Erlang unit
Encyclopedia
The erlang is a dimensionless unit that is used in telephony
as a statistical measure of offered load
or carried load on service-providing elements such as telephone circuits or telephone switching equipment. It is named after the Danish
telephone engineer
A. K. Erlang
, the originator of traffic engineering
and queueing theory
.
One erlang of carried traffic refers to a single resource being in continuous use, or two channels being in use fifty percent of the time, and so on. For example, if an office has two telephone operators who are both busy all the time, that would represent two erlangs (2 E) of traffic; or a radio channel that is occupied for one hour continuously is said to have a load of 1 Erlang.
When used to describe offered traffic, a value followed by “erlangs” represents the average number of concurrent calls that would have been carried if there were an unlimited number of circuits (that is, if the call-attempts that were made when all circuits were in use had not been rejected). The relationship between offered traffic and carried traffic depends on the design of the system and user behavior. Three common models are (a) callers whose call-attempts are rejected go away and never come back, (b) callers whose call-attempts are rejected try again within a fairly short space of time, and (c) the system allows users to wait in queue until a circuit becomes available.
A third measurement of traffic is instantaneous traffic, expressed as a certain number of erlangs, meaning the exact number of calls taking place at a point in time. In this case the number is an integer. Traffic-level-recording devices, such as moving-pen recorders, plot instantaneous traffic.
The concepts and mathematics introduced by Agner Krarup Erlang have broad applicability beyond telephony. They apply wherever users arrive more or less at random to receive exclusive service from any one of a group of service-providing elements without prior reservation, for example, where the service-providing elements are ticket-sales windows, toilets on an airplane, or motel rooms. (Erlang’s models do not apply where the server-providing elements are shared between several concurrent users or different amounts of service are consumed by different users, for instance, on circuits carrying data traffic.)
Offered traffic (in erlangs) is related to the call arrival rate, λ, and the average call-holding time, h, by:
provided that h and λ are expressed using the same units of time (seconds and calls per second, or minutes and calls per minute).
The practical measurement of traffic is typically based on continuous observations over several days or weeks, during which the instantaneous traffic is recorded at regular, short intervals (such as every few seconds). These measurements are then used to calculate a single result, most commonly the busy hour traffic (in erlangs). This is the average number of concurrent calls during a given one-hour period of the day, where that period is selected to give the highest result. (This result is called the time-consistent busy hour traffic). An alternative is to calculate a busy hour traffic value separately for each day (which may correspond to slightly different times each day) and take the average of these values. This generally gives a slightly higher value than the time-consistent busy hour value.
The goal of Erlang’s traffic theory is to determine exactly how many service-providing elements should be provided in order to satisfy users, without wasteful over-provisioning. To do this, a target is set for the grade of service
(GoS) or quality of service
(QoS). For example, in a system where there is no queuing, the GoS may be that no more than 1 call in 100 is blocked (i.e., rejected) due to all circuits being in use (a GoS of 0.01), which becomes the target probability of call blocking, Pb, when using the Erlang B formula.
There are several Erlang formulae, including Erlang B, Erlang C and the related Engset formula, based on different models of user behavior and system operation. These are discussed below, and may each be derived by means of a special case of continuous-time Markov processes known as a birth-death process
.
Where the existing busy-hour carried traffic, Ec, is measured on an already-overloaded system, with a significant level of blocking, it is necessary to take account of the blocked calls in estimating the busy-hour offered traffic Eo (which is the traffic value to be used in the Erlang formula). The offered traffic can be estimated by Eo = Ec/(1 - Pb). For this purpose, where the system includes a means of counting blocked calls and successful calls, Pb can be estimated directly from the proportion of calls that are blocked. Failing that, Pb can be estimated by using Ec in place of Eo in the Erlang formula and the resulting estimate of Pb can then be used in Eo = Ec/(1 - Pb) to estimate Eo. Another method of estimating Eo in an overloaded system is to measure the busy-hour call arrival rate, λ (counting successful calls and blocked calls), and the average call-holding time (for successful calls), h, and then estimate Eo using the formula E = λh.
