Abstract
The restart method is based purely on the task completion time. In the previous chapter conditions under which the method is triggered have been investigated. When applying the restart method the only relevant question from a quantitative analysis point is when to restart. For the task under consideration its processing time is monitored and if the processing time exceeds a given value τ then the task is aborted and restarted from beginning. In stochastic terms one may say restart uses a completion time distribution, and a job is restarted when the remaining expected completion time is longer than the expected completion time when restarting the job, taking into account the time already waited for completion. This is similar to age replacement in preventive maintenance.
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Notes
- 1.
At the cost of more notation, and with a proper discussion for special cases, the results in this section also apply to distributions defined over finite domains, as well as to defective distributions and distributions with jumps.
- 2.
At times we also refer to τ as the as restartinterval.
- 3.
There is no particular significance to the chosen parameter values. They happen to be the parameters of a lognormal fit for experimental data of HTTP GET completion times [128].
- 4.
Note that because of the workings of the Mathematica optimisation algorithm, the comparison in Fig.4.14 had to be based on convergence of\({\rm E}[{T_K^N}]\) as stopping criterion, while we were able to base the results for the backward/forward algorithm in Fig.4.15 on convergence of restart times, a stricter criterion. This explains the higher CPU usage for the backward algorithm in Fig.4.15 compared to Fig.4.14.
- 5.
Adhering to SOAP terminology, we do not call HTTP an application, but rather a transport for the layers above it.
- 6.
Where\({\rm argmin}_{i} \left\{x_{i\in \mathbb{I}}\right\} := \min \mathbb{I}_{\mathrm{Min}}\) with
$$\begin{aligned}\mathbb{I}_{\mathrm{Min}} :=& \left\{i\in \mathbb{I} : x_i \in Min\right\}\\ Min :=& \min\left\{x_i : i\in \mathbb{I}\right\}.\end{aligned}$$
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Wolter, K. (2010). Moments of Completion Time Under Restart. In: Stochastic Models for Fault Tolerance. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11257-7_4
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