Time redundancy

Schneeweiss, Winfrid G. GND

In this report some aspects of time redundancy, i.e. the use of extra time to cope with disturbances, are discussed. Specifically, it is supposed that an indivisible task needs t₀ units of time for completion. After a momentary or a finite length disturbance this task has to be redone from the beginning. The random variable of primary interest here is the time T₀ needed for the completion of the indivisible task. The probability distribution function and the mean value of T₀ are derived for several models, mostly via two methods to improve the insight into the problems at hand and the trustworthiness of the derived results. Another random variable of some interest is the nurnber N of necessary restarts. The probability distribution and the mean value of N are also derived. Finally, the case of an interruptable task is investigated. For computational problems, only the pdf of T₀ is given and, in the Poisson case, E(T₀). Also E(N) is derived. Note: This report assumes a working knowledge of basic renewal theory including the Laplace transform and basic probability theory. Hence terms like "ordinary renewal process" or "forward recurrence-time" are not explained; see e.g. [1].

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Schneeweiss, Winfrid: Time redundancy. Hagen 1983. FernUniversität in Hagen.

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