Time-adaptive self stabilization

Time-Adaptive Self Stabilization Shay Kutten Boaz Patt-Shamir* Dept. of Industrial Engineering College of Computer Science The Technion Northeastern University and boez~ccs. neu. edu IBM T.J, Watson Research Center kutten@ie. technion. ac. il We study the scenario where a transient fault hit ~ of the n nodes of a dktributed system by corrupting their state. We consider the basic problem of persistent bit, where the system is required to maintain a value in the face of transient failures by means of replication. We give an algorithm to recover the value quickly: the value of the bit is recovered at all nodes in 0(~) time units for any unknown value of j < n/2. Moreover, complete state quiescence occurs in O(dhun) time units, where diam denotes the diameter of the network. This means that the value persists indefinitely so long as any ~ < n/2 faults are followed by fl(diam) fault-free time units. We prove lower bounds which show that both time bounds are asymptotically optimal. Using the algorithm for persistent bit, we present a general transformer which takes a distributed nonreactive, non-stabilizing protocol P, and produces a self-stabilizing protocol P’ which solves the problem P solves, with the additional property that if the number of faults that hit the system after stabilization is j, for any unknown ~ < n/2, then the output of P’ regains stability in O(f) time units, and the state stabilizes in O(dlam) time units. ● Research supported by DARPA and Rome Laboratory under agreement F30602-96-0239. Permission to make digitalllmrd copies of fill or part of [his nmleriol for personal or clo.wroum use is granted wiU1outfee pmvi(ied UmtUw copies are not made or dislrihutcd for profit or commercin I w{vnnl~tgc.UWcopyrigbl notice. the tine oftlw publication and iL$date oppew’, *MInotice is given Uralcopyright is hy permission oftbe AChl, IIW To copy oUwn\,ise, to republish, to post on servers or to redisirilw! c to IISIS,requires specific Pemlissiotl oncVorfee 1997 F’(]D~ 97 Simla Bdmm (‘A lJ,V1 Copyright 1997 ACM 0-89791 -952 -1/97/8..$3 50