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="9.49473pt" id="M396" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -9.28833 7.30254 9.49473" width="7.30254pt" 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="M529 97L508 118C475 75 449 58 438 58C428 58 421 66 415 104C393 234 374 403 364 496C345 670 307 712 254 712C220 712 174 691 153 669L161 645C176 653 194 658 206 658C237 658 261 640 278 562C287 522 290 483 293 434C223 269 110 105 23 9L32 -12C59 -6 85 0 108 7C152 64 251 252 300 366C307 297 315 221 337 82C346 24 363 -12 393 -12C425 -12 475 13 529 97Z" id="g113-233"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="552" vert-adv-y="552" xpluscharwidth="7.176"></glyph.data></g></svg> on <svg height="10.3116pt" id="M397" style="vertical-align:-4.35069pt" version="1.1" viewbox="-0.0498162 -5.96091 19.0447 10.3116" width="19.0447pt" 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" xpluscharwidth="7.683"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,7.358,3.132)"><path d="M245 635C92 635 37 457 37 312C37 149 91 -12 244 -12C395 -12 449 166 449 312C449 469 395 635 245 635ZM243 598C332 598 358 454 358 312C358 173 334 26 245 26C158 26 128 174 128 313S152 598 243 598Z" id="g50-49"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="487" vert-adv-y="487" xpluscharwidth="11.789685389999999"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,11.79,3.132)"><path d="M98 134C72 134 46 117 46 90C46 73 55 65 60 64C95 55 124 32 124 -4C124 -42 95 -68 44 -89L57 -123C122 -104 194 -60 194 22C194 94 136 134 98 134Z" id="g50-45"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="237" vert-adv-y="237" xpluscharwidth="13.94669289"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,13.946,3.132)"><path d="M245 635C92 635 37 457 37 312C37 149 91 -12 244 -12C395 -12 449 166 449 312C449 469 395 635 245 635ZM243 598C332 598 358 454 358 312C358 173 334 26 245 26C158 26 128 174 128 313S152 598 243 598Z" id="g50-49"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="487" vert-adv-y="487" xpluscharwidth="18.37768539"></glyph.data></g></svg>.</div>

Mathematical Problems in Engineering

fig4

Figure 4

Figure 4: 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 4