Erlang (unit)
Generated by GPT-5-miniExpansion Funnel Raw 64 → Dedup 0 → NER 0 → Enqueued 0
| Erlang (unit) | |
|---|---|
| Name | Erlang |
| Quantity | Traffic intensity |
| Named after | Agner Krarup Erlang |
| Units | dimensionless |
| Derived | call-seconds per second |
Erlang (unit) is a dimensionless unit of telecommunication traffic intensity used to quantify load in telephone exchanges, switchboards, and queueing theory models. Originating from the work of Danish engineer Agner Krarup Erlang, it underpins standards and planning in organizations such as the International Telecommunication Union and the American National Standards Institute. The unit is central to modeling in systems studied by researchers at institutions like Bell Labs, AT&T, Nokia, and Ericsson.
Definition and Origin
The Erlang was introduced by Agner Krarup Erlang while working for the Københavns Telefon Aktieselskab to model telephone traffic and congestion on trunk lines and switchboards. Early analyses were motivated by problems encountered by operators in cities such as Copenhagen and later adopted across networks in London, New York City, and Paris. The concept influenced subsequent developments by mathematicians and engineers at Columbia University, Massachusetts Institute of Technology, and University of Cambridge who formalized blocking and delay models that trace back to Erlang's experiments. Standards bodies including the International Telecommunication Union and the European Telecommunications Standards Institute codified Erlang-based methods for dimensioning circuits and call centers.
Mathematical Formulation and Units
One Erlang represents one continuous resource being occupied for one unit of time, e.g., one line in use for one hour yields one Erlang when measured over that hour. In equations derived from the work of A. K. Erlang, traffic intensity A is calculated as A = λ·h where λ is the arrival rate (calls per time unit) and h is the average holding time; λ is treated in models influenced by researchers at Princeton University and Stanford University. Although dimensionless, Erlang is often expressed as call-seconds per second or call-hours per hour in technical documents from IEEE and ITU-T. Key formulae include the Erlang B and Erlang C functions, which were developed further in collaborations involving analysts at Bell Telephone Laboratories and statisticians from University College London.
Applications in Telecommunications and Queuing
Erlang metrics are applied to dimension trunk groups in legacy public switched telephone networks and to size resources in modern call center operations managed by firms such as Aviso and Genesys. Network planners at companies like Cisco Systems and Huawei use Erlang calculations to estimate required channel counts and to predict blocking probabilities using Erlang B, while contact center workforce management software from vendors such as Aspect Software and Verint Systems relies on Erlang C for delay and service level forecasts. Teletraffic engineering grounded in Erlang theory is taught in curricula at Imperial College London, University of Toronto, and Tsinghua University and is applied in studies involving congestion in systems analyzed by the World Bank and the OECD.
Measurement and Estimation Methods
Traffic measurement employs counters, probes, and sampling techniques developed in part at Bell Labs and standardized by ITU-T recommendations; these include busy-hour call attempts, traffic intensity sampling, and holding time measurement procedures used by operators such as Verizon Communications and British Telecom. Estimation methods use maximum likelihood and Bayesian approaches that reference work from scholars at Harvard University and Yale University; these approaches allow conversion of observed call-seconds and offered traffic into Erlang estimates. Tools and calculators from vendors and academic groups provide implementations of Erlang B and Erlang C; practitioners in companies like AT&T and Telefonica often validate estimates against operational telemetry from switches manufactured by Alcatel-Lucent or Ericsson.
Relation to Other Traffic and Performance Metrics
Erlang relates to blocking probability, waiting time, and utilization metrics widely used in studies by researchers at Cornell University and McGill University. Erlang B produces blocking probability under loss-system assumptions, while Erlang C gives queueing delay estimates under waiting-system assumptions; both are foundational alongside extensions such as the Kaufman–Roberts recursion and models from Palmström and authors at INRIA. Performance indicators like Grade of Service and Grade of Retained Service used by regulators including the Federal Communications Commission and the Canadian Radio-television and Telecommunications Commission draw on Erlang-based calculations. Modern extensions also connect Erlang measures with stochastic network calculus developed at CWI and queueing networks studied at Los Alamos National Laboratory.
Practical Examples and Case Studies
Classic case studies include trunk dimensioning for long-distance links during growth at AT&T and subscriber concentration analysis for municipal networks in Copenhagen and Oslo. Contact center implementations at corporations such as American Express and Delta Air Lines illustrate staffing derived from Erlang C models to meet service level agreements. Recent case studies incorporate data from internet telephony and VoIP deployments at companies like Skype and Vonage, comparing Erlang-based predictions with packet-switched traffic patterns analyzed by researchers at ETH Zurich and Carnegie Mellon University. Regulatory filings by incumbents such as Deutsche Telekom and Orange S.A. often include Erlang analyses to justify capacity investments.