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The exponential asymptotics $\\mathbf P(aM^{(a)}>x)\\sim e^{-2x/\\sigma^2}$, as $a\\to 0$, were found by Kingman and are known as heavy traffic approximation in the queueing theory. For subexponential random variables the large deviation asymptotics for $\\mathbf P(M^{(a)}>x)\\sim \\frac{1}{a}\\overline F^I(x)$ hold for fixed $a$ as $x\\to\\infty$. 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The exponential asymptotics $\\mathbf P(aM^{(a)}>x)\\sim e^{-2x/\\sigma^2}$, as $a\\to 0$, were found by Kingman and are known as heavy traffic approximation in the queueing theory. For subexponential random variables the large deviation asymptotics for $\\mathbf P(M^{(a)}>x)\\sim \\frac{1}{a}\\overline F^I(x)$ hold for fixed $a$ as $x\\to\\infty$. 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