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Run idnits with the --verbose option for more detailed information about the items above. -------------------------------------------------------------------------------- 2 Network Working Group A. Morton 3 Internet-Draft AT&T Labs 4 Intended status: Standards Track E. Stephan 5 Expires: December 27, 2010 France Telecom Division R&D 6 June 25, 2010 8 Spatial Composition of Metrics 9 draft-ietf-ippm-spatial-composition-13 11 Abstract 13 This memo utilizes IP Performance Metrics that are applicable to both 14 complete paths and sub-paths, and defines relationships to compose a 15 complete path metric from the sub-path metrics with some accuracy 16 w.r.t. the actual metrics. This is called Spatial Composition in RFC 17 2330. The memo refers to the Framework for Metric Composition, and 18 provides background and motivation for combining metrics to derive 19 others. The descriptions of several composed metrics and statistics 20 follow. 22 Requirements Language 24 The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT", 25 "SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this 26 document are to be interpreted as described in RFC 2119 [RFC2119]. 28 In this memo, the characters "<=" should be read as "less than or 29 equal to" and ">=" as "greater than or equal to". 31 Status of this Memo 33 This Internet-Draft is submitted in full conformance with the 34 provisions of BCP 78 and BCP 79. 36 Internet-Drafts are working documents of the Internet Engineering 37 Task Force (IETF). Note that other groups may also distribute 38 working documents as Internet-Drafts. The list of current Internet- 39 Drafts is at http://datatracker.ietf.org/drafts/current/. 41 Internet-Drafts are draft documents valid for a maximum of six months 42 and may be updated, replaced, or obsoleted by other documents at any 43 time. It is inappropriate to use Internet-Drafts as reference 44 material or to cite them other than as "work in progress." 46 This Internet-Draft will expire on December 27, 2010. 48 Copyright Notice 49 Copyright (c) 2010 IETF Trust and the persons identified as the 50 document authors. All rights reserved. 52 This document is subject to BCP 78 and the IETF Trust's Legal 53 Provisions Relating to IETF Documents 54 (http://trustee.ietf.org/license-info) in effect on the date of 55 publication of this document. Please review these documents 56 carefully, as they describe your rights and restrictions with respect 57 to this document. Code Components extracted from this document must 58 include Simplified BSD License text as described in Section 4.e of 59 the Trust Legal Provisions and are provided without warranty as 60 described in the Simplified BSD License. 62 This document may contain material from IETF Documents or IETF 63 Contributions published or made publicly available before November 64 10, 2008. The person(s) controlling the copyright in some of this 65 material may not have granted the IETF Trust the right to allow 66 modifications of such material outside the IETF Standards Process. 67 Without obtaining an adequate license from the person(s) controlling 68 the copyright in such materials, this document may not be modified 69 outside the IETF Standards Process, and derivative works of it may 70 not be created outside the IETF Standards Process, except to format 71 it for publication as an RFC or to translate it into languages other 72 than English. 74 Table of Contents 76 1. Contributors . . . . . . . . . . . . . . . . . . . . . . . . . 5 77 2. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 5 78 2.1. Motivation . . . . . . . . . . . . . . . . . . . . . . . . 6 79 3. Scope and Application . . . . . . . . . . . . . . . . . . . . 6 80 3.1. Scope of work . . . . . . . . . . . . . . . . . . . . . . 7 81 3.2. Application . . . . . . . . . . . . . . . . . . . . . . . 7 82 3.3. Incomplete Information . . . . . . . . . . . . . . . . . . 8 83 4. Common Specifications for Composed Metrics . . . . . . . . . . 8 84 4.1. Name: Type-P . . . . . . . . . . . . . . . . . . . . . . . 8 85 4.1.1. Metric Parameters . . . . . . . . . . . . . . . . . . 8 86 4.1.2. Definition and Metric Units . . . . . . . . . . . . . 9 87 4.1.3. Discussion and other details . . . . . . . . . . . . . 9 88 4.1.4. Statistic: . . . . . . . . . . . . . . . . . . . . . . 9 89 4.1.5. Composition Function . . . . . . . . . . . . . . . . . 9 90 4.1.6. Statement of Conjecture and Assumptions . . . . . . . 9 91 4.1.7. Justification of the Composition Function . . . . . . 10 92 4.1.8. Sources of Deviation from the Ground Truth . . . . . . 10 93 4.1.9. Specific cases where the conjecture might fail . . . . 11 94 4.1.10. Application of Measurement Methodology . . . . . . . . 12 95 5. One-way Delay Composed Metrics and Statistics . . . . . . . . 12 96 5.1. Name: 97 Type-P-Finite-One-way-Delay-Poisson/Periodic-Stream . . . 12 98 5.1.1. Metric Parameters . . . . . . . . . . . . . . . . . . 12 99 5.1.2. Definition and Metric Units . . . . . . . . . . . . . 12 100 5.1.3. Discussion and other details . . . . . . . . . . . . . 13 101 5.1.4. Statistic: . . . . . . . . . . . . . . . . . . . . . . 13 102 5.2. Name: Type-P-Finite-Composite-One-way-Delay-Mean . . . . . 13 103 5.2.1. Metric Parameters . . . . . . . . . . . . . . . . . . 13 104 5.2.2. Definition and Metric Units of the Mean Statistic . . 13 105 5.2.3. Discussion and other details . . . . . . . . . . . . . 