Hostname: page-component-586b7cd67f-l7hp2 Total loading time: 0 Render date: 2024-11-27T23:21:59.210Z Has data issue: false hasContentIssue false
  • English
  • Français

Age-replacement policy and optimal work size

Part of: Special processes

Published online by Cambridge University Press:  14 July 2016

Jie Mi
Jie Mi*
Affiliation:
Florida International University
*
∗ Postal address: Department of Statistics, Florida International University, University Park, Miami, FL 33199, USA. Email address: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Suppose that there is a sequence of programs or jobs that are scheduled to be executed one after another on a computer. A program may terminate its execution because of the failure of the computer, which will obliterate all work the computer has accomplished, and the program has to be run all over again. Hence, it is common to save the work just completed after the computer has been working for a certain amount of time, say y units. It is assumed that it takes a certain time to perform a save. During the saving process, the computer is still subject to random failure. No matter when the computer failure occurs, it is assumed that the computer will be repaired completely and the repair time will be negligible. If saving is successful, then the computer will continue working from the end of the last saved work; if the computer fails during the saving process, then only unsaved work needs to be repeated. This paper discusses the optimal work size y under which the long-run average amount of work saved is maximized. In particular, the case of an exponential failure time distribution is studied in detail. The properties of the optimal age-replacement policy are also derived when the work size y is fixed.

Keywords

Renewal processoptimal work sizebathtub-shaped failure rateage-replacement policy

MSC classification

Primary: 60K05: Renewal theory
Secondary: 60K10: Applications (reliability, demand theory, etc.)
Type
Research Papers
Information
Journal of Applied Probability , Volume 39 , Issue 2 , June 2002 , pp. 296 - 311
Copyright
Copyright © Applied Probability Trust 2002 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Barlow, R. E., and Proschan, F. (1967). Mathematical Theory of Reliability. John Wiley, New York.Google Scholar
Boguslavsky, L. B., Coffman, E. G. Jr, Gilbert, E. N., and Kreinin, A. Y. (1992). Scheduling checks and saves. ORSA J. Comput. 4, 60–69.Google Scholar
Bruno, J. L. et al. (1999). Processor shadowing: maximizing expected throughput in fault-tolerant systems. Math. Operat. Res. 24, 362–382.Google Scholar
Coffman, E. G. Jr, and Gilbert, E. N. (1990). Optimal strategies for scheduling saves and preventive maintenance. IEEE Trans. Reliab. 39, 9–18.CrossRefGoogle Scholar
Coffman, E. G. Jr, Flatto, L., and Wright, P. E. (1993). A stochastic checkpoint optimization problem. SIAM J. Comput. 22, 650–659.Google Scholar
Feller, W. (1971). An Introduction to Probability Theory and Its Applications, Vol II, 2nd edn. John Wiley, New York.Google Scholar
Geist, R., Reynolds, R., and Westall, J. (1988). Checkpoint interval selection in critical task environment. IEEE Trans. Reliab. 37, 395–400.CrossRefGoogle Scholar
Kulkarni, V. G., Nicola, V. F., and Trivedi, K. S. (1990). Effects of checkpointing and queueing on program performance. Stoch. Models 6, 615–648.CrossRefGoogle Scholar
Mi, J. (1994). Burn-in and maintenance policies. Adv. Appl. Prob. 26, 207–221.Google Scholar
Mi, J. (1999). Age-smooth properties of mixture models. Statist. Prob. Lett. 43, 225–236.CrossRefGoogle Scholar