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Run idnits with the --verbose option for more detailed information about the items above. -------------------------------------------------------------------------------- 1 IP Performance Metrics Working Group S. Ono, T. Miyata, H. Fukuda 2 Internet Draft NTT 3 Expiration Date: February 1999 Aug 1998 5 Loss Metrics of Grouped Packets for IPPM 6 8 1. Status of this Memo 10 This document is an Internet Draft. Internet Drafts are working doc- 11 uments of the Internet Engineering Task Force (IETF), its areas, and 12 its working groups. Note that other groups may also distribute work- 13 ing documents as Internet Drafts. 15 Internet Drafts are draft documents valid for a maximum of six 16 months, and may be updated, replaced, or obsoleted by other documents 17 at any time. It is inappropriate to use Internet Drafts as reference 18 material or to cite them other than as ``work in progress''. 20 To learn the current status of any Internet Draft, please check the 21 ``1id-abstracts.txt'' listing contained in the Internet Drafts shadow 22 directories on ftp.is.co.za (Africa), nic.nordu.net (Europe), 23 munnari.oz.au (Pacific Rim), ftp.ietf.org (US East Coast), or 24 ftp.isi.edu (US West Coast). 26 This memo provides information for the Internet community. This memo 27 does not specify an Internet standard of any kind. Distribution of 28 this memo is unlimited. 30 2. Introduction 32 This memo defines several metrics for loss of grouped packets across 33 Internet paths. It builds on notions introduced and discussed in the 34 IPPM Framework document (currently ''Framework for IP Performance 35 Metrics'' ); the reader is assumed 36 to be familiar with that document. 38 In addition, this memo is intended to be a generalization of the 39 document for Packet Loss [1] and to be very parallel in structure 40 to that document; the reader is also assumed to be familiar with 41 that document. 43 The structure of the memo is as follows: 45 + A 'singleton' analytic metric, called Type-P-One-way-Grouped- 46 Packets-Loss-Pattern, will be introduced to measure a single 47 observation, which is comprised of multiple related packet 48 transmissions, each of the transmissions may be successful or 49 loss. 50 (Section 3.1) 52 + A 'singleton' analytic metric, called Type-P-One-way-Grouped- 53 Packets-LossTh, will be introduced to measure a single 54 observation, 55 which can be derived from the metric Type-P-One-way-Grouped- 56 Packets-Loss-Pattern. This metric is generalization of Type-P- 57 One-way-Packet-Loss to a packet group such that a packet group is 58 said to be 'lost' when s or more out of w packets in the group are 59 lost, where w (0 < w) is a loss-window size, and s (0 < s <= w) is 60 a loss threshold count. When both w and s are set to 1, it is the 61 same 62 as the conventional metric Type-P-One-way-Packet-Loss. 63 (Section 3.2) 65 + A 'singleton' analytic metric, called Type-P-One-way-Grouped- 66 Packets-Loss, will be introduced to measure a single observation, 67 which is the specialization of Type-P-One-way-Grouped-Packets- 68 LossTh, such that the threshold value s is fixed to 1. 69 Namely, a packet group is said to be lost only when all of w 70 packets in the group are lost, where w (0 < w) is a loss-window 71 size. Naturally, when w is also set to 1, it is the same as 72 Type-P-One-way-Packet-Loss. 73 (Section 3.3) 75 + Using the singleton metric Type-P-One-way-Grouped-Packets- 76 Loss-Pattern, a 'sample', called Type-P-One-way-Grouped-Packets- 77 Loss-Pattern-Stream, will be introduced to measure a sequence of 78 singleton loss patterns of grouped packets, where each measurement 79 is started at times taken from a Poisson process. 80 (Section 4.1) 82 + Using the singleton metric Type-P-One-way-Grouped-Packets-LossTh, 83 a 'sample', called Type-P-One-way-Grouped-Packets-LossTh-Stream, 84 will be introduced to measure a sequence of singleton losses 85 of grouped packets, where each measurement is started at times 86 taken from a Poisson process. 