14 106 5.2.4. Statistic: . . . . . . . . . . . . . . . . . . . . . . 14 107 5.2.5. Composition Function: Sum of Means . . . . . . . . . . 14 108 5.2.6. Statement of Conjecture and Assumptions . . . . . . . 14 109 5.2.7. Justification of the Composition Function . . . . . . 15 110 5.2.8. Sources of Deviation from the Ground Truth . . . . . . 15 111 5.2.9. Specific cases where the conjecture might fail . . . . 15 112 5.2.10. Application of Measurement Methodology . . . . . . . . 15 113 5.3. Name: Type-P-Finite-Composite-One-way-Delay-Minimum . . . 15 114 5.3.1. Metric Parameters . . . . . . . . . . . . . . . . . . 15 115 5.3.2. Definition and Metric Units of the Minimum 116 Statistic . . . . . . . . . . . . . . . . . . . . . . 15 117 5.3.3. Discussion and other details . . . . . . . . . . . . . 16 118 5.3.4. Statistic: . . . . . . . . . . . . . . . . . . . . . . 16 119 5.3.5. Composition Function: Sum of Minima . . . . . . . . . 16 120 5.3.6. Statement of Conjecture and Assumptions . . . . . . . 16 121 5.3.7. Justification of the Composition Function . . . . . . 17 122 5.3.8. Sources of Deviation from the Ground Truth . . . . . . 17 123 5.3.9. Specific cases where the conjecture might fail . . . . 17 124 5.3.10. Application of Measurement Methodology . . . . . . . . 17 125 6. Loss Metrics and Statistics . . . . . . . . . . . . . . . . . 17 126 6.1. Type-P-Composite-One-way-Packet-Loss-Empirical-Probability 17 127 6.1.1. Metric Parameters: . . . . . . . . . . . . . . . . . . 17 128 6.1.2. Definition and Metric Units . . . . . . . . . . . . . 17 129 6.1.3. Discussion and other details . . . . . . . . . . . . . 17 130 6.1.4. Statistic: 131 Type-P-One-way-Packet-Loss-Empirical-Probability . . . 18 132 6.1.5. Composition Function: Composition of Empirical 133 Probabilities . . . . . . . . . . . . . . . . . . . . 18 134 6.1.6. Statement of Conjecture and Assumptions . . . . . . . 18 135 6.1.7. Justification of the Composition Function . . . . . . 18 136 6.1.8. Sources of Deviation from the Ground Truth . . . . . . 19 137 6.1.9. Specific cases where the conjecture might fail . . . . 19 138 6.1.10. Application of Measurement Methodology . . . . . . . . 19 139 7. Delay Variation Metrics and Statistics . . . . . . . . . . . . 19 140 7.1. Name: Type-P-One-way-pdv-refmin-Poisson/Periodic-Stream . 19 141 7.1.1. Metric Parameters: . . . . . . . . . . . . . . . . . . 19 142 7.1.2. Definition and Metric Units . . . . . . . . . . . . . 20 143 7.1.3. Discussion and other details . . . . . . . . . . . . . 20 144 7.1.4. Statistics: Mean, Variance, Skewness, Quanitle . . . . 20 145 7.1.5. Composition Functions: . . . . . . . . . . . . . . . . 21 146 7.1.6. Statement of Conjecture and Assumptions . . . . . . . 22 147 7.1.7. Justification of the Composition Function . . . . . . 22 148 7.1.8. Sources of Deviation from the Ground Truth . . . . . . 23 149 7.1.9. Specific cases where the conjecture might fail . . . . 23 150 7.1.10. Application of Measurement Methodology . . . . . . . . 23 151 8. Security Considerations . . . . . . . . . . . . . . . . . . . 23 152 8.1. Denial of Service Attacks . . . . . . . . . . . . . . . . 23 153 8.2. User Data Confidentiality . . . . . . . . . . . . . . . . 23 154 8.3. Interference with the metrics . . . . . . . . . . . . . . 24 155 9. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 24 156 10. Acknowlegements . . . . . . . . . . . . . . . . . . . . . . . 24 157 11. References . . . . . . . . . . . . . . . . . . . . . . . . . . 25 158 11.1. Normative References . . . . . . . . . . . . . . . . . . . 25 159 11.2. Informative References . . . . . . . . . . . . . . . . . . 25 160 Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 161 Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . . 26 163 1. Contributors 165 Thus far, the following people have contributed useful ideas, 166 suggestions, or the text of sections that have been incorporated into 167 this memo: 169 - Phil Chimento 171 - Reza Fardid 173 - Roman Krzanowski 175 - Maurizio Molina 177 - Lei Liang 179 - Dave Hoeflin 181 2. Introduction 183 The IPPM framework [RFC2330] describes two forms of metric 184 composition, spatial and temporal. The new composition framework 185 [RFC5835] expands and further qualifies these original forms into 186 three categories. This memo describes Spatial Composition, one of 187 the categories of metrics under the umbrella of the composition 188 framework. 190 Spatial composition encompasses the definition of performance metrics 191 that are applicable to a complete path, based on metrics collected on 192 various sub-paths. 194 The main purpose of this memo is to define the deterministic 195 functions that yield the complete path metrics using metrics of the 196 sub-paths. The effectiveness of such metrics is dependent on their 197 usefulness in analysis and applicability with practical measurement 198 methods. 200 The relationships may involve conjecture, and [RFC2330] lists four 201 points that the metric definitions should include: 203 o the specific conjecture applied to the metric and assumptions of 204 the statistical model of the process being measured (if any, see 205 [RFC2330] section 12), 207 o a justification of the practical utility of the composition in 208 terms of making accurate measurements of the metric on the path, 210 o a justification of the usefulness of the composition in terms of 211 making analysis of the path using A-frame concepts more effective, 212 and 214 o an analysis of how the conjecture could be incorrect. 