00521898 - An Optimal Internal Clock Synchronization...

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An Optimal Internal Clock Synchronization Algorithm* Christof Fetzer and Flaviu Cristian Department of Computer Science & Engineering University of California, San Diego La Jolla, CA 92093-0114 Abstract We propose an optimal convergence function for achieving fault-tolerant, internal clock synchroniza, tion in the presence of arbitrary process and clock fail- ures. The diflerential fault-tolerant midpoint conver- gence function guarantees an optimal maximum cor- rection, an optimal maximum drift rate, and an opti- mal maximum deviation. The proposed convergence function is simple and easy to compute. It bounds the maximum drift rate of correct clocks by the maximum drift rate of a correct hardware clock. The maximum correction is limited by the maximum drift between two correct hardware clocks during one round. The maximum deviation is approximately 44 + ~PT,,, , where A is the maximum remote clock reading error, p is the maximum drift rate of a correct hardware clock and rman is the max- imum duration of a synchronization round. 1 Introduction Tight internal clock synchronization is essential for many real-time and fault-tolerant applications. Inter- nal clock synchronization requires that (1) at any time the deviation between two correct clocks be bounded by a constant 6 (called the maximum deviation) and (2) the drift rate of clocks with respect to real-time be bounded by a constant pv. Clock synchronization is a non-trivial problem because of the need to toler- ate failures. Since in this paper we are only interested in internal clock synchronization algorithms capable of masking arbitrary clock and process failures, when we talk about a synchronization algorithm, we mean 'This work was partially supported by grants from the Air Force Office of Scientific Research, the German Academic Ex- change Service (DAAD), the Powell Foundation, Sun Microsys- tems, and the Microelectronics Innovation and Computer Re- search Opportunities in California 0-7803-2680-6/95/$4.00 0 1995 IEEE 187 an internal clock synchronization algorithm tolerant of arbitrary failures. Most synchronization algorithms can be described as instances of a single abstract, generic clock syn- chronization algorithm by using the notion of a con- vergence function introduced in [SI. This generic algo- rithm can be succintly described as follows: at the end of each synchronization round each process reads the clocks of all processes and then adjusts its clock value for the next round by applying a convergence function to the clock readings of the current round. A synchro- nization algorithms which can be obtained from the above generic algorithm by instantiating some con- crete function for the abstract notion of a convergence function will be termed a Convergence function based algorithm.
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This note was uploaded on 05/25/2011 for the course CS 889 taught by Professor Ib during the Spring '11 term at Columbia SC.

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00521898 - An Optimal Internal Clock Synchronization...

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