87 (Section 4.2) 89 + Using the singleton metric Type-P-One-way-Grouped-Packets-Loss, 90 a 'sample', called Type-P-One-way-Grouped-Packets-Loss-Stream, 91 will be introduced to measure a sequence of singleton losses 92 of grouped packets, where each measurement is started at times 93 taken from a Poisson process. 94 (Section 4.3) 96 + The relationships among these metrics are discussed. 97 (Section 5) 99 + Using these samples, several 'statistics' of the samples will 100 be defined and discussed. 101 (Section 6) 103 These progressions from singletons to samples to statistics, with 104 clear separation among them, are important. 106 Whenever a technical term from the IPPM Framework document is first 107 used in this memo, it will be tagged with a trailing asterisk, as 108 with >>term*<<. 110 2.1. Motivation: 112 The work-in-progress document [2] defines the notion of one-way 113 packet loss of type-P packets transmitted from a source host* to a 114 destination 115 host. In that document, the unit of measurement is a packet. 116 The main purpose of this document is to generalize it to a packet 117 group, i.e. a sequence of multiple related packets. 118 Such Generalization is useful for several reasons: 120 + When successive packets are injected at short intervals, 121 the loss probability of each packet may NOT be independent [3]; 122 For example, the loss probability of the next packet may become 123 lower, if the preceding packet has been lost. 124 Metrics using only one packet transmission for each sample 125 cannot detect this kind of conditional loss probability. 127 + The stream-oriented applications which handle audio and/or video 128 are likely to inject packets at short intervals. 130 + There exist applications that use FEC (forward error control/ 131 correction) technology. Typical FEC usage on packet networks is 132 as follows. Application data are scattered among w different 133 packets with redundancy so that the application data can be 134 recovered if only s (0 < s < w) or more packets out of the 135 w packets are successfully received. In such recovered cases, 136 losses of packets are invisible to the application. 138 + Some applications take advantage of both FEC and hierarchical 139 coding. For example, low-quality audio data may be protected 140 more thoroughly than high-quality audio, such that the low-quality 141 data can be retrieved even if only one packet in a group is 142 received. 143 In such a case, the application may provide degraded service to 144 a user due to a heavily lossy network. 146 It is outside the scope of this document to define precisely how 147 packet group loss metrics would be applied to specific problems. 149 2.2. General Issues Regarding Time 151 Whenever a time (i.e., a moment in history) is mentioned here, it is 152 understood to be measured in seconds (and fractions) relative to UTC. 154 Similar discussions are applicable as described in Section 2.2 of 155 the document for Packet Loss (''A Packet Loss Metric 156 for IPPM'' ). 158 3. Singleton Definitions for One-way Losses of Grouped Packets 160 3.1. A Singleton Definition for One-way Loss Pattern of Grouped Packets 162 3.1.1. Metric Name: 164 Type-P-One-way-Grouped-Packets-Loss-Pattern 166 3.1.2. Metric Parameters: 167 + Src, the IP address of a host 168 + Dst, the IP address of a host 169 + T, a time 170 + n, a group size (GS) (positive integer number) 171 + TS, a monotonic sequence of times with length n, 172 where t1 should be always equal to T. 173 + Path, the path* from Src to Dst; in cases where there is only one 174 path from Src to Dst, this optional parameter can be omitted. 175 {Comment: For the discussion on path, please refer to Section 3.2 of 176 the document for Packet Loss (''A Packet Loss Metric 177 for IPPM'' ). 