216 Also, [RFC2330] gives an example using the conjecture that the delay 217 of a path is very nearly the sum of the delays of the exchanges and 218 clouds of the corresponding path digest. This example is 219 particularly relevant to those who wish to assess the performance of 220 an Inter-domain path without direct measurement, and the performance 221 estimate of the complete path is related to the measured results for 222 various sub-paths instead. 224 Approximate functions between the sub-path and complete path metrics 225 are useful, with knowledge of the circumstances where the 226 relationships are/are not applicable. For example, we would not 227 expect that delay singletons from each sub-path would sum to produce 228 an accurate estimate of a delay singleton for the complete path 229 (unless all the delays were essentially constant - very unlikely). 230 However, other delay statistics (based on a reasonable sample size) 231 may have a sufficiently large set of circumstances where they are 232 applicable. 234 2.1. Motivation 236 One-way metrics defined in other IPPM RFCs all assume that the 237 measurement can be practically carried out between the source and the 238 destination of interest. Sometimes there are reasons that the 239 measurement can not be executed from the source to the destination. 240 For instance, the measurement path may cross several independent 241 domains that have conflicting policies, measurement tools and 242 methods, and measurement time assignment. The solution then may be 243 the composition of several sub-path measurements. This means each 244 domain performs the One-way measurement on a sub path between two 245 nodes that are involved in the complete path following its own 246 policy, using its own measurement tools and methods, and using its 247 own measurement timing. Under the appropriate conditions, one can 248 combine the sub-path One-way metric results to estimate the complete 249 path One-way measurement metric with some degree of accuracy. 251 3. Scope and Application 252 3.1. Scope of work 254 For the primary IPPM metrics of Loss, Delay, and Delay Variation, 255 this memo gives a set of metrics that can be composed from the same 256 or similar sub-path metrics. This means that the composition 257 function may utilize: 259 o the same metric for each sub-path; 261 o multiple metrics for each sub-path (possibly one that is the same 262 as the complete path metric); 264 o a single sub-path metric that is different from the complete path 265 metric; 267 o different measurement techniques like active [RFC2330], [RFC3432] 268 and passive [RFC5474]. 270 We note a possibility: Using a complete path metric and all but one 271 sub-path metric to infer the performance of the missing sub-path, 272 especially when the "last" sub-path metric is missing. However, such 273 de-composition calculations, and the corresponding set of issues they 274 raise, are beyond the scope of this memo. 276 3.2. Application 278 The new composition framework [RFC5835] requires the specification of 279 the applicable circumstances for each metric. In particular, each 280 section addresses whether the metric: 282 Requires the same test packets to traverse all sub-paths, or may use 283 similar packets sent and collected separately in each sub-path. 285 Requires homogeneity of measurement methodologies, or can allow a 286 degree of flexibility (e.g., active or passive methods produce the 287 "same" metric). Also, the applicable sending streams will be 288 specified, such as Poisson, Periodic, or both. 290 Needs information or access that will only be available within an 291 operator's domain, or is applicable to Inter-domain composition. 293 Requires synchronized measurement time intervals in all sub-paths, or 294 largely overlapping, or no timing requirements. 296 Requires assumption of sub-path independence w.r.t. the metric being 297 defined/composed, or other assumptions. 299 Has known sources of inaccuracy/error, and identifies the sources. 301 3.3. Incomplete Information 303 In practice, when measurements cannot be initiated on a sub-path (and 304 perhaps the measurement system gives up during the test interval), 305 then there will not be a value for the sub-path reported, and the 306 entire test result SHOULD be recorded as "undefined". This case 307 should be distinguished from the case where the measurement system 308 continued to send packets throughout the test interval, but all were 309 declared lost. 311 When a composed metric requires measurements from sub paths A, B, and 312 C, and one or more of the sub-path results are undefined, then the 313 composed metric SHOULD also be recorded as undefined. 315 4. Common Specifications for Composed Metrics 317 To reduce the redundant information presented in the detailed metrics 318 sections that follow, this section presents the specifications that 319 are common to two or more metrics. The section is organized using 320 the same subsections as the individual metrics, to simplify 321 comparisons. 323 Also, the following index variables represent the following: 325 o m = index for packets sent 327 o n = index for packets received 329 o s = index for involved sub-paths 331 4.1. Name: Type-P 333 All metrics use the Type-P convention as described in [RFC2330]. The 334 rest of the name is unique to each metric. 