# NAME

Time::Skew - Computes local clock skew with respect to a remote clock.

# SYNOPISI

```
use Time::Skew
# Init Convex Hull and timing data
my $hull=[];
my $result={};
# Iterate data point introduction
Time::Skew::convexhull($result,$datapoint,$hull);
```

# DESCRIPTION

This module supports the computation of the skew between two clocks: the (relative) skew is the speed with which two clocks diverge. For instance, if yesterday two clocks, at the same time, showed respectively 10:00 and 10:05, while today when the former shows 10:00 the latter shows 10:04, we say that their relative skew is 1 minute/24 hours, roughly 7E-4.

The module contains one single subroutine, which accepts as input a pair of timestamps, associated to a message from host A to host B: the timestamps correspond to the time when the message was sent, and to the time when message is received. Each timestamp reflects the value of the local clock where the operation takes place: the clock of host A for the send, the clock of B for the receive.

Please note that the module does _not_ contain any message exchange facility, but only the mathematics needed to perform the skew approximation, once timestamps are known.

The subroutine takes as argument:

a reference to a hash where values related to the timing of the network path from A to B;

a 2-elems array (a data point in the sequel) containing the timestamp of the receive event, and the differece between the send timestamp and the receive timestamp for one message;

a stack containing some data points, those that form the convex hull.

The usage is very simple, and is illustrated by the following example:

```
#!/usr/bin/perl -w
use strict;
use Time::Skew;
# Initialize data
my $hull=[];
my $result={};
while ( 1 ) {
# Exchange message and acquire a new data point
my $datapoint = acquire();
# Call the convexhull subroutine
Time::Skew::convexhull($result,$datapoint,$hull);
# After first message some results are still undefined
( defined $result->{skewjitter} ) || next;
# here you can use the results
};
}
```

The data returned in the "result" hash is the following:

result->{skew} the clock skew;

result->{skewjitter} the variance of the skew estimate, used to estimate convergence;

result->{jitter} difference between the current delay and the previous delay;

result->{delay} the communication delay, decremented by a constant (yet unknown) value, used to compute communication jitter;

result->{elems} the number of data points in the convex hull;

result->{select} the index of the data point in the convex hull used to compute the skew;

result->{itimestamp} the timestamp, first element in the data point just passed to the subroutine;

result->{delta} the timestamp difference, second element in the data point just passed to the subroutine;

The data returned in the "hull" stack is a series of data points, selected from those passed to successive calls of the subroutine. The number of data points in the "hull" stack usually does not exceed 20 units.

The algorithm is very fast: each call consists in scanning at most all data points in the "hull" stack, performing simple arithmetic operations for each element.

The algorithm must be fed with a sequence of data points before returning significant results. The accuracy of the estimate keeps growing while new data points are passed to the subroutine. A rough rule of thumb to evaluate estimate accuracy is to observe the skew jitter, and assume it corresponds to the skew estimate accuracy. Paths with quite regular communication delay (small jitter) converge faster.

# HISTORY

0.1 Original version

# BUGS

A rounding problem may cause an inconsistent negative number of magnitude E-15 as "delay", instead of 0. A warning is generated, and the algorithm compensates the problem.

# SEE ALSO

Augusto Ciuffoletti, "Packet Delay Monitoring without a GPS", Technical Report 05-16, Universita' degli Studi di Pisa, Dipartimento di Informatica, June 2005.

Sue B. Moon, Paul Skelly, and Don Towsley. "Estimation and removal of clock skew from network delay measurements". Technical Report 98-43, Department of Computer Science - University of Massachusetts at Amherst - USA, 1998.

# AUTHOR

Augusto Ciuffoletti, <augusto@di.unipi.it>

# COPYRIGHT AND LICENSE

Copyright (C) 2005 by Augusto Ciuffoletti

This library is free software; you can redistribute it and/or modify it under the same terms as Perl itself.