179 3.1.3. Metric Units: 181 The value of a Type-P-One-way-Grouped-Packets-Loss-Pattern is a 182 sequence of n (i.e. the group size) values, each of which is either 183 a zero (signifying successful transmission of the packet) or 184 a one (signifying loss). 186 3.1.4. Definition: 188 >>The *Type-P-One-way-Grouped-Packets-Loss-Pattern* from Src to Dst 189 at for GS n (1 <= n) [via path] is << means that for each i (1 <= i <= n), Src sent the first bit 191 of the i-th type-P packet [via path] to Dst at wire-time ti, and that 192 Dst received that packet correctly if Li is 0, and did not if Li is 193 1, 194 respectively. 196 3.1.5. Discussion: 198 It is a rather straight forward extension of 199 Type-P-One-way-Packet-Loss, 200 such that grouped n packets are sent in sequence, and the loss 201 is recorded packet-wise. 203 As can be easily seen, when the group size n is set to 1, the Type-P- 204 One-way-Grouped-Packets-Loss-Pattern is the same as 205 Type-P-One-way-Packet- 206 Loss. 208 + Although no assumption is made for t1, ..., tn, the following are 209 a partial list of possible alternatives. 210 Stream type: 211 Take ti such that ti = t1 + delta * (i - 1) where delta 212 is a constant packet interval. 213 Random type: 214 ti is taken from a Poisson process. 215 Burst type: 216 Take ti as close as possible to the preceding packet. 218 + Similar discussions are applicable as described in Section 3.5 of 219 the document for Packet Loss (''A Packet Loss Metric 220 for IPPM'' ). 222 3.1.6. Methodologies: 224 Similar discussions are applicable as described in Section 3.6 of 225 the document for Packet Loss (''A Packet Loss Metric 226 for IPPM'' ). 228 3.1.7. Errors and Uncertainties: 230 Similar discussions are applicable as described in Section 3.7 of 231 the document for Packet Loss (''A Packet Loss Metric 232 for IPPM'' ). 234 3.2. A Singleton Definition for Window-based One-way Loss of 235 Grouped Packets where Loss is Defined using Thresholds 237 3.2.1. Metric Name: 239 Type-P-One-way-Grouped-Packets-LossTh 241 3.2.2. Metric Parameters: 243 + Src, the IP address of a host 244 + Dst, the IP address of a host 245 + T, a time 246 + n, a group size (GS) (positive integer number) 247 + TS, a monotonic sequence of times with length n, 248 where t1 should be always equal to T 249 + w, a loss window size (LWS) (positive integer number, and w <= n) 250 + s, a loss threshold count (LTC) (positive integer number and s <= 251 w) 252 + Path, the path from Src to Dst; in cases where there is only one 253 path from Src to Dst, this optional parameter can be omitted. 255 3.2.3. Metric Units: 257 The value of a type-P-One-way-Grouped-Packets-LossTh is either a zero 258 (signifying that at least s packets out of w packets have been 259 successfully 260 transmitted) or a one (signifying that less than s packets out of 261 w packets have been successfully transmitted, or all of the w packets 262 have been lost). 264 3.2.4. Definition: 266 >>The *Type-P-One-way-Grouped-Packets-LossTh* from Src to Dst at 267 for GS n (1 <= n), LWS w (1 <= w <= n), and LTC s 268 (1 <= s <= w) [via path] is 0 << means that for each i (1 <= i <= n), 269 Src sent the first bit of the i-th type-P packet Pi [via path] to Dst 270 at wire-time ti, and that Dst received at least s packets among 271 packets {P1, P2, ..., Pw}. 273 >>The *Type-P-One-way-Grouped-Packets-LossTh* from Src to Dst at 274 for GS n (1 <= n), LWS w (1 <= w <= n), and LTC s 275 (1 <= s <= w) [via path] is 1 << means that for each i (1 <= i <= n), 276 Src sent the first bit of the i-th type-P packet Pi [via path] to Dst 277 at wire-time ti, and that Dst received less than s or none of the 278 packets {P1, P2, ..., Pw}. 280 3.2.5. Discussion: 282 This metric can be naturally derived from the Type-P-One-way-Grouped- 283 Packets-Loss-Pattern. 