336 4.1.1. Metric Parameters 338 o Src, the IP address of a host 340 o Dst, the IP address of a host 342 o T, a time (start of test interval) 344 o Tf, a time (end of test interval) 346 o lambda, a rate in reciprocal seconds (for Poisson Streams) 347 o incT, the nominal duration of inter-packet interval, first bit to 348 first bit (for Periodic Streams) 350 o T0, a time that MUST be selected at random from the interval [T, 351 T+dT] to start generating packets and taking measurements (for 352 Periodic Streams) 354 o TstampSrc, the wire time of the packet as measured at MP(Src) 356 o TstampDst, the wire time of the packet as measured at MP(Dst), 357 assigned to packets that arrive within a "reasonable" time. 359 o Tmax, a maximum waiting time for packets at the destination, set 360 sufficiently long to disambiguate packets with long delays from 361 packets that are discarded (lost), thus the distribution of delay 362 is not truncated. 364 o M, the total number of packets sent between T0 and Tf 366 o N, the total number of packets received at Dst (sent between T0 367 and Tf) 369 o S, the number of sub-paths involved in the complete Src-Dst path 371 o Type-P, as defined in [RFC2330], which includes any field that may 372 affect a packet's treatment as it traverses network 374 4.1.2. Definition and Metric Units 376 This section is unique for every metric. 378 4.1.3. Discussion and other details 380 This section is unique for every metric. 382 4.1.4. Statistic: 384 This section is unique for every metric. 386 4.1.5. Composition Function 388 This section is unique for every metric. 390 4.1.6. Statement of Conjecture and Assumptions 392 This section is unique for each metric. 394 4.1.7. Justification of the Composition Function 396 It is sometimes impractical to conduct active measurements between 397 every Src-Dst pair. Since the full mesh of N measurement points 398 grows as N x N, the scope of measurement may be limited by testing 399 resources. 401 There may be varying limitations on active testing in different parts 402 of the network. For example, it may not be possible to collect the 403 desired sample size in each test interval when access link speed is 404 limited, because of the potential for measurement traffic to degrade 405 the user traffic performance. The conditions on a low-speed access 406 link may be understood well-enough to permit use of a small sample 407 size/rate, while a larger sample size/rate may be used on other sub- 408 paths. 410 Also, since measurement operations have a real monetary cost, there 411 is value in re-using measurements where they are applicable, rather 412 than launching new measurements for every possible source-destination 413 pair. 415 4.1.8. Sources of Deviation from the Ground Truth 417 4.1.8.1. Sub-path List Differs from Complete Path 419 The measurement packets, each having source and destination addresses 420 intended for collection at edges of the sub-path, may take a 421 different specific path through the network equipment and links when 422 compared to packets with the source and destination addresses of the 423 complete path. Examples sources of parallel paths include Equal Cost 424 Multi-Path and parallel (or bundled) links. Therefore, the 425 performance estimated from the composition of sub-path measurements 426 may differ from the performance experienced by packets on the 427 complete path. Multiple measurements employing sufficient sub-path 428 address pairs might produce bounds on the extent of this error. 430 We also note the possibility of re-routing during a measurement 431 interval, as it may affect the correspondence between packets 432 traversing the complete path and the sub-paths that were "involved" 433 prior to the re-route. 435 4.1.8.2. Sub-path Contains Extra Network Elements 437 Related to the case of an alternate path described above is the case 438 where elements in the measured path are unique to measurement system 439 connectivity. For example, a measurement system may use a dedicated 440 link to a LAN switch, and packets on the complete path do not 441 traverse that link. The performance of such a dedicated link would 442 be measured continuously, and its contribution to the sub-path 443 metrics SHOULD be minimized as a source of error. 445 4.1.8.3. Sub-paths Have Incomplete Coverage 447 Measurements of sub-path performance may not cover all the network 448 elements on the complete path. For example, the network exchange 449 points might be excluded unless a cooperative measurement is 450 conducted. In this example, test packets on the previous sub-path 451 are received just before the exchange point and test packets on the 452 next sub-path are injected just after the same exchange point. 453 Clearly, the set of sub-path measurements SHOULD cover all critical 454 network elements in the complete path. 456 4.1.8.4. Absence of route 458 At a specific point in time, no viable route exists between the 459 complete path source and destination. The routes selected for one or 460 more sub-paths therefore differs from the complete path. 461 Consequently, spatial composition may produce finite estimation of a 462 ground truth metric between a source and a destination, even when the 463 route between them is undefined. 465 4.1.9. Specific cases where the conjecture might fail 467 This section is unique for most metrics (see the metric-specific 468 sections). 