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="M414" 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="11.5564pt" id="M415" style="vertical-align:-2.26807pt" version="1.1" viewbox="-0.0498162 -9.28833 29.8769 11.5564" width="29.8769pt" 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="M593 650H142L136 622C219 616 224 611 209 531L130 120C114 39 108 34 23 28L17 0H501C518 32 557 130 568 158L540 169C519 132 495 93 469 70C439 43 409 35 332 35C272 35 241 37 225 50C211 61 211 89 222 149L253 320H350C441 320 443 312 441 239H471L510 434H481C455 366 448 358 360 358H260L303 572C311 613 312 615 348 615H431C509 615 522 603 532 581C544 555 546 531 545 491L574 493C583 555 592 631 593 650Z" id="g113-70"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="616" vert-adv-y="616" xpluscharwidth="8.008"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,8.008,0)"><path d="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z" id="g113-41"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="346" vert-adv-y="346" xpluscharwidth="12.506"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,12.506,0)"><path d="M962 650H739L732 622L760 619C812 613 819 604 798 552C760 457 671 267 606 131H604L511 638H480L237 131H233L183 554C177 607 183 614 226 619L248 622L257 650H24L17 622C88 615 92 611 103 524L173 -11H203L450 491H453L543 -11H575L839 529C882 609 886 613 953 622L962 650Z" id="g113-88"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="974" vert-adv-y="974" xpluscharwidth="25.168"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,25.175,0)"><path d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z" id="g113-42"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="346" vert-adv-y="346" xpluscharwidth="29.673000000000002"></glyph.data></g></svg> for three interarrival time distributions (<svg height="9.49473pt" id="M416" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -9.28833 37.0231 9.49473" width="37.0231pt" 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="M475 507C475 612 440 712 326 712C139 712 23 420 23 215C23 96 58 -12 180 -12C369 -12 475 293 475 507ZM391 522C391 486 387 448 379 394H126C155 538 222 677 310 677C386 677 391 571 391 522ZM373 346C344 193 283 22 189 22C126 22 106 114 106 196C106 243 111 293 118 346H373Z" id="g113-230"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="498" vert-adv-y="498" xpluscharwidth="6.474"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,10.107,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z" id="g117-34"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="587" vert-adv-y="587" xpluscharwidth="17.738"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,21.37,0)"><path d="M384 0V27C293 34 287 42 287 114V635C232 613 172 594 109 583V559L157 557C201 555 205 550 205 499V114C205 42 199 34 109 27V0H384Z" id="g113-50"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="480" vert-adv-y="480" xpluscharwidth="27.61"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,27.61,0)"><path d="M113 -12C146 -12 170 11 170 46C170 78 146 103 114 103S58 78 58 46C58 11 82 -12 113 -12Z" id="g113-47"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="228" vert-adv-y="228" xpluscharwidth="30.573999999999998"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,30.574,0)"><path d="M153 550H386L412 615L406 623H120L82 318C104 327 142 338 184 338C294 338 347 275 347 187C347 112 305 39 221 39C160 39 119 71 97 89C88 97 80 96 71 90C59 80 50 67 49 57C48 45 52 36 66 23C80 9 123 -12 169 -12C221 -11 288 15 342 59C403 109 431 165 431 225C431 308 366 395 238 395C212 395 165 379 127 364L153 550Z" id="g113-54"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="480" vert-adv-y="480" xpluscharwidth="36.814"></glyph.data></g></svg>).</div>

Mathematical Problems in Engineering

fig7

Figure 7

Figure 7: 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 7