285 Assume a sample of Type-P-One-way-Grouped-Packets-Loss-Pattern of 286 GS n (1 <= n) be 287 < , >. 288 Then, Type-P-One-way-Grouped-Packets-LossTh of LWS w (1 <= w <= n) 289 and LTC s (1 <= s <= w) be 290 < , 0 > if ((L1 + L2 + ... + Lw) <= w - s), 291 and 292 < , 1 > if ((L1 + L2 + ... + Lw) > w - s). 294 When w < n, if we ignore the effect of packets Pw+1, ..., Pn to 295 L1, ..., Lw, we can assume the group size to be equal to w. 297 3.2.6. Methodologies: 299 See Section 3.1.6 of this document. 301 3.2.7. Errors and Uncertainties: 303 See Section 3.1.7 of this document. 305 3.3. A Singleton Definition for Window-based One-way Loss of 306 Grouped Packets 308 3.3.1. Metric Name: 310 Type-P-One-way-Grouped-Packets-Loss 312 3.3.2. Metric Parameters: 313 + Src, the IP address of a host 314 + Dst, the IP address of a host 315 + T, a time 316 + n, a group size (GS) (positive integer number) 317 + TS, a monotonic sequence of times with length n, 318 where t1 should be always equals to T 319 + Path, the path from Src to Dst; in cases where there is only one 320 path from Src to Dst, this optional parameter can be omitted. 321 + w, a loss window size (LWS) (positive integer number, and w <= n) 323 3.3.3. Metric Units: 325 The value of a type-P-One-way-Grouped-Packets-Loss is either a zero 326 (signifying that at least one packet out of w packets has been 327 successfully transmitted) or a one (signifying that none of 328 w packets has been successfully transmitted. 330 3.3.4. Definition: 332 >>The *Type-P-One-way-Grouped-Packets-Loss* from Src to Dst at 333 for GS n (1 <= n), LWS w (1 <= w <= n) [via path] 334 is 0 << means that for each i (1 <= i <= n), Src sent the first bit 335 of the i-th type-P packet Pi [via path] to Dst at wire-time ti, 336 and that Dst received at least one of the packets 337 {P1, P2, ..., Pw}. 339 >>The *Type-P-One-way-Grouped-Packets-Loss* from Src to Dst at 340 for GS n (1 <= n), LWS w (1 <= w <= n) [via path] 341 is 1 << means that for each i (1 <= i <= n), Src sent the first bit 342 of the i-th type-P packet Pi [via path] to Dst at wire-time ti, 343 and that Dst received none of the packets {P1, P2, ..., Pw}. 345 3.3.5. Discussion: 347 This metric is specialization of 348 Type-P-One-way-Grouped-Packets-LossTh, 349 such that LTC is always fixed to 1. 351 In case w < n, if we ignore the effect of packets Pw+1, ..., Pn to 352 L1, ..., Lw, we can assume the group size be equal to w. 354 3.3.6. Methodologies: 356 See Section 3.1.6 of this document. 358 3.3.7. Errors and Uncertainties: 360 See Section 3.1.7 of this document. 362 4. Definitions for Samples of One-way Losses of Grouped Packets 364 Given the above-defined singleton metrics, namely 365 (1) Type-P-One-way-Grouped-Packets-Loss-Pattern, 366 (2) Type-P-One-way-Grouped-Packets-LossTh and 367 (3) Type-P-One-way-Grouped-Packets-Loss, 368 we now define one particular sample of such singletons. The idea 369 of the sample is to select a particular binding of the parameters 370 Src, Dst, path, Type-P, GS n, LWS w (for metrics (2) and (3)) and 371 LTC s (for the metric (2)), define a sample of values of parameter T. 372 The way to define the values of T is to select a beginning time 373 T0, a final time Tf, and an average rate lambda, then define a 374 pseudo-random Poisson arrival process of rate lambda, whose values 375 fall between T0 and Tf. The time interval between successive values 376 of T will then average 1/lambda. 378 4.1 A Definition for Samples of One-way Loss Pattern of Grouped Packets 380 4.1.1. Metric Name: 382 Type-P-One-way-Grouped-Packets-Loss-Pattern-Stream 384 4.1.2. Metric Parameters: 385 + Src, the IP address of a host 386 + Dst, the IP address of a host 387 + Path, the path from Src to Dst; in cases where there is only one 388 path from Src to Dst, this optional parameter can be omitted 389 + n, a group size (GS) (positive integer number) 390 + T0, a time 391 + Tf, a time 392 + lambda, a rate in reciprocal seconds 393 + Tseq, a (possibly non-deterministic) mapping from a time to 394 a monotonic sequence of times of length n. The first member of 395 the resulting sequence is always the same as the input parameter. 