Recovery time of dynamic allocation processes

Document Type

Article

Publication Date

1-1-2000

Abstract

Many distributed protocols arising in on-line 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 general 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 rate 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 improve estimations of the recovery time significantly for various allocation processes related to allocations of balls into bins, and for the edge orientation problem studied before by Ajtai et al.

Identifier

0034560194 (Scopus)

Publication Title

Theory of Computing Systems

External Full Text Location

https://doi.org/10.1007/s002240010012

e-ISSN

14330490

ISSN

14324350

First Page

465

Last Page

487

Issue

5-6

Volume

33

This document is currently not available here.

Share

COinS