For a situation where the traffic to be handled is completely new traffic, the only choice is to try to model expected user behavior, estimating active user population, N, expected level of use, U (number of calls/transactions per user per day), busy-hour concentration factor, C (proportion of daily activity that will fall in the busy hour), and average holding time/service time, h (expressed in minutes). A projection of busy-hour offered traffic would then be Eo = (NUC/60)h erlangs. (The division by 60 translates the busy-hour call/transaction arrival rate into a per-minute value, to match the units in which h is expressed.)
and is not limited to telephone networks, since it describes a probability in a queuing system (albeit a special case with a number of servers but no buffer spaces for incoming calls to wait for a free server). Hence, the formula is also used in certain inventory systems with lost sales.
The formula applies under the condition that an unsuccessful call, because the line is busy, is not queued or retried, but instead really lost forever. It is assumed that call attempts arrive following a Poisson process
, so call arrivals are independent. Further it is assumed that message length (holding times) are exponentially distributed (Markovian system) although the formula turns out to apply under general holding time distributions.
Erlangs are a dimensionless quantity calculated as the average arrival rate, λ, multiplied by the average call length, h. (see Little's Law
)
The Erlang B formula assumes an infinite population of sources (such as telephone subscribers), which jointly offer traffic to N servers (such as links in a trunk group). The rate of arrival of new calls (birth rate) is equal to λ and is constant, not depending on the number of active sources, because the total number of sources is assumed to be infinite. The rate of call departure (death rate) is equal to the number of calls in progress divided by h, the mean call holding time. The formula calculates blocking probability in a loss system, where if a request is not served immediately when it tries to use a resource, it is aborted. Requests are therefore not queued. Blocking occurs when there is a new request from a source, but all the servers are already busy. The formula assumes that blocked traffic is immediately cleared.
The formula provides the GoS (grade of service
) which is the probability Pb that a new call arriving at the circuit group is rejected because all servers (circuits) are busy: B(E, m) when E Erlang of traffic are offered to m trunks (communication channels).
where:
This may be expressed recursively as follows, in a form that is used to simplify the calculation of tables of the Erlang B formula:
.
Typically, instead of B(E, m) the inverse 1/B(E, m) is calculated in numerical computation in order to ensure numerical stability
:
Function ErlangB (E as Double, m As Integer) As Double
Dim InvB As Double
Dim j As Integer
InvB = 1.0
For j = 1 To m
InvB = 1.0 + j / E * InvB
Next j
ErlangB = 1.0 / InvB
End Function
The Erlang B formula applies to loss systems, such as telephone systems on both fixed and mobile networks, which do not provide traffic buffering, and are not intended to do so. It assumes that the call arrivals may be modeled by a Poisson process
, but is valid for any statistical distribution of call holding times with finite mean.
Erlang B is a trunk sizing tool for voice switch to voice switch traffic.
The Erlang B formula is decreasing and convex
in m.
, rather than a formula, that adds an extra parameter, the Recall Factor, which defines the recall attempts.
The steps in the process are as follows:
1. Calculate
as above for Erlang B.
2. Calculate the probable number of blocked calls
3. Calculate the number of recalls,
assuming a Recall Factor, 
:
4. Calculate the new offered traffic
where
is the initial (baseline) level of traffic.
5. Return to step 1 and iterate until a stable value of
is obtained.
, for a specified desired probability of queuing.
where:
It is assumed that the call arrivals can be modeled by a Poisson process
and that call holding times are described by a negative exponential distribution. A common use for Erlang C is modeling and dimensioning call center agents in a call center environment.
, used to determine the probability of congestion occurring within a telephony
circuit group
. It deals with a finite population of S sources rather than the infinite population of sources that Erlang assumes. The formula requires that the user knows the expected peak traffic, the number of sources (callers) and the number of circuits in the network.
it needs to have to and from the telephone network. An approximate approach is to use the Erlang-B formula. However, if the business has a small number of extensions
, then it should instead use the more exact Engset calculation, which reflects the fact that extensions already in use will not make additional simultaneous calls. (For a large user population, the Engset and the Erlang-B calculations give the same result.)
, while Engset specifies a finite number of
callers
.
Thus Engset's equation should be used when the source population is small (say less than 200 users, extensions or customers).
where
In practice, like Erlang's equations, Engset's formula requires recursion to solve for the blocking or congestion probability. There are several recursions that could be used. One way to determine this probability, one first determines an initial estimate. This initial estimate is substituted into the equation and the equation then is solved. The answer to this initial calculation is then substituted back into the equation, resulting in a new answer which is again substituted. This iterative process continues until the equation converges
to a stable result.
