On the <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-0.8235998pt" id="M1" height="12.3608pt" version="1.1" viewBox="-0.0657574 -11.5372 49.5999 12.3608" width="49.5999pt"><g transform="matrix(.017,0,0,-0.017,0,0)"><path id="g189-72" d="M654 477C658 546 663 603 666 633C636 643 571 664 490 664C241 664 67 499 67 271C67 88 190 -15 363 -15C443 -15 512 7 575 21C572 43 574 70 580 100L596 184C611 259 614 262 670 271L676 297H432L426 270C525 261 530 258 515 184L495 90C485 37 443 19 381 19C240 19 164 129 164 279C164 464 280 630 465 630C569 630 626 587 625 474L654 477Z"/></g><g transform="matrix(.017,0,0,-0.017,11.686,0)"><path id="g189-74" d="M380 649H125L119 622C202 615 209 610 195 536L113 116C99 40 92 33 14 27L7 0H263L269 27C187 33 181 39 196 116L276 536C291 609 295 615 374 622L380 649Z"/></g><g transform="matrix(.017,0,0,-0.017,17.435,0)"><path id="g189-48" d="M357 664H304L-18 -45H35L357 664Z"/></g><g transform="matrix(.017,0,0,-0.017,22.96,0)"><path id="g189-78" d="M910 649H748L436 148C396 327 361 485 327 649H161L154 622C248 613 254 607 225 507L169 317C132 189 113 129 97 88C81 46 61 32 3 27L-4 0H222L228 27C154 34 145 46 152 89C156 125 171 179 199 282L271 545H273C311 354 343 183 375 4H398L729 556H731C709 415 687 283 665 135C651 39 645 34 568 27L561 0H814L821 27C741 34 734 37 747 135C764 267 779 384 801 528C814 611 816 615 903 622L910 649Z"/></g><g transform="matrix(.017,0,0,-0.017,37.992,0)"><use xlink:href="#g189-48"/></g><g transform="matrix(.017,0,0,-0.017,43.518,0)"><path id="g189-213" d="M303 635C245 609 181 592 116 583L111 558L151 557C205 555 210 551 198 490L127 128C110 40 104 35 17 26L11 0H279L285 26C196 35 188 40 205 128L303 635Z"/></g></svg> Queue with Vacations and Multiple Service Phases

<div>The effect of <svg height="9.39034pt" id="M456" style="vertical-align:-3.42943pt" version="1.1" viewbox="-0.0498162 -5.96091 11.9619 9.39034" width="11.9619pt" 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="M538 96L524 119C492 88 454 63 446 63C439 63 434 70 440 101C463 223 491 341 518 448H508L433 422L401 276C355 192 240 56 188 56C163 56 154 89 163 133C184 233 207 338 235 443L230 448L152 424L58 17C40 -60 23 -143 23 -185C23 -241 42 -261 63 -261C92 -261 117 -241 125 -227L124 -221C109 -209 89 -165 89 -103C89 -55 96 -13 105 26H107C121 -3 134 -12 151 -12C172 -12 194 -5 221 16C279 61 330 124 384 194H386C381 159 377 141 368 105C343 3 363 -12 383 -12C416 -12 486 35 538 96Z" id="g113-234"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="555" vert-adv-y="555" xpluscharwidth="7.215"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,6.89,3.132)"><path d="M389 0V32C297 38 291 46 291 118V635C234 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154 89 163 133C184 233 207 338 235 443L230 448L152 424L58 17C40 -60 23 -143 23 -185C23 -241 42 -261 63 -261C92 -261 117 -241 125 -227L124 -221C109 -209 89 -165 89 -103C89 -55 96 -13 105 26H107C121 -3 134 -12 151 -12C172 -12 194 -5 221 16C279 61 330 124 384 194H386C381 159 377 141 368 105C343 3 363 -12 383 -12C416 -12 486 35 538 96Z" id="g113-234"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="555" vert-adv-y="555" xpluscharwidth="7.215"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,10.874,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z" id="g117-34"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="587" vert-adv-y="587" xpluscharwidth="18.505000000000003"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,22.137,0)"><path d="M412 140C382 77 369 73 315 73H129L270 222C362 320 402 379 402 466C402 571 322 635 234 635C177 635 130 609 99 576L42 495L64 475C90 514 133 568 201 568C274 568 318 519 318 435C318 349 255 267 193 193C144 135 87 78 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Mathematical Problems in Engineering

fig10

Figure 10

Figure 10: On the <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-0.8235998pt" id="M1" height="12.3608pt" version="1.1" viewBox="-0.0657574 -11.5372 49.5999 12.3608" width="49.5999pt"><g transform="matrix(.017,0,0,-0.017,0,0)"><path id="g189-72" d="M654 477C658 546 663 603 666 633C636 643 571 664 490 664C241 664 67 499 67 271C67 88 190 -15 363 -15C443 -15 512 7 575 21C572 43 574 70 580 100L596 184C611 259 614 262 670 271L676 297H432L426 270C525 261 530 258 515 184L495 90C485 37 443 19 381 19C240 19 164 129 164 279C164 464 280 630 465 630C569 630 626 587 625 474L654 477Z"/></g><g transform="matrix(.017,0,0,-0.017,11.686,0)"><path id="g189-74" d="M380 649H125L119 622C202 615 209 610 195 536L113 116C99 40 92 33 14 27L7 0H263L269 27C187 33 181 39 196 116L276 536C291 609 295 615 374 622L380 649Z"/></g><g transform="matrix(.017,0,0,-0.017,17.435,0)"><path id="g189-48" d="M357 664H304L-18 -45H35L357 664Z"/></g><g transform="matrix(.017,0,0,-0.017,22.96,0)"><path id="g189-78" d="M910 649H748L436 148C396 327 361 485 327 649H161L154 622C248 613 254 607 225 507L169 317C132 189 113 129 97 88C81 46 61 32 3 27L-4 0H222L228 27C154 34 145 46 152 89C156 125 171 179 199 282L271 545H273C311 354 343 183 375 4H398L729 556H731C709 415 687 283 665 135C651 39 645 34 568 27L561 0H814L821 27C741 34 734 37 747 135C764 267 779 384 801 528C814 611 816 615 903 622L910 649Z"/></g><g transform="matrix(.017,0,0,-0.017,37.992,0)"><use xlink:href="#g189-48"/></g><g transform="matrix(.017,0,0,-0.017,43.518,0)"><path id="g189-213" d="M303 635C245 609 181 592 116 583L111 558L151 557C205 555 210 551 198 490L127 128C110 40 104 35 17 26L11 0H279L285 26C196 35 188 40 205 128L303 635Z"/></g></svg> Queue with Vacations and Multiple Service Phases 

Mathematical Problems in Engineering

On the Queue with Vacations and Multiple Service Phases

Figure 10