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Processor sharing

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In multilevel processor sharing a finite set of thresholds are defined and jobs partitioned according to how much service they have received. The lowest level (containing jobs which have received the least service) has the highest priority and higher levels monotonically decreasing priorities. Within
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Generalized processor sharing is a multi-class adaptation of the policy which shares service capacity according to positive weight factors to all non-empty job classes at the node, irrespective of the number of jobs of each class present. Often it is assumed that the jobs within a class form a queue
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where the customers, clients or jobs are all served simultaneously, each receiving an equal fraction of the service capacity available. In such a system all jobs start service immediately (there is no queueing).
97:, generalized processor sharing is "an idealized scheduling algorithm that achieves perfect fairness. All practical schedulers approximate GPS and use it as a reference to measure fairness." 327: 616: 176: 533: 392: 604: 320: 80: 685: 574: 647: 490: 652: 457: 798: 779: 675: 462: 313: 87: 763: 558: 758: 548: 397: 281: 193: 131: 94: 61: 37: 589: 452: 579: 500: 419: 431: 286: 748: 728: 723: 495: 198: 753: 738: 705: 599: 247: 184: 154: 370: 743: 642: 553: 483: 267:"Efficient and scalable multiprocessor fair scheduling using distributed weighted round-robin" 172: 594: 538: 424: 291: 239: 230: 203: 146: 382: 611: 478: 336: 49: 621: 584: 680: 222: 792: 733: 718: 695: 507: 690: 517: 251: 158: 713: 670: 637: 414: 409: 404: 387: 377: 365: 360: 355: 350: 68: 57: 53: 436: 243: 512: 295: 266: 150: 207: 67:
The sojourn time jobs experience has no closed form solution, even in an
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basis, but this assumption is not necessary for many GPS applications.
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Aalto, S.; Ayesta, U.; Borst, S.; Misra, V.; Núñez-Queija, R. (2007).
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The processor sharing algorithm "emerged as an idealisation of
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scheduling algorithms in time-shared computer systems".
223:"Sojourn time asymptotics in processor-sharing queues" 704: 663: 630: 567: 526: 471: 445: 343: 221:Borst, S.; Núñez-Queija, R.; Zwart, B. (2006). 18:Form of resource sharing for tasks in computing 177:"Time-shared Systems: A theoretical treatment" 321: 8: 139:ACM SIGMETRICS Performance Evaluation Review 60:) with a processor sharing discipline has a 106:each level an internal discipline is used. 48:A single server queue operating subject to 328: 314: 306: 285: 265:Li, T.; Baumberger, D.; Hahn, S. (2009). 197: 125: 123: 121: 119: 115: 7: 14: 775: 774: 86:and that queue is served on a 1: 605:Flow-equivalent server method 81:generalized processor sharing 75:Generalized processor sharing 26:egalitarian processor sharing 686:Adversarial queueing network 575:Continuous-time Markov chain 101:Multilevel processor sharing 648:Heavy traffic approximation 393:Pollaczek–Khinchine formula 815: 132:"Beyond processor sharing" 78: 772: 653:Reflected Brownian motion 458:Markovian arrival process 244:10.1007/s11134-006-7585-9 64:stationary distribution. 676:Layered queueing network 463:Rational arrival process 88:first-come, first-served 764:Teletraffic engineering 559:Shortest remaining time 296:10.1145/1594835.1504188 151:10.1145/1243401.1243409 759:Scheduling (computing) 398:Matrix analytic method 590:Product-form solution 491:Gordon–Newell theorem 453:Poisson point process 344:Single queueing nodes 208:10.1145/321386.321388 52:arrivals (such as an 617:Decomposition method 95:processor scheduling 749:Pipeline (software) 729:Flow control (data) 724:Erlang distribution 706:Information systems 496:Mean value analysis 274:ACM SIGPLAN Notices 754:Quality of service 739:Network congestion 600:Quasireversibility 580:Kendall's notation 185:Journal of the ACM 786: 785: 744:Network scheduler 643:Mean-field theory 554:Shortest job next 544:Processor sharing 501:Buzen's algorithm 484:Traffic equations 472:Queueing networks 446:Arrival