Engset's equation follows:
Telephony
In telecommunications, telephony encompasses the general use of equipment to provide communication over distances, specifically by connecting telephones to each other....
as a statistical measure of offered load
Offered load
In the mathematical theory of probability, offered load is a concept in queuing theory. The offered load is a measure of traffic in the queue. The offered load is given by Little's law: the arrival rate into the queue multiplied by the mean holding time , the average amount of time spent by items...
or carried load on service-providing elements such as telephone circuits or telephone switching equipment. It is named after the Danish
Denmark
Denmark is a Scandinavian country in Northern Europe. The countries of Denmark and Greenland, as well as the Faroe Islands, constitute the Kingdom of Denmark . It is the southernmost of the Nordic countries, southwest of Sweden and south of Norway, and bordered to the south by Germany. Denmark...
telephone engineer
Engineer
An engineer is a professional practitioner of engineering, concerned with applying scientific knowledge, mathematics and ingenuity to develop solutions for technical problems. Engineers design materials, structures, machines and systems while considering the limitations imposed by practicality,...
A. K. Erlang
Agner Krarup Erlang
Agner Krarup Erlang was a Danish mathematician, statistician and engineer, who invented the fields of traffic engineering and queueing theory....
, the originator of traffic engineering
Teletraffic engineering
Telecommunications traffic engineering, teletraffic engineering, or traffic engineering is the application of traffic engineering theory to telecommunications...
and queueing theory
Queueing theory
Queueing theory is the mathematical study of waiting lines, or queues. The theory enables mathematical analysis of several related processes, including arriving at the queue, waiting in the queue , and being served at the front of the queue...
.
Traffic measurements of a telephone circuit
When used to represent carried traffic, a value (which can be a non-integer such as 43.5) followed by “erlangs” represents the average number of concurrent calls carried by the circuits (or other service-providing elements), where that average is calculated over some reasonable period of time. The period over which the average is calculated is often one hour, but shorter periods (e.g., 15 minutes) may be used where it is known that there are short spurts of demand and a traffic measurement is desired that does not mask these spurts.One erlang of carried traffic refers to a single resource being in continuous use, or two channels being in use fifty percent of the time, and so on. For example, if an office has two telephone operators who are both busy all the time, that would represent two erlangs (2 E) of traffic; or a radio channel that is occupied for one hour continuously is said to have a load of 1 Erlang.
When used to describe offered traffic, a value followed by “erlangs” represents the average number of concurrent calls that would have been carried if there were an unlimited number of circuits (that is, if the call-attempts that were made when all circuits were in use had not been rejected). The relationship between offered traffic and carried traffic depends on the design of the system and user behavior. Three common models are (a) callers whose call-attempts are rejected go away and never come back, (b) callers whose call-attempts are rejected try again within a fairly short space of time, and (c) the system allows users to wait in queue until a circuit becomes available.
A third measurement of traffic is instantaneous traffic, expressed as a certain number of erlangs, meaning the exact number of calls taking place at a point in time. In this case the number is an integer. Traffic-level-recording devices, such as moving-pen recorders, plot instantaneous traffic.
The concepts and mathematics introduced by Agner Krarup Erlang have broad applicability beyond telephony. They apply wherever users arrive more or less at random to receive exclusive service from any one of a group of service-providing elements without prior reservation, for example, where the service-providing elements are ticket-sales windows, toilets on an airplane, or motel rooms. (Erlang’s models do not apply where the server-providing elements are shared between several concurrent users or different amounts of service are consumed by different users, for instance, on circuits carrying data traffic.)
Offered traffic (in erlangs) is related to the call arrival rate, λ, and the average call-holding time, h, by:
provided that h and λ are expressed using the same units of time (seconds and calls per second, or minutes and calls per minute).
The practical measurement of traffic is typically based on continuous observations over several days or weeks, during which the instantaneous traffic is recorded at regular, short intervals (such as every few seconds). These measurements are then used to calculate a single result, most commonly the busy hour traffic (in erlangs). This is the average number of concurrent calls during a given one-hour period of the day, where that period is selected to give the highest result. (This result is called the time-consistent busy hour traffic). An alternative is to calculate a busy hour traffic value separately for each day (which may correspond to slightly different times each day) and take the average of these values. This generally gives a slightly higher value than the time-consistent busy hour value.
The goal of Erlang’s traffic theory is to determine exactly how many service-providing elements should be provided in order to satisfy users, without wasteful over-provisioning. To do this, a target is set for the grade of service
Grade of service
In telecommunication engineering, and in particular teletraffic engineering, the quality of voice service is specified by two measures: the grade of service and the quality of service ....