397 4.1.3. Metric Units: 399 A sequence of triplets; the elements of each triplets are: 401 + T, a time, 402 + TS, a monotonic sequence of times with length n, a valid instance 403 of Tseq(T), 404 + LS, a sequence of values with length n, each of which is either 405 a zero or a one.The values of T in the sequence increase 406 monotonically. 407 Note that T and TS would be valid parameters for the 408 Type-P-One-way-Grouped-Packets-Loss-Pattern, and that LS would be 409 a 410 valid value of the Type-P-One-way-Grouped-Packets-Loss-Pattern. 412 4.1.4. Definition: 414 Given T0, Tf, and lambda, we compute a pseudo-random Poisson process 415 beginning at or before T0, with an average arrival rate lambda, and 416 end- 417 ing at or after Tf. Those time values greater than or equal to T0 418 and less than or equal to Tf are then selected. At each time T of 419 the times in this process, we compute a time sequence TS = Tseq(T), 420 and obtain the value of the 421 Type-P-One-way-Grouped-Packets-Loss-Pattern 422 using this time sequence. The value of the sample is the sequence 423 made up of the resulting triplets. If there are no 424 such 425 triplets, the sequence is of length zero and the sample is said to be 426 empty. 428 4.1.5. Discussion: 430 Similar discussions are applicable as described in Section 4.5 of 431 the document for Packet Loss (''A Packet Loss Metric 432 for IPPM'' ). 434 4.1.6. Methodologies: 436 Similar discussions are applicable as described in Section 4.6 of 437 the document for Packet Loss (''A Packet Loss Metric 438 for IPPM'' ). 440 4.1.7. Errors and Uncertainties: 442 Similar discussions are applicable as described in Section 4.7 of 443 the document for Packet Loss (''A Packet Loss Metric 444 for IPPM'' ). 446 Note also that errors could be caused by the algorithm of Tseq, 447 and inaccuracy in the wire-time of the sending of the grouped 448 packets. 450 4.2. A Definition for Samples of Window-based One-way Loss of 451 Grouped Packets where Loss is Defined using Thresholds 453 4.2.1. Metric Name: 455 Type-P-One-way-Grouped-Packets-LossTh-Stream 457 4.2.2. Metric Parameters: 458 + Src, the IP address of a host 459 + Dst, the IP address of a host 460 + Path, the path from Src to Dst; in cases where there is only one 461 path from Src to Dst, this optional parameter can be omitted 462 + n, a group size (GS) (positive integer number) 463 + T0, a time 464 + Tf, a time 465 + lambda, a rate in reciprocal seconds 466 + Tseq, a (possibly non-deterministic) mapping from a time to 467 a monotonic sequence of times of length n. The first member of 468 the resulting sequence is always same as the input parameter. 469 + w, a loss window size (LWS) (positive integer number, and w <= n) 470 + s, a loss threshold count (LTC) (positive integer number and s <= 471 w) 473 4.2.3. Metric Units: 475 A sequence of triplets; the elements of each triplets are: 477 + T, a time, 478 + TS, a monotonic sequence of times with length n, a valid instance 479 of Tseq(T), 480 + L, either a zero or a one 481 The values of T in the sequence increase monotonically. Note that 482 T and TS would be valid parameters for 483 Type-P-One-way-Grouped-Packets- 484 LossTh, and that L would be a valid value of Type-P-One-way- 485 Grouped-Packets-LossTh. 487 4.2.4. Definition: 489 Given T0, Tf, and lambda, we compute a pseudo-random Poisson process 490 beginning at or before T0, with an average arrival rate lambda, and 491 end- 492 ing at or after Tf. Those time values greater than or equal to T0 493 and less than or equal to Tf are then selected. At each time T of 494 the times in this process, we compute a time sequence TS = Tseq(T), 495 and obtain the value of Type-P-One-way-Grouped-Packets-LossTh 496 using this time sequence. The value of the sample is the sequence 497 made up of the resulting triplets. If there are no such 498 triplets, the sequence is of length zero and the sample is said to be 499 empty. 