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COS 461 Fall 1997 Time and Clocks u uses of time in distributed systems: –time-based algorithms (e.g. in security) –distributed make –gathering event traces for debugging –proving or disproving causality (insider trading) u common element: need to know in which order events happened

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COS 461 Fall 1997 Absolute Time u this is what clocks tell us u strategy: keep clocks synchronized; put time-stamp on each event u problems –hard to synchronize distributed clocks –clock speeds vary unpredictably –handling time zones, daylight savings time, year 2000, etc.

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COS 461 Fall 1997 Synchronizing Clocks u many protocols exist –NTP (Network Time Protocol) standard –will discuss simpler protocol here u use reference clock as baseline –Coordinated Universal Time (UCT) –from atomic clocks run by NIST u other machines try to sync with UCT

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COS 461 Fall 1997 Clock Synchronization Protocol u A sends to B: My clock says –only possible building block u problem: message takes time to get to B –network delay is unknown and variable u work-around: measure round-trip time between A and B, assume it doesnt vary much and that delay is equal in both directions –not completely accurate

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COS 461 Fall 1997 Clock Synchronization Problems u synchronization is necessarily inaccurate –happens before judgements might be wrong u can get out of sync badly if network is partitioned u vulnerable to dishonest time-servers u bottom line: OK for some applications u alternative: logical time

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COS 461 Fall 1997 Logical Time u insight: often dont care about when something happened, only about which thing happened first u logical time talks about happened before relationships, without reference to absolute time u (analogies to Einsteins relativity are common but bogus)

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COS 461 Fall 1997 Example Process P1 Process P2 Process P3 AB CD EF

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COS 461 Fall 1997 The Happened Before Relation u X --> Y means X happened before Y –captures logical ordering, not temporal u three rules: –if X and Y occur in the same process, and X occurs before Y, then X --> Y –if M is a message, then send(M) --> receive(M) –if X --> Y and Y --> Z, then X --> Z

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COS 461 Fall 1997 Example Process P1 Process P2 Process P3 AB CD EF

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COS 461 Fall 1997 Logical Time Relationships u Given two events X and Y, either –X --> Y, or –Y --> X, or –neither »X and Y are concurrent »X could not have caused Y, and vice versa u --> relation defines a partial order u How to determine --> in practice?

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COS 461 Fall 1997 Logical Timestamp Algorithms u simple algorithms to capture --> u assign numerical timestamp to each event –no relation to absolute time u simple timestamps –if X --> Y, then TS(X) < TS(Y) u vector timestamps –X --> Y if and only if TS(X) --> TS(Y)

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COS 461 Fall 1997 Simple Logical Timestamps u timestamp is an integer u each process has a logical clock –starts at zero –incremented on each local event u each message has a timestamp –equal to senders logical clock when sent –on receive, receivers logical clock set to 1 + max(message timestamp, receivers previous logical clock)

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COS 461 Fall 1997 Logical Timestamp Example Process P1 Process P2 Process P3 AB CD EF 1 1 2 34 5 0 0 0

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COS 461 Fall 1997 Simple Logical Timestamps u successfully capture all --> relationships u also capture some false relationships –TS(X) Y u good scheme to use if extra ordering isnt a problem u otherwise, need something fancier

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COS 461 Fall 1997 Vector Timestamps u captures --> exactly u more complicated than simple timestamps –uses more time and space u represent a logical time as a vector with P entries (assuming P processes) u each process has logical clock u each message has a logical timestamp

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COS 461 Fall 1997 Vector Timestamp Algorithm u local event in process I –process I increments the Ith element of its logical clock u message sent –message timestamp = logical clock of sender u message received –for all J, receiver sets Jth element of logical clock to max of »Jth component in message timestamp »Jth component in receivers logical clock

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COS 461 Fall 1997 Vector Time Example Process P1 Process P2 Process P3 AB CD EF (1,0,0)(2,0,0) (2,1,0) (2,2,0) (0,0,1) (2,2,2)

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COS 461 Fall 1997 Vector Time and Ordering u given two events X and Y, –X --> Y iff some X[i]

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COS 461 Fall 1997 Interpreting Vector Time u each process numbers its events sequentially –represented by Ith element of process Is clock u each process keeps track of which events on other processes have happened before the present time –if the Ith element of Ps clock is N, that means that the first N events at I happened before the present on process P

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COS 461 Fall 1997 Application: Event Logging Tool u maintain vector logical clocks u each process dumps events of interest to a local file –mark with logical timestamp u postmortem analysis tool can interleave the local traces correctly –can answer questions of possible causality

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COS 461 Fall 1997 Critique of Logical Time u fine for some applications, but u doesnt capture all of the real relationships –messages can flow outside the system »insider trading example u happened before doesnt capture causality –absolute time has this problem too

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