(GoS) or quality of service
Quality of service
The quality of service refers to several related aspects of telephony and computer networks that allow the transport of traffic with special requirements...
(QoS). For example, in a system where there is no queuing, the GoS may be that no more than 1 call in 100 is blocked (i.e., rejected) due to all circuits being in use (a GoS of 0.01), which becomes the target probability of call blocking, Pb, when using the Erlang B formula.
There are several Erlang formulae, including Erlang B, Erlang C and the related Engset formula, based on different models of user behavior and system operation. These are discussed below, and may each be derived by means of a special case of continuous-time Markov processes known as a birth-death process
Birth-death process
The birth–death process is a special case of continuous-time Markov process where the states represent the current size of a population and where the transitions are limited to births and deaths...
.
Where the existing busy-hour carried traffic, Ec, is measured on an already-overloaded system, with a significant level of blocking, it is necessary to take account of the blocked calls in estimating the busy-hour offered traffic Eo (which is the traffic value to be used in the Erlang formula). The offered traffic can be estimated by Eo = Ec/(1 - Pb). For this purpose, where the system includes a means of counting blocked calls and successful calls, Pb can be estimated directly from the proportion of calls that are blocked. Failing that, Pb can be estimated by using Ec in place of Eo in the Erlang formula and the resulting estimate of Pb can then be used in Eo = Ec/(1 - Pb) to estimate Eo. Another method of estimating Eo in an overloaded system is to measure the busy-hour call arrival rate, λ (counting successful calls and blocked calls), and the average call-holding time (for successful calls), h, and then estimate Eo using the formula E = λh.
For a situation where the traffic to be handled is completely new traffic, the only choice is to try to model expected user behavior, estimating active user population, N, expected level of use, U (number of calls/transactions per user per day), busy-hour concentration factor, C (proportion of daily activity that will fall in the busy hour), and average holding time/service time, h (expressed in minutes). A projection of busy-hour offered traffic would then be Eo = (NUC/60)h erlangs. (The division by 60 translates the busy-hour call/transaction arrival rate into a per-minute value, to match the units in which h is expressed.)
Erlang B formula
Erlang-B (sometimes also written without the hyphen Erlang B), also known as the Erlang loss formula, is a formula for the blocking probability derived from the Erlang distribution to describe the probability of call loss on a group of circuits (in a circuit switched network, or equivalent). It is, for example, used in planning telephone networks. The formula was derived by Agner Krarup ErlangAgner Krarup Erlang
Agner Krarup Erlang was a Danish mathematician, statistician and engineer, who invented the fields of traffic engineering and queueing theory....
and is not limited to telephone networks, since it describes a probability in a queuing system (albeit a special case with a number of servers but no buffer spaces for incoming calls to wait for a free server). Hence, the formula is also used in certain inventory systems with lost sales.
The formula applies under the condition that an unsuccessful call, because the line is busy, is not queued or retried, but instead really lost forever. It is assumed that call attempts arrive following a Poisson process
Poisson process
A Poisson process, named after the French mathematician Siméon-Denis Poisson , is a stochastic process in which events occur continuously and independently of one another...
, so call arrivals are independent. Further it is assumed that message length (holding times) are exponentially distributed (Markovian system) although the formula turns out to apply under general holding time distributions.
Erlangs are a dimensionless quantity calculated as the average arrival rate, λ, multiplied by the average call length, h. (see Little's Law
Little's law
In the mathematical theory of queues, Little's result, theorem, lemma, law or formula says:It is a restatement of the Erlang formula, based on the work of Danish mathematician Agner Krarup Erlang...
)
The Erlang B formula assumes an infinite population of sources (such as telephone subscribers), which jointly offer traffic to N servers (such as links in a trunk group). The rate of arrival of new calls (birth rate) is equal to λ and is constant, not depending on the number of active sources, because the total number of sources is assumed to be infinite. The rate of call departure (death rate) is equal to the number of calls in progress divided by h, the mean call holding time. The formula calculates blocking probability in a loss system, where if a request is not served immediately when it tries to use a resource, it is aborted. Requests are therefore not queued. Blocking occurs when there is a new request from a source, but all the servers are already busy. The formula assumes that blocked traffic is immediately cleared.
The formula provides the GoS (grade of service
Grade of service
In telecommunication engineering, and in particular teletraffic engineering, the quality of voice service is specified by two measures: the grade of service and the quality of service ....
