The distribution of the queueing delay in the stationary <mml:math alttext="${{{G \mathord{\left/  {\vphantom {G G}} \right.  \kern-\nulldelimiterspace} G}} \mathord{\left/  {\vphantom {{{G \mathord{\left/  {\vphantom {G G}} \right.  \kern-\nulldelimiterspace} G}} s}} \right.  \kern-\nulldelimiterspace} s}$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mrow><mml:mrow><mml:mrow><mml:mi>G</mml:mi><mml:mo>/</mml:mo><mml:mi>G</mml:mi></mml:mrow></mml:mrow><mml:mo>/</mml:mo><mml:mi>s</mml:mi></mml:mrow></mml:mrow></mml:math> queue is 
given with an application to the <mml:math alttext="${{{{GI} \mathord{\left/  {\vphantom {{GI} G}} \right.  \kern-\nulldelimiterspace} G}} \mathord{\left/  {\vphantom {{{{GI} \mathord{\left/  {\vphantom {{GI} G}} \right.  \kern-\nulldelimiterspace} G}} s}} \right.  \kern-\nulldelimiterspace} s}$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><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:mrow><mml:mo>/</mml:mo><mml:mi>s</mml:mi></mml:mrow></mml:mrow></mml:math> queue and to the <mml:math alttext="${{{M \mathord{\left/  {\vphantom {G G}} \right.  \kern-\nulldelimiterspace} G}} \mathord{\left/  {\vphantom {{{G \mathord{\left/  {\vphantom {G G}} \right.  \kern-\nulldelimiterspace} G}} s}} \right.  \kern-\nulldelimiterspace} s}$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mrow><mml:mrow><mml:mrow><mml:mi>M</mml:mi><mml:mo>/</mml:mo><mml:mi>G</mml:mi></mml:mrow></mml:mrow><mml:mo>/</mml:mo><mml:mi>s</mml:mi></mml:mrow></mml:mrow></mml:math> queue.

The stationary <mml:math alttext="${{{G \mathord{\left/  {\vphantom {G G}} \right.  \kern-\nulldelimiterspace} G}} \mathord{\left/  {\vphantom {{{G \mathord{\left/  {\vphantom {G G}} \right.  \kern-\nulldelimiterspace} G}} s}} \right.  \kern-\nulldelimiterspace} s}$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mrow><mml:mrow><mml:mrow><mml:mi>G</mml:mi><mml:mo>/</mml:mo><mml:mi>G</mml:mi></mml:mrow></mml:mrow><mml:mo>/</mml:mo><mml:mi>s</mml:mi></mml:mrow></mml:mrow></mml:math> queue

The stationary <svg style="vertical-align:-2.22495pt" height="14.85" version="1.1" viewBox="0 0 45.125 14.85" width="45.125" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,12.012)"><path id="x1D43A" d="M713 296l-5 -25q-47 -7 -59 -20t-23 -72l-15 -79q-9 -48 -3 -74q-15 -3 -55 -13t-63 -15t-59.5 -10t-70.5 -5q-149 0 -243 80t-94 220q0 169 127.5 276.5t336.5 107.5q91 0 206 -36l-10 -165l-29 -1q1 85 -47.5 126t-146.5 41q-153 0 -243.5 -97t-90.5 -242&#xA;q0 -122 68.5 -198.5t188.5 -76.5q121 0 139 75l20 86q13 58 -1.5 70.5t-99.5 20.5l5 26h267z" /></g><g transform="matrix(.017,-0,0,-.017,12.37,12.012)"><path id="x2F" d="M368 703l-264 -866h-60l265 866h59z" /></g><g transform="matrix(.017,-0,0,-.017,19.373,12.012)"><use xlink:href="#x1D43A"/></g><g transform="matrix(.017,-0,0,-.017,31.68,12.012)"><use xlink:href="#x2F"/></g><g transform="matrix(.017,-0,0,-.017,38.684,12.012)"><path id="x1D460" d="M352 391q0 -31 -27 -44q-14 -7 -24 6q-39 48 -84 48q-23 0 -39.5 -15t-16.5 -40q0 -43 73 -90q49 -32 70 -58t21 -57q0 -58 -62 -105.5t-129 -47.5q-40 0 -75.5 25t-35.5 52q0 28 32 46q7 4 15 3t11 -6q19 -31 48.5 -50.5t54.5 -19.5q34 0 54 19.5t20 42.5q0 43 -65 81&#xA;q-97 56 -97 123q0 50 51 96q19 17 58 32.5t62 15.5q37 0 61 -18t24 -39z" /></g></svg> queue

International Journal of Stochastic Analysis

The stationary G/G/s queue

Abstract

Copyright