithms (PRA's) which contain certain algorithms of practical and theoretical interest. Analytical results are derived using the assumption that the references to the pages are independent identically distributed (iid) random variables. The algorithms of the first family are intervening between FIFO and LRU and the algorithms of the second family estimate the most frequently referenced pages considerably better than LRU. Explicit expressions of the page fault probabilities are obtained for these families and least upper bounds of performance are established which are independent of the page request probabilities. It is shown that for the second family the fault probabilities are less than twice the optimal one.