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For the GI/G/1 queueing model with traffic load a&#x3C;1, service time distribution B(t) and interarrival time distribution A(t), whenever for t&#x2192;&#x221E;1&#x2212;B(t)&#x223C;c(t/&#x3B2;)&#x3BD;+O(e&#x2212;&#x3B4;t),c&#x3E;0,1&#x3C;&#x3BD;&#x3C;2,&#x3B4;&#x3E;0, and &#x222B;0&#x221E;t&#x3BC;dA(t)&#x3C;&#x221E;&#x2009;for&#x2009;&#x3BC;&#x3E;&#x3BD;, (1&#x2212;a)1&#x3BD;&#x2212;1w converges in distribution for a&#x2191;1. Here w is distributed as the stationary waiting time distribution. The L.-S. transform of the limiting distribution is derived and an asymptotic series for its tail probabilities is obtained. The theorem actually proved in the text concerns a slightly more general asymptotic behavior of 1&#x2212;B(t), t&#x2192;&#x221E;, than mentioned above

journal of applied mathematics and stochastic analysis

A heavy-traffic theorem for the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="${{{{GI} \mathord{\left/ {\vphantom {{GI} G}} \right. \kern-\nulldelimiterspace} G}} \mathord{\left/ {\vphantom {{{{GI} \mathord{\left/ {\vphantom {{GI} G}} \right. \kern-\nulldelimiterspace} G}} 1}} \right. \kern-\nulldelimiterspace} 1}$" id="E1"><mml:mrow><mml:mrow><mml:mrow><mml:mrow><mml:mrow><mml:mi>G</mml:mi><mml:mi>I</mml:mi></mml:mrow><mml:mo>/</mml:mo><mml:mi>G</mml:mi></mml:mrow></mml:…

A heavy-traffic theorem for the GI/G