processes 420:Kingman's formula 22:Processor sharing 806: 778: 777: 595:Balance equation 527:Service policies 425:Lindley equation 330: 323: 316: 307: 300: 299: 289: 271: 262: 256: 255: 231:Queueing Systems 227: 218: 212: 211: 201: 181: 169: 163: 162: 136: 127: 814: 813: 809: 808: 807: 805: 804: 803: 799:Queueing theory 789: 788: 787: 782: 768: 700: 659: 626: 612:Arrival theorem 563: 522: 479:Jackson network 467: 441: 432:Fork–join queue 371:Burke's theorem 339: 337:Queueing theory 334: 304: 303: 287:10.1.1.567.2170 269: 264: 263: 259: 225: 220: 219: 215: 179: 171: 170: 166: 134: 129: 128: 117: 112: 103: 83: 77: 46: 44:Queueing theory 19: 12: 11: 5: 812: 810: 802: 801: 791: 790: 784: 783: 773: 770: 769: 767: 766: 761: 756: 751: 746: 741: 736: 731: 726: 721: 716: 710: 708: 702: 701: 699: 698: 693: 688: 683: 681:Polling system 678: 673: 667: 665: 661: 660: 658: 657: 656: 655: 645: 640: 634: 632: 631:Limit theorems 628: 627: 625: 624: 619: 614: 609: 608: 607: 602: 597: 587: 582: 577: 571: 569: 565: 564: 562: 561: 556: 551: 546: 541: 536: 530: 528: 524: 523: 521: 520: 515: 510: 505: 504: 503: 498: 488: 487: 486: 475: 473: 469: 468: 466: 465: 460: 455: 449: 447: 443: 442: 440: 439: 434: 429: 428: 427: 422: 412: 407: 402: 401: 400: 395: 385: 380: 375: 374: 373: 363: 358: 353: 347: 345: 341: 340: 335: 333: 332: 325: 318: 310: 302: 301: 257: 238:(1–2): 31–51. 213: 199:10.1.1.74.3945 192:(2): 242–261. 164: 114: 113: 111: 108: 102: 99: 79:Main article: 76: 73: 45: 42: 17: 13: 10: 9: 6: 4: 3: 2: 811: 800: 797: 796: 794: 781: 771: 765: 762: 760: 757: 755: 752: 750: 747: 745: 742: 740: 737: 735: 734:Message queue 732: 730: 727: 725: 722: 720: 719:Erlang (unit) 717: 715: 712: 711: 709: 707: 703: 697: 696:Retrial queue 694: 692: 689: 687: 684: 682: 679: 677: 674: 672: 669: 668: 666: 662: 654: 651: 650: 649: 646: 644: 641: 639: 636: 635: 633: 629: 623: 620: 618: 615: 613: 610: 606: 603: 601: 598: 596: 593: 592: 591: 588: 586: 583: 581: 578: 576: 573: 572: 570: 566: 560: 557: 555: 552: 550: 547: 545: 542: 540: 537: 535: 532: 531: 529: 525: 519: 516: 514: 511: 509: 508:Kelly network 506: 502: 499: 497: 494: 493: 492: 489: 485: 482: 481: 480: 477: 476: 474: 470: 464: 461: 459: 456: 454: 451: 450: 448: 444: 438: 435: 433: 430: 426: 423: 421: 418: 417: 416: 413: 411: 408: 406: 403: 399: 396: 394: 391: 390: 389: 386: 384: 381: 379: 376: 372: 369: 368: 367: 364: 362: 359: 357: 354: 352: 349: 348: 346: 342: 338: 331: 326: 324: 319: 317: 312: 311: 308: 297: 293: 288: 283: 279: 275: 268: 261: 258: 253: 249: 245: 241: 237: 233: 232: 224: 217: 214: 209: 205: 200: 195: 191: 187: 186: 178: 174: 173:Kleinrock, L. 168: 165: 160: 156: 152: 148: 144: 140: 133: 126: 124: 122: 120: 116: 109: 107: 100: 98: 96: 91: 89: 82: 74: 72: 70: 65: 63: 59: 55: 51: 43: 41: 39: 34: 31: 28:is a service 27: 23: 16: 691:Loss network 622:Beneš method 585:Little's law 568:Key concepts 543: 518:BCMP network 277: 273: 260: 235: 229: 216: 189: 183: 167: 142: 138: 104: 92: 84: 66: 47: 35: 25: 21: 20: 15: 714:Data buffer 671:Fluid queue 638:Fluid limit 549:Round-robin 415:G/G/1 queue 410:G/M/1 queue 405:M/G/k queue 388:M/G/1 queue 383:M/M/∞ queue 378:M/M/c queue 366:M/M/1 queue 361:M/D/c queue 356:M/D/1 queue 351:D/M/1 queue 69:M/M/1 queue 58:M/G/1 queue 54:M/M/1 queue 38:round-robin 664:Extensions 437:Bulk queue 110:References 513:G-network 282:CiteSeerX 280:(4): 65. 194:CiteSeerX 145:(4): 36. 62:geometric 793:Category 780:Category 175:(1967). 252:7704706 159:7692913 50:Poisson 284:  250:  196:  157:  30:policy 270:(PDF) 248:S2CID 226:(PDF) 180:(PDF) 155:S2CID 135:(PDF) 539:LIFO 534:FIFO 292:doi 240:doi 204:doi 147:doi 93:In 56:or 24:or 795:: 290:. 278:44 276:. 272:. 246:. 236:53 234:. 228:. 202:. 190:14 188:. 182:. 153:. 143:34 141:. 137:. 118:^ 71:. 329:e 322:t 315:v 298:. 294:: 254:. 242:: 210:. 206:: 161:. 149::

Index

policy
round-robin
Poisson
M/M/1 queue
M/G/1 queue
geometric
M/M/1 queue
generalized processor sharing
first-come, first-served
processor scheduling




"Beyond processor sharing"
doi
10.1145/1243401.1243409
S2CID
7692913
Kleinrock, L.
"Time-shared Systems: A theoretical treatment"
Journal of the ACM
CiteSeerX
10.1.1.74.3945
doi
10.1145/321386.321388
"Sojourn time asymptotics in processor-sharing queues"
Queueing Systems
doi
10.1007/s11134-006-7585-9

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