) which is the probability Pb that a new call arriving at the circuit group is rejected because all servers (circuits) are busy: B(E, m) when E Erlang of traffic are offered to m trunks (communication channels).
where:
-
is the probability of blocking - m is the number of resources such as servers or circuits in a group
- E = λh is the total amount of traffic offered in erlangs
This may be expressed recursively as follows, in a form that is used to simplify the calculation of tables of the Erlang B formula:
.Typically, instead of B(E, m) the inverse 1/B(E, m) is calculated in numerical computation in order to ensure numerical stability
Numerical stability
In the mathematical subfield of numerical analysis, numerical stability is a desirable property of numerical algorithms. The precise definition of stability depends on the context, but it is related to the accuracy of the algorithm....
:
Function ErlangB (E as Double, m As Integer) As Double
Dim InvB As Double
Dim j As Integer
InvB = 1.0
For j = 1 To m
InvB = 1.0 + j / E * InvB
Next j
ErlangB = 1.0 / InvB
End Function
The Erlang B formula applies to loss systems, such as telephone systems on both fixed and mobile networks, which do not provide traffic buffering, and are not intended to do so. It assumes that the call arrivals may be modeled by a Poisson process
Poisson process
A Poisson process, named after the French mathematician Siméon-Denis Poisson , is a stochastic process in which events occur continuously and independently of one another...
, but is valid for any statistical distribution of call holding times with finite mean.
Erlang B is a trunk sizing tool for voice switch to voice switch traffic.
The Erlang B formula is decreasing and convex
Convex
'The word convex means curving out or bulging outward, as opposed to concave. Convex or convexity may refer to:Mathematics:* Convex set, a set of points containing all line segments between each pair of its points...
in m.
Extended Erlang B
Extended Erlang B is an iterative calculationIteration
Iteration means the act of repeating a process usually with the aim of approaching a desired goal or target or result. Each repetition of the process is also called an "iteration," and the results of one iteration are used as the starting point for the next iteration.-Mathematics:Iteration in...
, rather than a formula, that adds an extra parameter, the Recall Factor, which defines the recall attempts.
The steps in the process are as follows:
1. Calculate
as above for Erlang B.
2. Calculate the probable number of blocked calls
3. Calculate the number of recalls,
assuming a Recall Factor, :4. Calculate the new offered traffic
where
is the initial (baseline) level of traffic.5. Return to step 1 and iterate until a stable value of
is obtained.Erlang C formula
The Erlang C formula expresses the waiting probability in a queuing system. Just as the Erlang B formula, Erlang C assumes an infinite population of sources, which jointly offer traffic of A erlangs to N servers. However, if all the servers are busy when a request arrives from a source, the request is queued. An unlimited number of requests may be held in the queue in this way simultaneously. This formula calculates the probability of queuing offered traffic, assuming that blocked calls stay in the system until they can be handled. This formula is used to determine the number of agents or customer service representatives needed to staff a call centreCall centre
A call centre or call center is a centralised office used for the purpose of receiving and transmitting a large volume of requests by telephone. A call centre is operated by a company to administer incoming product support or information inquiries from consumers. Outgoing calls for telemarketing,...
, for a specified desired probability of queuing.
where:
- A is the total traffic offered in units of erlangs
- N is the number of servers
- PW is the probability that a customer has to wait for service
It is assumed that the call arrivals can be modeled by a Poisson process
Poisson process
A Poisson process, named after the French mathematician Siméon-Denis Poisson , is a stochastic process in which events occur continuously and independently of one another...
and that call holding times are described by a negative exponential distribution. A common use for Erlang C is modeling and dimensioning call center agents in a call center environment.
Engset formula
The Engset calculation is a related formula, named after its developer, T. O. EngsetT. O. Engset
Tore Olaus Engset was a Norwegian mathematician and engineer who did pioneering work in the field of telephone traffic queuing theory.Engset got a M.Sc...
, used to determine the probability of congestion occurring within a telephony
Telephony
In telecommunications, telephony encompasses the general use of equipment to provide communication over distances, specifically by connecting telephones to each other....
circuit group
Trunking
In modern communications, trunking is a concept by which a communications system can provide network access to many clients by sharing a set of lines or frequencies instead of providing them individually. This is analogous to the structure of a tree with one trunk and many branches. Examples of...