470 For delay-related metrics, One-way delay always depends on packet 471 size and link capacity, since it is measured in [RFC2679] from first 472 bit to last bit. If the size of an IP packet changes on route (due 473 to encapsulation), this can influence delay performance. However, 474 the main error source may be the additional processing associated 475 with encapsulation and encryption/decryption if not experienced or 476 accounted for in sub-path measurements. 478 Fragmentation is a major issue for composition accuracy, since all 479 metrics require all fragments to arrive before proceeding, and 480 fragmented complete path performance is likely to be different from 481 performance with non-fragmented packets and composed metrics based on 482 non-fragmented sub-path measurements. 484 Highly manipulated routing can cause measurement error if not 485 expected and compensated. For example, policy-based MPLS routing 486 could modify the class of service for the sub-paths and complete 487 path. 489 4.1.10. Application of Measurement Methodology 491 The methodology: 493 SHOULD use similar packets sent and collected separately in each sub- 494 path, where "similar" in this case means that the Type-P contains as 495 many equal attributes as possible, while recognizing that there will 496 be differences. Note that Type-P includes stream characteristics 497 (e.g., Poisson, Periodic). 499 Allows a degree of flexibility regarding test stream generation 500 (e.g., active or passive methods can produce an equivalent result, 501 but the lack of control over the source, timing and correlation of 502 passive measurements is much more challenging). 504 Poisson and/or Periodic streams are RECOMMENDED. 506 Applies to both Inter-domain and Intra-domain composition. 508 SHOULD have synchronized measurement time intervals in all sub-paths, 509 but largely overlapping intervals MAY suffice. 511 REQUIRES assumption of sub-path independence w.r.t. the metric being 512 defined/composed. 514 5. One-way Delay Composed Metrics and Statistics 516 5.1. Name: Type-P-Finite-One-way-Delay-Poisson/Periodic-Stream 518 This metric is a necessary element of Delay Composition metrics, and 519 its definition does not formally exist elsewhere in IPPM literature. 521 5.1.1. Metric Parameters 523 See the common parameters section above. 525 5.1.2. Definition and Metric Units 527 Using the parameters above, we obtain the value of Type-P-One-way- 528 Delay singleton as per [RFC2679]. 530 For each packet [i] that has a finite One-way Delay (in other words, 531 excluding packets which have undefined one-way delay): 533 Type-P-Finite-One-way-Delay-Poisson/Periodic-Stream[i] = 535 FiniteDelay[i] = TstampDst - TstampSrc 536 The units of measure for this metric are time in seconds, expressed 537 in sufficiently low resolution to convey meaningful quantitative 538 information. For example, resolution of microseconds is usually 539 sufficient. 541 5.1.3. Discussion and other details 543 The "Type-P-Finite-One-way-Delay" metric permits calculation of the 544 sample mean statistic. This resolves the problem of including lost 545 packets in the sample (whose delay is undefined), and the issue with 546 the informal assignment of infinite delay to lost packets (practical 547 systems can only assign some very large value). 549 The Finite-One-way-Delay approach handles the problem of lost packets 550 by reducing the event space. We consider conditional statistics, and 551 estimate the mean one-way delay conditioned on the event that all 552 packets in the sample arrive at the destination (within the specified 553 waiting time, Tmax). This offers a way to make some valid statements 554 about one-way delay, and at the same time avoiding events with 555 undefined outcomes. This approach is derived from the treatment of 556 lost packets in [RFC3393], and is similar to [Y.1540] . 558 5.1.4. Statistic: 560 All statistics defined in [RFC2679] are applicable to the finite one- 561 way delay,and additional metrics are possible, such as the mean (see 562 below). 564 5.2. Name: Type-P-Finite-Composite-One-way-Delay-Mean 566 This section describes a statistic based on the Type-P-Finite-One- 567 way-Delay-Poisson/Periodic-Stream metric. 569 5.2.1. Metric Parameters 571 See the common parameters section above. 573 5.2.2. Definition and Metric Units of the Mean Statistic 575 We define 576 Type-P-Finite-One-way-Delay-Mean = 577 N 578 --- 579 1 \ 580 MeanDelay = - * > (FiniteDelay [n]) 581 N / 582 --- 583 n = 1 585 where all packets n= 1 through N have finite singleton delays. 587 The units of measure for this metric are time in seconds, expressed 588 in sufficiently fine resolution to convey meaningful quantitative 589 information. For example, resolution of microseconds is usually 590 sufficient. 592 5.2.3. Discussion and other details 594 The Type-P-Finite-One-way-Delay-Mean metric requires the conditional 595 delay distribution described in section 5.1. 597 5.2.4. Statistic: 599 This metric, a mean, does not require additional statistics. 601 5.2.5. Composition Function: Sum of Means 603 The Type-P-Finite--Composite-One-way-Delay-Mean, or CompMeanDelay, 604 for the complete Source to Destination path can be calculated from 605 sum of the Mean Delays of all its S constituent sub-paths. 