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# NAME

Math::Telephony::ErlangB - Erlang B calculations from Perl

# VERSION

I'm too lazy to track the VERSION in two places (the module and the doc). You can get the version with:

`````` perl -MMath::Telephony::ErlangB \
-le 'print \$Math::Telephony::ErlangB::VERSION'``````

# SYNOPSIS

``````  use Math::Telephony::ErlangB qw( :all );

# Evaluate blocking probability
\$bprob = blocking_probability(\$traffic, \$servers);
\$gos = gos(\$traffic, \$servers); # Same result as above

# Dimension minimum number of needed servers
\$servers = servers(\$traffic, \$gos);

# Calculate maximum serveable traffic
\$traffic = traffic(\$servers, \$gos); # Default precision 0.001
\$traffic = traffic(\$servers, \$gos, 1e-10);

``````

# DESCRIPTION

This module contains various functions to deal with Erlang B calculations.

The Erlang B model allows dimensioning the number of servers in a M/M/S/0/inf model (Kendall notation):

• The input process is Markovian (Poisson in this case)

• The serving process is Markovian (ditto)

• There are S servers

• There's no wait line (pure loss)

• The input population is infinite

# INTERFACE

## EXPORT

None by default. Following functions can be imported at once via the ":all" keyword.

## VARIABLES

These variables control different aspects of this module, such as default values.

\$default_precision = 0.001;

This variable is the default precision used when evaluating the maximum traffic sustainable using the traffic() function below.

## FUNCTIONS

The following functions are available for exporting. Three "concepts" are common to them all:

• traffic is the offered traffic expressed in Erlang. When an input parameter, this value must be defined and greater or equal to 0.

• servers is the number of servers in the queue. When an input parameter, this must be a defined value, greater or equal to 0.

• blocking probability is the probability that a given service request will be blocked due to congestion.

• gos is the grade of service, that corresponds to the blocking probability for Erlang B calculation. The concept of Grade of Service is a little different in perspective: in general, it should give us an estimate of how the service is good (or bad). In the Erlang B model this role is played by the blocking probability, thus the gos is equal to it.

\$bprob = blocking_probability(\$traffic, \$servers);

Evaluate the blocking probability from given traffic and numer of servers.

\$gos = gos(\$traffic, \$servers);

Evaluate the grade of service from given traffic and number of servers. For Erlang B, the GoS figure corresponds to the blocking probability.

\$servers = servers(\$traffic, \$bprob);

Calculate minimum number of servers needed to serve the given traffic with a blocking probability not greater than that given.

\$traffic = traffic(\$servers, \$bprob);
\$traffic = traffic(\$servers, \$bprob, \$prec);

Calculate the maximum offered traffic that can be served by the given number of serves with a blocking probability not greater than that given.

The prec parameter allows to set the precision in this traffic calculation. If undef it defaults to \$default_precision in this package.

# DIAGNOSTICS

All public functions return undef upon invalid input, so there should be nothing to complain with. In a future version we could stick to a more exception-oriented interface.

# CONFIGURATION AND ENVIRONMENT

Math::Telephony::ErlangB requires no configuration files or environment variables.

# DEPENDENCIES

Among the non-standard modules, only version.

None reported.

# BUGS AND LIMITATIONS

No bugs have been reported.

Please report any bugs or feature requests through http://rt.cpan.org/

# AUTHOR

Flavio Poletti `<flavio [at] polettix [dot] it>`

Copyright (c) 2007, Flavio Poletti `<flavio [at] polettix [dot] it>`. All rights reserved.

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

Questo modulo è software libero: potete ridistribuirlo e/o modificarlo negli stessi termini di Perl stesso. Vedete anche perlartistic e perlgpl.

# DISCLAIMER OF WARRANTY

BECAUSE THIS SOFTWARE IS LICENSED FREE OF CHARGE, THERE IS NO WARRANTY FOR THE SOFTWARE, TO THE EXTENT PERMITTED BY APPLICABLE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT HOLDERS AND/OR OTHER PARTIES PROVIDE THE SOFTWARE "AS IS" WITHOUT WARRANTY OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE. THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE SOFTWARE IS WITH YOU. SHOULD THE SOFTWARE PROVE DEFECTIVE, YOU ASSUME THE COST OF ALL NECESSARY SERVICING, REPAIR, OR CORRECTION.

IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MAY MODIFY AND/OR REDISTRIBUTE THE SOFTWARE AS PERMITTED BY THE ABOVE LICENCE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY GENERAL, SPECIAL, INCIDENTAL, OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE USE OR INABILITY TO USE THE SOFTWARE (INCLUDING BUT NOT LIMITED TO LOSS OF DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD PARTIES OR A FAILURE OF THE SOFTWARE TO OPERATE WITH ANY OTHER SOFTWARE), EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGES.

# NEGAZIONE DELLA GARANZIA

Poiché questo software viene dato con una licenza gratuita, non c'è alcuna garanzia associata ad esso, ai fini e per quanto permesso dalle leggi applicabili. A meno di quanto possa essere specificato altrove, il proprietario e detentore del copyright fornisce questo software "così com'è" senza garanzia di alcun tipo, sia essa espressa o implicita, includendo fra l'altro (senza però limitarsi a questo) eventuali garanzie implicite di commerciabilità e adeguatezza per uno scopo particolare. L'intero rischio riguardo alla qualità ed alle prestazioni di questo software rimane a voi. Se il software dovesse dimostrarsi difettoso, vi assumete tutte le responsabilità ed i costi per tutti i necessari servizi, riparazioni o correzioni.

In nessun caso, a meno che ciò non sia richiesto dalle leggi vigenti o sia regolato da un accordo scritto, alcuno dei detentori del diritto di copyright, o qualunque altra parte che possa modificare, o redistribuire questo software così come consentito dalla licenza di cui sopra, potrà essere considerato responsabile nei vostri confronti per danni, ivi inclusi danni generali, speciali, incidentali o conseguenziali, derivanti dall'utilizzo o dall'incapacità di utilizzo di questo software. Ciò include, a puro titolo di esempio e senza limitarsi ad essi, la perdita di dati, l'alterazione involontaria o indesiderata di dati, le perdite sostenute da voi o da terze parti o un fallimento del software ad operare con un qualsivoglia altro software. Tale negazione di garanzia rimane in essere anche se i dententori del copyright, o qualsiasi altra parte, è stata avvisata della possibilità di tali danneggiamenti.

Se decidete di utilizzare questo software, lo fate a vostro rischio e pericolo. Se pensate che i termini di questa negazione di garanzia non si confacciano alle vostre esigenze, o al vostro modo di considerare un software, o ancora al modo in cui avete sempre trattato software di terze parti, non usatelo. Se lo usate, accettate espressamente questa negazione di garanzia e la piena responsabilità per qualsiasi tipo di danno, di qualsiasi natura, possa derivarne.