Markov Renewal Methods in Restart Problems in Complex Systems

DOI10.1007/978-3-319-25826-3_23zbMath1354.60109OpenAlexW2341880209MaRDI QIDQ2956068

Stephen Thompson, Lester R. Lipsky, Soren Asmussen

Publication date: 16 January 2017

Published in: The Fascination of Probability, Statistics and their Applications (Search for Journal in Brave)

Full work available at URL: http://math.au.dk/publs?publid=1034

zbMATH Keywords

spectral radiusfailure ratephase-type distributionheavy tailsPerron-Frobenius theorydata transmissionMarkov renewal equationrestartmatrix perturbationfault-tolerant computingalternating renewal processcomputer reliabilitytail~asymptotics

Mathematics Subject Classification ID

Markov renewal processes, semi-Markov processes (60K15) Applications of renewal theory (reliability, demand theory, etc.) (60K10) Continuous-time Markov processes on discrete state spaces (60J27)

Related Items (5)

On preemptive-repeat LIFO queues ⋮ Markov dependence in renewal equations and random sums with heavy tails ⋮ On the longest gap between power-rate arrivals ⋮ Time inhomogeneity in longest gap and longest run problems ⋮ Modelling failures times with dependent renewal type models via exchangeability

Cites Work

• Asymptotics for sums of random variables with local subexponential behaviour
• Asymptotic Behavior of Total Times for Jobs That Must Start Over if a Failure Occurs
• Computation of the distribution of the completion time when the work requirement is a ph random variableThis work was supported in part by the US Office of Naval Research under Contract no. N3014-88-K-0623, by NASA under Grant NAG-1-70, and by the Italian National Research Council CNR under the project “Material and Devices for Solid State Electronics” Grant no. 86.02177.61.
• The completion time of a job on multimode systems
• A New Class of Multivariate Phase Type Distributions
• On cycle maxima, first passage problems and extreme value theory for queues
• Characterizing Heavy-Tailed Distributions Induced by Retransmissions
• Distribution of the Number of Retransmissions of Bounded Documents

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