ErlangB

ErlangB[c,a]

computes the Erlang B loss probability for an M/M/c/c queue.

Examples

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Basic Examples(2)

Compute a loss probability using ErlangB:

Obtain the same result using Probability:

Plot for a different number of servers c:

Scope(4)

Use exact values for the parameters:

Machine precision:

Higher precision:

Symbolic parameters:

Applications(2)

A company has five 1 Mbps lines to carry video conferences between two company sites. Suppose that each video conference requires 1 Mbps and lasts for an average of one hour. Assume that requests for video conferences arrive according to a Poisson process with a rate of three calls per hour. Find the probability that a call request is blocked due to lack of lines:

A modem pool consists of four modems and the offered traffic intensity is 2 Erlangs. Find the probability that a connection fails due to blocking:

Blocking probability with six modems:

Properties & Relations(3)

ErlangB gives the loss probability for an M/M/c/c queue:

ErlangB satisfies a nonlinear difference equation:

ErlangB is related to ErlangC:

Wolfram Research (2012), ErlangB, Wolfram Language function, https://reference.wolfram.com/language/ref/ErlangB.html.

Text

Wolfram Research (2012), ErlangB, Wolfram Language function, https://reference.wolfram.com/language/ref/ErlangB.html.

CMS

Wolfram Language. 2012. "ErlangB." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/ErlangB.html.

APA

Wolfram Language. (2012). ErlangB. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/ErlangB.html

BibTeX

@misc{reference.wolfram_2024_erlangb, author="Wolfram Research", title="{ErlangB}", year="2012", howpublished="\url{https://reference.wolfram.com/language/ref/ErlangB.html}", note=[Accessed: 26-May-2024 ]}

BibLaTeX

@online{reference.wolfram_2024_erlangb, organization={Wolfram Research}, title={ErlangB}, year={2012}, url={https://reference.wolfram.com/language/ref/ErlangB.html}, note=[Accessed: 26-May-2024 ]}