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The Erlang distribution is a two-parameter family of continuous probability distributions with support . The two parameters are: a positive integer the "shape", and. a positive real number the "rate". The "scale", the reciprocal of the rate, is sometimes used instead. The Erlang distribution is the distribution of a sum of independent ...
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]
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.
An Erlang distribution with k as the shape parameter (i.e., sum of k i.i.d. exponential random variables). G: General distribution: Although G usually refers to independent arrivals, some authors prefer to use GI to be explicit. PH: Phase-type distribution: Some of the above distributions are special cases of the phase-type, often used in place ...
Queueing theory is one of the major areas of study in the discipline of management science. Through management science, businesses are able to solve a variety of problems using different scientific and mathematical approaches. Queueing analysis is the probabilistic analysis of waiting lines, and thus the results, also referred to as the ...
Mathematical definition. A Galton–Watson process is a stochastic process {Xn} which evolves according to the recurrence formula X0 = 1 and. where is a set of independent and identically-distributed natural number-valued random variables. In the analogy with family names, Xn can be thought of as the number of descendants (along the male line ...
Hypoexponential. 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.
Memorylessness. In probability and statistics, memorylessness is a property of certain probability distributions. It describes situations where the time already spent waiting for an event does not affect how much longer the wait will be. To model memoryless situations accurately, we have to disregard the past state of the system – the ...