. It deals with a finite population of S sources rather than the infinite population of sources that Erlang assumes. The formula requires that the user knows the expected peak traffic, the number of sources (callers) and the number of circuits in the network.
Example application
A business installing a PABX needs to know the minimum number of voice circuitsTelecommunication circuit
A telecommunication circuit is any line, conductor, or other conduit by which information is transmitted.A dedicated circuit, private circuit, or leased line is a line that is dedicated to only one use...
it needs to have to and from the telephone network. An approximate approach is to use the Erlang-B formula. However, if the business has a small number of extensions
Extension (telephone)
An extension telephone is an additional telephone wired to the same telephone line as another. In middle 20th century telephone jargon, the first telephone on a line was a "Main Station" and subsequent ones "Extensions". Such extension phones allow making or receiving calls in different rooms,...
, then it should instead use the more exact Engset calculation, which reflects the fact that extensions already in use will not make additional simultaneous calls. (For a large user population, the Engset and the Erlang-B calculations give the same result.)
Technical details
Engset's equation is similar to the Erlang-B formula; however it contains one major difference: Erlang's equation assumes an infinite source of calls, yielding a Poisson arrival processMarkovian arrival processes
In queueing theory, Markovian arrival processes are used to model the arrival of customers to a queue.Some of the most common include the Poisson process, Markov arrival process and the batch Markov arrival process.-Background:...
, while Engset specifies a finite number of
callers
.
Thus Engset's equation should be used when the source population is small (say less than 200 users, extensions or customers).
where
- A = offered traffic intensity in erlangs, from all sources
- S = number of sources of traffic
- N = number of circuits in group
- P(b) = probabilityProbabilityProbability is ordinarily used to describe an attitude of mind towards some proposition of whose truth we arenot certain. The proposition of interest is usually of the form "Will a specific event occur?" The attitude of mind is of the form "How certain are we that the event will occur?" The...
of blocking or congestion
In practice, like Erlang's equations, Engset's formula requires recursion to solve for the blocking or congestion probability. There are several recursions that could be used. One way to determine this probability, one first determines an initial estimate. This initial estimate is substituted into the equation and the equation then is solved. The answer to this initial calculation is then substituted back into the equation, resulting in a new answer which is again substituted. This iterative process continues until the equation converges
Limit of a sequence
The limit of a sequence is, intuitively, the unique number or point L such that the terms of the sequence become arbitrarily close to L for "large" values of n...
to a stable result.
Engset's equation follows:
See also
- System spectral efficiency (discussing cellular network capacity in Erlang/MHz/cell)
- A. K. ErlangAgner Krarup ErlangAgner Krarup Erlang was a Danish mathematician, statistician and engineer, who invented the fields of traffic engineering and queueing theory....
- Call centreCall centreA call centre or call center is a centralised office used for the purpose of receiving and transmitting a large volume of requests by telephone. A call centre is operated by a company to administer incoming product support or information inquiries from consumers. Outgoing calls for telemarketing,...
- Erlang programming languageErlang programming languageErlang is a general-purpose concurrent, garbage-collected programming language and runtime system. The sequential subset of Erlang is a functional language, with strict evaluation, single assignment, and dynamic typing. For concurrency it follows the Actor model. It was designed by Ericsson to...
- Erlang distribution
- Poisson distributionPoisson distributionIn probability theory and statistics, the Poisson distribution is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time and/or space if these events occur with a known average rate and independently of the time since...
- Traffic mixTraffic MixTraffic mix is a traffic model in telecommunication engineering and teletraffic theory.-Definitions:A traffic mix is a modelisation of user behaviour. In telecommunications, user behaviour activities may be described by a number of systems, ranging from simple to complex...
Tools
- Online Erlang C Calculator from Vrije University, Netherlands
- http://www.cs.usyd.edu.au/~dcorbett/erlang.cgiOnline Erlang B Calculator with source code in CC (programming language)C is a general-purpose computer programming language developed between 1969 and 1973 by Dennis Ritchie at the Bell Telephone Laboratories for use with the Unix operating system....
and JavaScriptJavaScriptJavaScript is a prototype-based scripting language that is dynamic, weakly typed and has first-class functions. It is a multi-paradigm language, supporting object-oriented, imperative, and functional programming styles....
] - A Robust Erlang B Calculator from McMaster University, Canada
- Erlang C using spreadsheets from Mitan Ltd.
- Call Center Designer Erlang C tool from Portage Communications, Inc.
- Extended Erlang B Calculator with equation, Had2Know Technology