501 4.2.5. Discussion: 503 Similar discussions are applicable as described in Section 4.5 of 504 the document for Packet Loss (''A Packet Loss Metric 505 for IPPM'' ). 507 4.2.6. Methodologies: 509 Similar discussions are applicable as described in Section 4.6 of 510 the document for Packet Loss (''A Packet Loss Metric 511 for IPPM'' ). 513 4.2.7. Errors and Uncertainties: 515 Similar discussions are applicable as described in Section 4.7 of 516 the document for Packet Loss (''A Packet Loss Metric 517 for IPPM'' ). 519 Note also that errors could be caused by the algorithm of Tseq, 520 and inaccuracy in the wire-time of the sending of the grouped 521 packets. 523 4.3. A Definition for Samples of Window-based One-way Loss of 524 Grouped Packets 526 4.3.1. Metric Name: 528 Type-P-One-way-Grouped-Packets-Loss-Stream 530 4.3.2. Metric Parameters: 532 + Src, the IP address of a host 533 + Dst, the IP address of a host 534 + Path, the path from Src to Dst; in cases where there is only one 535 path from Src to Dst, this optional parameter can be omitted 536 + n, a group size (GS) (positive integer number) 537 + T0, a time 538 + Tf, a time 539 + lambda, a rate in reciprocal seconds 540 + Tseq, a (possibly non-deterministic) mapping from a time to 541 a monotonic sequence of times of length n. The first member of 542 the resulting sequence is always same as the input parameter. 543 + w, a loss window size (LWS) (positive integer number, and w <= n) 545 4.3.3. Metric Units: 547 A sequence of triplets; the elements of each triplets are: 549 + T, a time, 550 + TS, a monotonic sequence of times with length n, a valid instance 551 of Tseq(T), 552 + L, either a zero or a one 553 The values of T in the sequence increase monotonically. Note that 554 T and TS would be valid parameters for Type-P-One-way-Grouped-Packets- 555 Loss, and that L would be a valid value of Type-P-One-way-Grouped- 556 Packets-Loss. 558 4.3.4. Definition: 560 Given T0, Tf, and lambda, we compute a pseudo-random Poisson process 561 beginning at or before T0, with an average arrival rate lambda, and end- 562 ing at or after Tf. Those time values greater than or equal to T0 563 and less than or equal to Tf are then selected. At each time T of 564 the times in this process, we compute a time sequence TS = Tseq(T), 565 and obtain the value of Type-P-One-way-Grouped-Packets-Loss 566 using this time sequence. The value of the sample is the sequence 567 made up of the resulting triplets. If there are no such 568 triplets, the sequence is of length zero and the sample is said to be 569 empty. 571 4.3.5. Discussion: 573 Similar discussions are applicable as described in Section 4.5 of 574 the document for Packet Loss (''A Packet Loss Metric 575 for IPPM'' ). 577 4.3.6. Methodologies: 579 Similar discussions are applicable as described in Section 4.6 of 580 the document for Packet Loss (''A Packet Loss Metric 581 for IPPM'' ). 583 4.3.7. Errors and Uncertainties: 585 Similar discussions are applicable as described in Section 4.7 of 586 the document for Packet Loss (''A Packet Loss Metric 587 for IPPM'' ). 589 Note also that errors could be caused by the algorithm of Tseq, 590 and inaccuracy in the wire-time of the sending of the grouped 591 packets. 593 5. Metrics Conversion Examples for One-way Loss of Grouped Packets 595 Among the three metrics defined in Section 3, the first one, i.e. 596 Type-P-One-way-Grouped-Packets-Loss-Pattern, is the most general, 597 and the other two can be computed from it. 599 We will demonstrate this using examples. 