On the Two-Moment Approximation of the Discrete-Time GI/G/1 Queue with a Single Vacation

<table class="figure-group"><tr class="fig-image" id="a"><td><object data="https://static.hindawi.com/articles/ddns/volume-2016/5345374/figures/5345374.fig.001a.svgz" name="5345374.fig.001a" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(a) </b><svg height="11.439pt" id="M167" style="vertical-align:-2.15067pt" version="1.1" viewbox="-0.0498162 -9.28833 90.5797 11.439" width="90.5797pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M692 302H438V274C537 267 543 260 543 188V103C543 61 531 48 511 37C489 26 458 20 424 20C231 20 146 188 146 333C146 517 258 630 411 630C507 630 582 597 606 474L634 480C627 546 622 601 619 636C586 643 510 665 426 665C230 665 44 552 44 321C44 122 191 -15 411 -15C491 -15 573 7 635 21C629 49 628 81 628 116V202C628 261 632 266 692 274V302Z" id="g121-69"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="715" vert-adv-y="715"></glyph.data></g><g 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<div>Approximation of <svg height="9.25202pt" id="M163" style="vertical-align:-3.29111pt" version="1.1" viewbox="-0.0498162 -5.96091 12.66 9.25202" width="12.66pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M574 449L545 460C526 432 516 430 487 430C404 430 311 435 226 435C104 435 56 379 25 341L43 318C81 354 121 372 181 372C161 246 87 53 23 3L30 -12C48 -12 88 -4 113 11C157 75 207 248 232 371L386 367L326 109C321 86 318 66 318 50C318 4 339 -12 366 -12C410 -12 461 21 505 69L492 96C467 79 434 60 418 60C406 60 400 78 411 147C422 217 439 300 457 366C487 366 524 367 536 370C547 385 558 408 574 449Z" id="g113-238"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="591" vert-adv-y="591"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,7.358,3.132)"><path d="M504 89L488 119C453 85 428 69 416 69C408 69 405 75 412 102L462 304C492 438 460 451 436 451S388 441 356 423C311 397 229 336 170 256H168L189 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Discrete Dynamics in Nature and Society

fig1

Figure 1

Figure 1: On the Two-Moment Approximation of the Discrete-Time GI/G/1 Queue with a Single Vacation 