Erlang distribution


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Erlang distribution

[′er‚läŋ ‚dis·trə‚byü·shən]
(statistics)
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Galliher, Morse, and Simond (1959) further built on this early work for order sizes Q [greater than or equal to] 1 using an E/M/n inventory queueing system where arrivals are distributed according to an Erlang distribution with Poisson demands.
Ahmed, "On parameter estimation of erlang distribution using bayesian method under different loss functions," in Proceedings of International Conference on Advances in Computers, Communication, and Electronic Engineering, pp.
The Erlang distribution with a parameter of 2 and 9 and exponential distribution are denoted by "ERL2," "ERL9," and "EXP," respectively.
It is also clear that the distribution with smaller coefficient of variation (CV) has the smaller mean system size for the identical policy; for example, in Figure 1(b), the CV values of the exponential distribution and the Erlang distribution with a parameter 9 are 1 and 1/3, respectively.
The batch production time at manufacturing level is represented by the Erlang distribution Erl (k = 3) with multiple means.
The transportation time between SC levels is represented by the Erlang distribution Erl (k = 2) with multiple means.
1999) collected headway data from different sites in Japan and used Synthetic erlang distribution model to investigate the effects of some factors on time headway distribution.
The distribution allows to model one or more inter-related Poisson processes occurring in sequence and is generalisation of Erlang distribution (which requires all phases in the sequence to be identical).
Thus, the Erlang distribution was chosen to describe the inter-arrival distribution.
It was found that negative exponential, shifted exponential and gamma distributions reasonably fitted time headways at low and medium flow rates on freeways, whereas the Erlang distribution was found to be appropriate in high traffic flows.
Other distribution that have been reported in literature are Lognormal distribution, which is a special form of the normal distribution, Gamma and Erlang distributions which uses exponential approximations, inverse Gaussian distribution is also used and is popular in meteorology studies, additionally other alternatives for wind speed analysis include Skewed generalized error distribution, Skewed t distribution and Burr distribution [24].
ij](t), one has just to add as many of such distributions as the number the paths, leading to a weighted combination of general Erlang distributions, with each weighting factor corresponding to the probability of taking the respective path.