# ErlangC

ErlangC[c,a]

computes the Erlang C probability for nonzero waiting time in an M/M/c queue.

# Examples

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## Basic Examples(2)

Compute a nonzero waiting time probability using ErlangC:

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)

Calls to a technical support center arrive according to a Poisson process with a rate of 30 per hour. The time for a support person to serve a customer is exponentially distributed with a mean of five minutes. Find the minimum number of employees that are needed if the call center wishes to have a probability of 90% that a call will not be delayed.

Find the arrival and service rates for the center:

Hence, this is the minimum number of employees required:

A company has two 1 Mbps lines connecting two of its sites. Suppose that packets for these lines arrive according to a Poisson process at a rate of 150 packets per second, and that packets are exponentially distributed with mean 10 kilobits. When both lines are busy, the system queues the packets and transmits them on the first available line.

Find the probability that a packet has to wait in queue:

## Properties & Relations(3)

ErlangC gives the nonzero waiting probability for an M/M/c queue:

ErlangC is related to ErlangB:

The mean queue length of an M/M/c queue is related to ErlangC:

## Possible Issues(1)

ErlangC is not defined for some values of the parameters:

Wolfram Research (2012), ErlangC, Wolfram Language function, https://reference.wolfram.com/language/ref/ErlangC.html (updated 2017).

#### Text

Wolfram Research (2012), ErlangC, Wolfram Language function, https://reference.wolfram.com/language/ref/ErlangC.html (updated 2017).

#### CMS

Wolfram Language. 2012. "ErlangC." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2017. https://reference.wolfram.com/language/ref/ErlangC.html.

#### APA

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

#### BibTeX

@misc{reference.wolfram_2024_erlangc, author="Wolfram Research", title="{ErlangC}", year="2017", howpublished="\url{https://reference.wolfram.com/language/ref/ErlangC.html}", note=[Accessed: 24-July-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_erlangc, organization={Wolfram Research}, title={ErlangC}, year={2017}, url={https://reference.wolfram.com/language/ref/ErlangC.html}, note=[Accessed: 24-July-2024 ]}