/ 
TrafficModeling-ErlangB-0.01
/ TrafficModeling::ErlangB

NAME

TrafficModeling::ErlangB - Perl extension for Erlang B calculations

SYNOPSIS

use TrafficModeling::ErlangB;

# Evaluate blocking probability
$gos = gos($traffic, $servers);

# 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

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.

  • gos is the grade of service, i.e. the blocking probability.

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

Evaluate the grade of service from given traffic and number of servers.

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

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

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

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

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

SEE ALSO

You can google for plenty of information about Erlang B.

AUTHOR

Flavio Poletti <flavio@polettix.it>

COPYRIGHT AND LICENSE

Copyright (C) 2005 by Flavio Poletti

This library is free software; you can redistribute it and/or modify it under the same terms as Perl itself, either Perl version 5.8.6 or, at your option, any later version of Perl 5 you may have available.