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(The related question of the number of events in a given amount of time is described by the Poisson distribution.) The Erlang distribution, which measures the time between incoming calls, can be used in conjunction with the expected duration of incoming calls to produce information about the traffic load measured in erlangs.
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 continuously during the period of interest (e.g. one hour) is said to have a load of 1 erlang. When used to describe offered traffic, a value followed by “erlangs ...
Erlang (/ ˈ ɜːr l æ ŋ / UR-lang) is a general-purpose, concurrent, functional high-level programming language, and a garbage-collected runtime system.The term Erlang is used interchangeably with Erlang/OTP, or Open Telecom Platform (OTP), which consists of the Erlang runtime system, several ready-to-use components (OTP) mainly written in Erlang, and a set of design principles for Erlang ...
In telecommunications networks, traffic intensity is a measure of the average occupancy of a server or resource during a specified period of time, normally a busy hour.It is measured in traffic units and defined as the ratio of the time during which a facility is cumulatively occupied to the time this facility is available for occupancy.
Exponential service time with a random variable Y for the size of the batch of entities serviced at one time. M X /M Y /1 queue: D: Degenerate distribution: A deterministic or fixed service time. M/D/1 queue: E k: Erlang distribution: An Erlang distribution with k as the shape parameter (i.e., sum of k i.i.d. exponential random variables). G ...
The generalization to vector time was developed several times, apparently independently, by different authors in the early 1980s. [3] At least 6 papers contain the concept. [ 4 ] The papers canonically cited in reference to vector clocks are Colin Fidge’s and Friedemann Mattern ’s 1988 works, [ 5 ] [ 6 ] as they (independently) established ...
Then the waiting time for the n-th event to occur is the gamma distribution with integer shape =. This construction of the gamma distribution allows it to model a wide variety of phenomena where several sub-events, each taking time with exponential distribution, must happen in sequence for a major event to occur. [29]
In queueing theory, a discipline within the mathematical theory of probability, the M/M/c queue (or Erlang–C model [1]: 495 ) is a multi-server queueing model. [2] In Kendall's notation it describes a system where arrivals form a single queue and are governed by a Poisson process , there are c servers, and job service times are exponentially ...