607 Then the 609 Type-P-Finite-Composite-One-way-Delay-Mean = 610 S 611 --- 612 \ 613 CompMeanDelay = > (MeanDelay [s]) 614 / 615 --- 616 s = 1 617 where sub-paths s = 1 to S are involved in the complete path. 619 5.2.6. Statement of Conjecture and Assumptions 621 The mean of a sufficiently large stream of packets measured on each 622 sub-path during the interval [T, Tf] will be representative of the 623 ground truth mean of the delay distribution (and the distributions 624 themselves are sufficiently independent), such that the means may be 625 added to produce an estimate of the complete path mean delay. 627 It is assumed that the one-way delay distributions of the sub-paths 628 and the complete path are continuous. The mean of multi-modal 629 distributions have the unfortunate property that such a value may 630 never occur. 632 5.2.7. Justification of the Composition Function 634 See the common section. 636 5.2.8. Sources of Deviation from the Ground Truth 638 See the common section. 640 5.2.9. Specific cases where the conjecture might fail 642 If any of the sub-path distributions are multi-modal, then the 643 measured means may not be stable, and in this case the mean will not 644 be a particularly useful statistic when describing the delay 645 distribution of the complete path. 647 The mean may not be sufficiently robust statistic to produce a 648 reliable estimate, or to be useful even if it can be measured. 650 If a link contributing non-negligible delay is erroneously included 651 or excluded, the composition will be in error. 653 5.2.10. Application of Measurement Methodology 655 The requirements of the common section apply here as well. 657 5.3. Name: Type-P-Finite-Composite-One-way-Delay-Minimum 659 This section describes is a statistic based on the Type-P-Finite-One- 660 way-Delay-Poisson/Periodic-Stream metric, and the composed metric 661 based on that statistic. 663 5.3.1. Metric Parameters 665 See the common parameters section above. 667 5.3.2. Definition and Metric Units of the Minimum Statistic 669 We define 670 Type-P-Finite-One-way-Delay-Minimum = 671 = MinDelay = (FiniteDelay [j]) 673 such that for some index, j, where 1<= j <= N 674 FiniteDelay[j] <= FiniteDelay[n] for all n 676 where all packets n = 1 through N have finite singleton delays. 678 The units of measure for this metric are time in seconds, expressed 679 in sufficiently fine resolution to convey meaningful quantitative 680 information. For example, resolution of microseconds is usually 681 sufficient. 683 5.3.3. Discussion and other details 685 The Type-P-Finite-One-way-Delay-Minimum metric requires the 686 conditional delay distribution described in section 5.1.3. 688 5.3.4. Statistic: 690 This metric, a minimum, does not require additional statistics. 692 5.3.5. Composition Function: Sum of Minima 694 The Type-P-Finite--Composite-One-way-Delay-Minimum, or CompMinDelay, 695 for the complete Source to Destination path can be calculated from 696 sum of the Minimum Delays of all its S constituent sub-paths. 698 Then the 700 Type-P-Finite-Composite-One-way-Delay-Minimum = 701 S 702 --- 703 \ 704 CompMinDelay = > (MinDelay [s]) 705 / 706 --- 707 s = 1 709 5.3.6. Statement of Conjecture and Assumptions 711 The minimum of a sufficiently large stream of packets measured on 712 each sub-path during the interval [T, Tf] will be representative of 713 the ground truth minimum of the delay distribution (and the 714 distributions themselves are sufficiently independent), such that the 715 minima may be added to produce an estimate of the complete path 716 minimum delay. 718 It is assumed that the one-way delay distributions of the sub-paths 719 and the complete path are continuous. 721 5.3.7. Justification of the Composition Function 723 See the common section. 725 5.3.8. Sources of Deviation from the Ground Truth 727 See the common section. 729 5.3.9. Specific cases where the conjecture might fail 731 If the routing on any of the sub-paths is not stable, then the 732 measured minimum may not be stable. In this case the composite 733 minimum would tend to produce an estimate for the complete path that 734 may be too low for the current path. 736 5.3.10. Application of Measurement Methodology 738 The requirements of the common section apply here as well. 740 6. Loss Metrics and Statistics 742 6.1. Type-P-Composite-One-way-Packet-Loss-Empirical-Probability 744 6.1.1. Metric Parameters: 746 Same as section 4.1.1. 748 6.1.2. Definition and Metric Units 750 Using the parameters above, we obtain the value of Type-P-One-way- 751 Packet-Loss singleton and stream as per [RFC2680]. 753 We obtain a sequence of pairs with elements as follows: 755 o TstampSrc, as above 757 o L, either zero or one, where L=1 indicates loss and L=0 indicates 758 arrival at the destination within TstampSrc + Tmax. 760 6.1.3. Discussion and other details 761 6.1.4. Statistic: Type-P-One-way-Packet-Loss-Empirical-Probability 763 Given the stream parameter M, the number of packets sent, we can 764 define the Empirical Probability of Loss Statistic (Ep), consistent 765 with Average Loss in [RFC2680], as follows: 767 Type-P-One-way-Packet-Loss-Empirical-Probability = 768 M 769 --- 770 1 \ 771 Ep = - * > (L[m]) 772 M / 773 --- 774 m = 1 776 where all packets m = 1 through M have a value for L. 778 6.1.5. Composition Function: Composition of Empirical Probabilities 780 The Type-P-One-way-Composite-Packet-Loss-Empirical-Probability, or 781 CompEp for the complete Source to Destination path can be calculated 782 by combining Ep of all its constituent sub-paths (Ep1, Ep2, Ep3, ... 