英语词汇“erlang distribution”的英英意思、用法、释义、翻译、读音、例句、短语、词组-英语词典

1. Used to designate various formulæ, functions, etc., derived by Erlang or arising out of his work; as Erlang('s) distribution, a distribution function of the time required for the occurrence of n random events (see quot. 1960¹); also, an Erlang loss formula; Erlang('s) formula, a formula giving the probability that a given number of lines in a communication system are occupied; spec., Erlang('s) congestion (or B- or first loss) formula, a formula giving the probability of congestion assuming that calls finding all lines occupied are cleared; Erlang('s) delay (or second loss) formula, a formula giving the probability of congestion assuming that such calls are delayed until a line is available.

ΚΠ

1918 Post Office Electr. Engin. Jrnl. 11 151 These durations are very far from complying with either of Mr. Erlang's distribution laws, yet the results agree closely with the theoretical curve. I think, therefore, Mr. Erlang's formula can be looked upon as being of quite general application.

1920 Post Office Electr. Engin. Jrnl. 15 215 Erlang's formula states that if the average number of simultaneous calls is A, the probability of exactly r switches being engaged if the total number of switches is x, is (A^r/r!)/(1 + A + A²/2! + .. + A^r/r! + .. + A^x/x!).

1948 Bell Syst. Techn. Jrnl. 27 425 The..assumption underlying the Erlang B formula is that of no delay. A call which encounters all trunks busy is cleared out.

1954 A. Jensen Distribution Model v. 16 Erlang's distribution corresponds to Poisson's distribution just as that of Pascal corresponds to the binomial distribution.

1960 R. Syski Introd. Congestion Theory Teleph. Syst. iv. 139 One has: f_n(t)dt = (nμt)^{n − 1}e^−μntnμdt/(n − 1)!, t ≧ o where μ is a positive constant. This form is known as the Erlang distribution... In several cases, the Erlang distribution is the only one which yields explicit solutions to congestion problems.

1960 R. Syski Introd. Congestion Theory Teleph. Syst. v. 252 The famous Erlang's loss formula (his B-formula—denoted usually by E_r(A))..serves as the basis of traffic calculations for most telephone administrations.

1968 P. A. P. Moran Introd. Probability Theory ii. 87 We can also truncate the Poisson distribution on the other tail and obtain a bounded distribution p_n = .. = λⁿ? n! ∑Nj = 0 λ^j(j!)⁻¹ ,n = 0, 1,…, N. This is also known as ‘Erlang's distribution’ and arises in the theory of telephone traffic.

单词	erlang distribution
释义	> as lemmas Erlang('s) distribution 1. Used to designate various formulæ, functions, etc., derived by Erlang or arising out of his work; as Erlang('s) distribution, a distribution function of the time required for the occurrence of n random events (see quot. 1960¹); also, an Erlang loss formula; Erlang('s) formula, a formula giving the probability that a given number of lines in a communication system are occupied; spec., Erlang('s) congestion (or B- or first loss) formula, a formula giving the probability of congestion assuming that calls finding all lines occupied are cleared; Erlang('s) delay (or second loss) formula, a formula giving the probability of congestion assuming that such calls are delayed until a line is available. ΚΠ 1918 Post Office Electr. Engin. Jrnl. 11 151 These durations are very far from complying with either of Mr. Erlang's distribution laws, yet the results agree closely with the theoretical curve. I think, therefore, Mr. Erlang's formula can be looked upon as being of quite general application. 1920 Post Office Electr. Engin. Jrnl. 15 215 Erlang's formula states that if the average number of simultaneous calls is A, the probability of exactly r switches being engaged if the total number of switches is x, is (A^r/r!)/(1 + A + A²/2! + .. + A^r/r! + .. + A^x/x!). 1948 Bell Syst. Techn. Jrnl. 27 425 The..assumption underlying the Erlang B formula is that of no delay. A call which encounters all trunks busy is cleared out. 1954 A. Jensen Distribution Model v. 16 Erlang's distribution corresponds to Poisson's distribution just as that of Pascal corresponds to the binomial distribution. 1960 R. Syski Introd. Congestion Theory Teleph. Syst. iv. 139 One has: f_n(t)dt = (nμt)^{n − 1}e^−μntnμdt/(n − 1)!, t ≧ o where μ is a positive constant. This form is known as the Erlang distribution... In several cases, the Erlang distribution is the only one which yields explicit solutions to congestion problems. 1960 R. Syski Introd. Congestion Theory Teleph. Syst. v. 252 The famous Erlang's loss formula (his B-formula—denoted usually by E_r(A))..serves as the basis of traffic calculations for most telephone administrations. 1968 P. A. P. Moran Introd. Probability Theory ii. 87 We can also truncate the Poisson distribution on the other tail and obtain a bounded distribution p_n = .. = λⁿ? n! ∑Nj = 0 λ^j(j!)⁻¹ ,n = 0, 1,…, N. This is also known as ‘Erlang's distribution’ and arises in the theory of telephone traffic. extracted from Erlangn. < as lemmas
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