Recovery time of dynamic allocation processes

Recovery time of dynamic allocation processes (1998)

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by Artur Czumaj

Venue:	IN PROCEEDINGS OF THE 10TH ANNUAL ACM SYMPOSIUM ON PARALLEL ALGORITHMS AND ARCHITECTURES, PUERTO VALLARTA, MEXICO, 28 JUNE–2
Citations:	11 - 3 self

BibTeX

@INPROCEEDINGS{Czumaj98recoverytime,
    author = {Artur Czumaj},
    title = {Recovery time of dynamic allocation processes},
    booktitle = {IN PROCEEDINGS OF THE 10TH ANNUAL ACM SYMPOSIUM ON PARALLEL ALGORITHMS AND ARCHITECTURES, PUERTO VALLARTA, MEXICO, 28 JUNE–2},
    year = {1998},
    pages = {202--211},
    publisher = {ACM Press}
}

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Abstract

Many distributed protocols arising in applications in online load balancing and dynamic resource allocation can be modeled by dynamic allocation processes related to the “balls into bin” problems. Traditionally the main focus of the research on dynamic allocation processes is on verifying whether a given process is stable, and if so, on analyzing its behavior in the limit (i.e., after sufficiently many steps). Once we know that the process is stable and we know its behavior in the limit, it is natural to analyze its recovery time, which is the time needed by the process to recover from any arbitrarily bad situation and to arrive very closely to a stable (i.e., a typical) state. This investigation is important to provide assurance that even if at some stage the process has reached a highly undesirable state, we can predict with high confidence its behavior after the estimated recovery time. In this paper we present a genera / framework to study the recovery time of discrete-time dynamic allocation processes. We model allocation processes by suitably chosen ergodic Markov chains. For a given Markov chain we apply path coupling arguments to bound its convergence rates to the stationary distribution, which directly yields the estimation of the recovery time of the corresponding allocation process. Our coupling approach provides in a relatively simple way an accurate prediction of the recovery time. In particular, we show that our method can be applied to significantly improve estimations of the recovery time for various allocation processes related to allocations of balls into bins, and for the edge orientation problem studied before by Ajtai et al.

Keyphrases

recovery time dynamic allocation process dynamic allocation convergence rate undesirable state high confidence markov chain corresponding allocation process bad situation estimated recovery time online load balancing simple way edge orientation problem allocation process accurate prediction discrete-time dynamic allocation process stationary distribution bin problem genus framework ergodic markov chain various allocation process main focus many step dynamic resource allocation