Asymptotic Behavior of Total Times for Jobs That Must Start Over if a Failure Occurs

Published Online:https://doi.org/10.1287/moor.1080.0329

References

  • Andersen L. N., Asmussen S. Parallel computing, failure recovery and extreme values. J. Statist. Theory Appl. (2008) . ForthcomingGoogle Scholar
  • Asmussen S.Ruin Probabilities (2000) (World Scientific, Singapore) CrossrefGoogle Scholar
  • Asmussen S.Applied Probability and Queues (2003) 2nd ed.(Springer-Verlag, New York) Google Scholar
  • Bingham N. H., Goldie C. M.Regular Variation (1987) (Cambridge University Press, Cambridge, UK) CrossrefGoogle Scholar
  • Bobbio A., Trivedi K. Computation of the distribution of the completion time when the work requirement is a ph random variable. Stochastic Models (1990) 6:133–150CrossrefGoogle Scholar
  • Castillo X., Siewiorek D. P. A performance-reliability model for computing systems. Proc. FTCS-10 (1980) (IEEE Computer Soc., Silver Spring, MD) 187–192Google Scholar
  • Chimento P. F., Trivedi K. S. The completion time of programs on processors subject to failure and repair. IEEE Trans. Comput. (1993) 42(1Google Scholar
  • Chlebus B. S., De Prisco R., Shvartsman A. A. Performing tasks on synchronous restartable message-passing processors. Distributed Comput. (2001) 14:49–64CrossrefGoogle Scholar
  • DePrisco R., Mayer A., Yung M. Time-optimal message-efficient work performance in the presence of faults. Proc. 13th ACM PODC (1994) 161–172Google Scholar
  • Finkelstein M., Esaulova V. Asymptotic behavior of a general class of mixture failure rates. Adv. Appl. Probab. (2006) 38:244–262CrossrefGoogle Scholar
  • Jagerman D. An inversion technique for the laplace transform. Bell Syst. Tech. J. (1982) 61:1995–2002CrossrefGoogle Scholar
  • Jelenković P., Tan J. Can retransmissions of superexponential documents cause subexponential delays. Proc. IEEE INFOCMO'07 (2007) Anchorage:892–900CrossrefGoogle Scholar
  • Jelenković P., Tan J. Characterizing heavy-tailed distributions induced by retransmissions. (2007) Workshop of Transient and Asymptotic Analysis of QueuesOctober 17–19EURANDOM, Eindhoven, The NetherlandsGoogle Scholar
  • Kalashnikov V.Geometric Sums: Bounds for Rare Events with Applications. Risk Analysis, Reliability, Queueing (1997) (Kluwer, Dordrecht, The Netherlands) CrossrefGoogle Scholar
  • Kartashov N. V. A uniform asymptotic renewal theorem. Th. Probab. Appl. (1980) 25:589–592CrossrefGoogle Scholar
  • Kartashov N. V. Equivalence of uniform renewal theorems and their criteria. Teor. Veoryuatnost. i Mat. Statist. (1982) 27:51–60[In Russian.]Google Scholar
  • Kulkarni V., Nicola V., Trivedi K. On modeling the performance and reliability of multimode systems. J. Systems Software (1986) 6:175–183CrossrefGoogle Scholar
  • Kulkarni V., Nicola V., Trivedi K. The completion time of a job on a multimode system. Adv. Appl. Probab. (1987) 19:932–954CrossrefGoogle Scholar
  • Lipsky L.Queueing Theory. A Linear Algebraic Approach (2007) 2nd ed.(Springer-Verlag, New York) Google Scholar
  • Müller A., Stoyan D.Comparison Methods for Stochastic Models and Risks (2002) (Wiley, Chichester, UK) Google Scholar
  • Sheahan R., Lipsky L., Fiorini P., Asmussen S. On the distribution of task completion times for tasks that must restart from the beginning if failure occurs. SIGMETRICS Performance Eval. Rev. (2006) 34:24–26CrossrefGoogle Scholar
  • Wang M., Woodroofe M. A uniform renewal theorem. Sequential Anal. (1996) 15:21–36CrossrefGoogle Scholar
  • Willmot G. E., Lin X. S. Lundberg approximations for compound distributions with insurance applications. Lecture Notes in Statistics (2001) 156(Springer-Verlag, New York) Google Scholar
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