783 Epn) as 785 Type-P-Composite-One-way-Packet-Loss-Empirical-Probability = 786 CompEp = 1 - {(1 - Ep1) x (1 - Ep2) x (1 - Ep3) x ... x (1 - EpS)} 788 If any Eps is undefined in a particular measurement interval, 789 possibly because a measurement system failed to report a value, then 790 any CompEp that uses sub-path s for that measurement interval is 791 undefined. 793 6.1.6. Statement of Conjecture and Assumptions 795 The empirical probability of loss calculated on a sufficiently large 796 stream of packets measured on each sub-path during the interval [T, 797 Tf] will be representative of the ground truth empirical loss 798 probability (and the probabilities themselves are sufficiently 799 independent), such that the sub-path probabilities may be combined to 800 produce an estimate of the complete path empirical loss probability. 802 6.1.7. Justification of the Composition Function 804 See the common section. 806 6.1.8. Sources of Deviation from the Ground Truth 808 See the common section. 810 6.1.9. Specific cases where the conjecture might fail 812 A concern for loss measurements combined in this way is that root 813 causes may be correlated to some degree. 815 For example, if the links of different networks follow the same 816 physical route, then a single catastrophic event like a fire in a 817 tunnel could cause an outage or congestion on remaining paths in 818 multiple networks. Here it is important to ensure that measurements 819 before the event and after the event are not combined to estimate the 820 composite performance. 822 Or, when traffic volumes rise due to the rapid spread of an email- 823 born worm, loss due to queue overflow in one network may help another 824 network to carry its traffic without loss. 826 6.1.10. Application of Measurement Methodology 828 See the common section. 830 7. Delay Variation Metrics and Statistics 832 7.1. Name: Type-P-One-way-pdv-refmin-Poisson/Periodic-Stream 834 This packet delay variation (PDV) metric is a necessary element of 835 Composed Delay Variation metrics, and its definition does not 836 formally exist elsewhere in IPPM literature. 838 7.1.1. Metric Parameters: 840 In addition to the parameters of section 4.1.1: 842 o TstampSrc[i], the wire time of packet[i] as measured at MP(Src) 843 (measurement point at the source) 845 o TstampDst[i], the wire time of packet[i] as measured at MP(Dst), 846 assigned to packets that arrive within a "reasonable" time. 848 o B, a packet length in bits 850 o F, a selection function unambiguously defining the packets from 851 the stream that are selected for the packet-pair computation of 852 this metric. F(current packet), the first packet of the pair, 853 MUST have a valid Type-P-Finite-One-way-Delay less than Tmax (in 854 other words, excluding packets which have undefined one-way delay) 855 and MUST have been transmitted during the interval T, Tf. The 856 second packet in the pair, F(min_delay packet) MUST be the packet 857 with the minimum valid value of Type-P-Finite-One-way-Delay for 858 the stream, in addition to the criteria for F(current packet). If 859 multiple packets have equal minimum Type-P-Finite-One-way-Delay 860 values, then the value for the earliest arriving packet SHOULD be 861 used. 863 o MinDelay, the Type-P-Finite-One-way-Delay value for F(min_delay 864 packet) given above. 866 o N, the number of packets received at the Destination meeting the 867 F(current packet) criteria. 869 7.1.2. Definition and Metric Units 871 Using the definition above in section 5.1.2, we obtain the value of 872 Type-P-Finite-One-way-Delay-Poisson/Periodic-Stream[n], the singleton 873 for each packet[i] in the stream (a.k.a. FiniteDelay[i]). 875 For each packet[n] that meets the F(first packet) criteria given 876 above: Type-P-One-way-pdv-refmin-Poisson/Periodic-Stream[n] = 878 PDV[n] = FiniteDelay[n] - MinDelay 880 where PDV[i] is in units of time in seconds, expressed in 881 sufficiently fine resolution to convey meaningful quantitative 882 information. For example, resolution of microseconds is usually 883 sufficient. 885 7.1.3. Discussion and other details 887 This metric produces a sample of delay variation normalized to the 888 minimum delay of the sample. The resulting delay variation 889 distribution is independent of the sending sequence (although 890 specific FiniteDelay values within the distribution may be 891 correlated, depending on various stream parameters such as packet 892 spacing). This metric is equivalent to the IP Packet Delay Variation 893 parameter defined in [Y.1540]. 895 7.1.4. Statistics: Mean, Variance, Skewness, Quanitle 897 We define the mean PDV as follows (where all packets n = 1 through N 898 have a value for PDV[n]): 900 Type-P-One-way-pdv-refmin-Mean = MeanPDV = 901 N 902 --- 903 1 \ 904 - * > (PDV[n]) 905 N / 906 --- 907 n = 1 909 We define the variance of PDV as follows: 911 Type-P-One-way-pdv-refmin-Variance = VarPDV = 912 N 913 --- 914 1 \ 2 915 ------- > (PDV[n] - MeanPDV) 916 (N - 1) / 917 --- 918 n = 1 920 We define the skewness of PDV as follows: 922 Type-P-One-way-pdv-refmin-Skewness = SkewPDV = 923 N 924 --- 3 925 \ / \ 926 > | PDV[n]- MeanPDV | 927 / \ / 928 --- 929 n = 1 930 ----------------------------------- 931 / \ 932 | ( 3/2 ) | 933 \ (N - 1) * VarPDV / 935 We define the Quantile of the PDVRefMin sample as the value where the 936 specified fraction of singletons is less than the given value. 