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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 ...
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., = /):
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 ...
The degenerate distribution at x 0, where X is certain to take the value x 0. This does not look random, but it satisfies the definition of random variable. This is useful because it puts deterministic variables and random variables in the same formalism. The discrete uniform distribution, where all elements of a finite set are equally likely ...
In probability theory the hypoexponential distribution or the generalized Erlang distribution is a continuous distribution, that has found use in the same fields as the Erlang distribution, such as queueing theory, teletraffic engineering and more generally in stochastic processes.
An M/M/1 queueing node. A M/M/1 queue means that the time between arrivals is Markovian (M), i.e. the inter-arrival time follows an exponential distribution of parameter λ. The second M means that the service time is Markovian: it follows an exponential distribution of parameter μ. The last parameter is the number of service channel which one ...
Consider the case where all elements of A are either 0 or 1 and for each route r calls requiring use of the route arrive according to a Poisson process of rate v r. When a call arrives if there is sufficient capacity remaining on all the required links the call is accepted and occupies the network for an exponentially distributed length of time ...
An M/D/1 queue is a stochastic process whose state space is the set {0,1,2,3,...} where the value corresponds to the number of entities in the system, including any currently in service. Arrivals occur at rate λ according to a Poisson process and move the process from state i to i + 1.