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The Erlang B formula (or Erlang-B with a hyphen), also known as the Erlang loss formula, is a formula for the blocking probability that describes the probability of call losses for a group of identical parallel resources (telephone lines, circuits, traffic channels, or equivalent), sometimes referred to as an M/M/c/c queue. [5]
For example, one call-hour could be one call for an hour or two (possibly concurrent) calls for half an hour each. Call-seconds give a measure of the average number of concurrent calls. Offered load is defined as the traffic density per unit time, measured in erlangs. An erlang is defined as one call-hour per hour, or 3,600 call-seconds per hour.
Teletraffic engineering, or telecommunications traffic engineering is the application of transportation traffic engineering theory to telecommunications.Teletraffic engineers use their knowledge of statistics including queuing theory, the nature of traffic, their practical models, their measurements and simulations to make predictions and to plan telecommunication networks such as a telephone ...
The probability density function of the Erlang distribution is (;,) = ()!,,The parameter k is called the shape parameter, and the parameter is called the rate parameter.. An alternative, but equivalent, parametrization uses the scale parameter , which is the reciprocal of the rate parameter (i.e., = /):
In 1909, Agner Krarup Erlang, a Danish engineer who worked for the Copenhagen Telephone Exchange, published the first paper on what would now be called queueing theory. [9] [10] [11] He modeled the number of telephone calls arriving at an exchange by a Poisson process and solved the M/D/1 queue in 1917 and M/D/k queueing model in 1920. [12]
Agner Krarup Erlang (1 January 1878 – 3 February 1929) was a Danish mathematician, statistician and engineer, who invented the fields of traffic engineering [2] [3] and queueing theory. [ 3 ] Erlang's 1909 paper, and subsequent papers over the decades, are regarded as containing some of most important concepts and techniques for queueing theory.
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In telecommunications, busy-hour call attempts (BHCA) is a teletraffic engineering measurement used to evaluate and plan capacity for telephone networks. [1] BHCA is the number of telephone calls attempted at the sliding 60-minute period during which occurs the maximum total traffic load in a given 24-hour period (BHCA), and the higher the BHCA, the higher the stress on the network processors.