600 Suppose that a sample of Type-P-One-way-Grouped-Packets-Loss-Pattern 601 -Stream (group size 3) be as follows: 603 Stream1 = < 604 < t11, , <1, 0, 1> > 605 < t21, , <0, 0, 0> > 606 < t31, , <1, 1, 1> > 607 < t41, , <1, 1, 0> > 608 < t51, , <0, 1, 0> > 609 < t61, , <1, 0, 0> > 610 > 612 From this sample, Type-P-One-way-Grouped-Packets-LossTh-Streams 613 with various loss window sizes and loss threshold counts can be 614 computed as follows: 615 (Comments are added for readers' convenience. A comment starts with 616 a mark '//' and ends at the end of the line.) 618 (1) 619 < // Threshold is 2. 620 < t11, , 1 > // <1,0,1> Only 1 packet arrived. 621 < t21, , 0 > // <0,0,0> 3 packets arrived. 622 < t31, , 1 > // <1,1,1> No packets arrived. 623 < t41, , 1 > // <1,1,0> Only 1 packet arrived. 624 < t51, , 0 > // <0,1,0> 2 packets arrived. 625 < t61, , 0 > // <1,0,0> 2 packets arrived. 626 > 628 (2) 629 < // Threshold is 1. 630 < t11, , 0 > 631 < t21, , 0 > 632 < t31, , 1 > // <1,1,1> No packets arrived. 633 < t41, , 0 > 634 < t51, , 0 > 635 < t61, , 0 > 636 > 638 (3) 639 < // Loss window size is 2. 640 < t11, , 0 > // <1,0> One packet arrived. 641 < t21, , 0 > // <0,0> All packets arrived. 642 < t31, , 1 > // <1,1> No packets arrived. 643 < t41, , 1 > // <1,1> No packets arrived. 644 < t51, , 0 > // <0,1> One packet arrived. 645 < t61, , 0 > // <1,0> One packet arrived. 646 > 647 (We set the group size to be LWS. See Section 3.2.5.) 649 (4) 650 < // Loss window size is 1. 651 < t11, , 1 > // <1> Lost. 652 < t21, , 0 > // <0> Arrived. 653 < t31, , 1 > // <1> Lost. 654 < t41, , 1 > // <1> Lost. 655 < t51, , 0 > // <0> Arrived. 656 < t61, , 1 > // <1> Lost. 657 > 658 (We set the group size to be LWS. See Section 3.2.5.) 660 6. Some Statistics Definitions for One-way Loss of Grouped Packets 662 Given sample metrics such as Type-P-One-way-Grouped-Packets-Loss- 663 Pattern defined in Section 4 above, we now offer several statistics 664 of that sample. These statistics are offered mostly to be 665 illustrative 666 of what could be done. 668 6.1. Type-P-One-way-Grouped-Packets-LossTh-Average 670 Given a Type-P-One-way-Grouped-Packets-LossTh-Stream, the average 671 of all the L values in the Stream. In addition, the Type-P-One-way- 672 Grouped-Packets-LossTh-Average is undefined if the sample is empty. 674 Example: Suppose we take a sample and the results are: 676 Stream2 = < 677 < t11, , 1 > 678 < t21, , 0 > 679 < t31, , 1 > 680 < t41, , 1 > 681 < t51, , 0 > 682 < t61, , 0 > 683 > 685 Then the average would be 0.5. 687 7. Security Considerations 689 This memo raises no security issues. 691 8. Acknowledgments 693 The authors are indebted to Jean-Chrysostome Bolot and Sacha 694 Fosse-Parisis of the Rodeo 695 Project at inria for their valuable discussions regarding this draft. 697 in addition, we are grateful to guy almes and sunil kalidindi for 698 their valuable internet 699 drafts on metrics. 701 Thanks are also due to Haruhisa Ichikawa of NTT Sofware Laboratories 702 for his 703 helpful comments. 705 9. References 707 [1] G. Almes and S. Kalidindi, "A One-way Loss Metric for IPPM", 708 Inter- 709 net Draft , November 1997. 711 [2] V. Paxson, G. Almes, J. Mahdavi, and M. Mathis, "Framework for 712 IP 713 Performance Metrics", Internet Draft 714 , November 1997. 717 [3] T. Miyata, H. Fukuda, S. Ono, "New network QoS measures for 718 FEC-based audio application over the Internet", IEEE IPCCC'98, 719 pp. 355 - 362, February 1998. 721 10. Authors' Addresses 723 Satoshi Ono 724 NTT Software Laboratories 725 3-9-11, Midori-cho, Musashino-Shi, 726 Tokyo, 180-8585 727 JAPAN 728 Phone: +81 422/59-3542 730 Teruko Miyata 731 NTT Software Laboratories 732 3-9-11, Midori-cho, Musashino-Shi, 733 Tokyo, 180-8585 734 JAPAN 735 Phone: +81 422/59-2927 737 Harumoto Fukuda 738 NTT Software Laboratories 739 3-9-11, Midori-cho, Musashino-Shi, 740 Tokyo, 180-8585 741 JAPAN 742 Phone: +81 422/59-2882