938 7.1.5. Composition Functions: 940 This section gives two alternative composition functions. The 941 objective is to estimate a quantile of the complete path delay 942 variation distribution. The composed quantile will be estimated 943 using information from the sub-path delay variation distributions. 945 7.1.5.1. Approximate Convolution 947 The Type-P-Finite-One-way-Delay-Poisson/Periodic-Stream samples from 948 each sub-path are summarized as a histogram with 1 ms bins 949 representing the one-way delay distribution. 951 From [Stats], the distribution of the sum of independent random 952 variables can be derived using the relation: 954 Type-P-Composite-One-way-pdv-refmin-quantile-a = 955 / / 956 P(X + Y + Z <= a) = | | P(X <= a-y-z) * P(Y = y) * P(Z = z) dy dz 957 / / 958 z y 959 where X, Y, and Z are random variables representing the delay 960 variation distributions of the sub-paths of the complete path (in 961 this case, there are three sub-paths), and a is the quantile of 962 interest. Note dy and dz indicate partial integration here.This 963 relation can be used to compose a quantile of interest for the 964 complete path from the sub-path delay distributions. The histograms 965 with 1 ms bins are discrete approximations of the delay 966 distributions. 968 7.1.5.2. Normal Power Approximation 970 Type-P-One-way-Composite-pdv-refmin-NPA for the complete Source to 971 Destination path can be calculated by combining statistics of all the 972 constituent sub-paths in the process described in [Y.1541] clause 8 973 and Appendix X. 975 7.1.6. Statement of Conjecture and Assumptions 977 The delay distribution of a sufficiently large stream of packets 978 measured on each sub-path during the interval [T, Tf] will be 979 sufficiently stationary and the sub-path distributions themselves are 980 sufficiently independent, so that summary information describing the 981 sub-path distributions can be combined to estimate the delay 982 distribution of complete path. 984 It is assumed that the one-way delay distributions of the sub-paths 985 and the complete path are continuous. 987 7.1.7. Justification of the Composition Function 989 See the common section. 991 7.1.8. Sources of Deviation from the Ground Truth 993 In addition to the common deviations, a few additional sources exist 994 here. For one, very tight distributions with range on the order of a 995 few milliseconds are not accurately represented by a histogram with 1 996 ms bins. This size was chosen assuming an implicit requirement on 997 accuracy: errors of a few milliseconds are acceptable when assessing 998 a composed distribution quantile. 1000 Also, summary statistics cannot describe the subtleties of an 1001 empirical distribution exactly, especially when the distribution is 1002 very different from a classical form. Any procedure that uses these 1003 statistics alone may incur error. 1005 7.1.9. Specific cases where the conjecture might fail 1007 If the delay distributions of the sub-paths are somehow correlated, 1008 then neither of these composition functions will be reliable 1009 estimators of the complete path distribution. 1011 In practice, sub-path delay distributions with extreme outliers have 1012 increased the error of the composed metric estimate. 1014 7.1.10. Application of Measurement Methodology 1016 See the common section. 1018 8. Security Considerations 1020 8.1. Denial of Service Attacks 1022 This metric requires a stream of packets sent from one host (source) 1023 to another host (destination) through intervening networks. This 1024 method could be abused for denial of service attacks directed at 1025 destination and/or the intervening network(s). 1027 Administrators of source, destination, and the intervening network(s) 1028 should establish bilateral or multi-lateral agreements regarding the 1029 timing, size, and frequency of collection of sample metrics. Use of 1030 this method in excess of the terms agreed between the participants 1031 may be cause for immediate rejection or discard of packets or other 1032 escalation procedures defined between the affected parties. 1034 8.2. User Data Confidentiality 1036 Active use of this method generates packets for a sample, rather than 1037 taking samples based on user data, and does not threaten user data 1038 confidentiality. Passive measurement must restrict attention to the 1039 headers of interest. Since user payloads may be temporarily stored 1040 for length analysis, suitable precautions MUST be taken to keep this 1041 information safe and confidential. In most cases, a hashing function 1042 will produce a value suitable for payload comparisons. 1044 8.3. Interference with the metrics 1046 It may be possible to identify that a certain packet or stream of 1047 packets is part of a sample. With that knowledge at the destination 1048 and/or the intervening networks, it is possible to change the 1049 processing of the packets (e.g. increasing or decreasing delay) that 1050 may distort the measured performance. It may also be possible to 1051 generate additional packets that appear to be part of the sample 1052 metric. These additional packets are likely to perturb the results 1053 of the sample measurement. 1055 To discourage the kind of interference mentioned above, packet 1056 interference checks, such as cryptographic hash, may be used. 1058 9. IANA Considerations 1060 Metrics defined in IETF are typically registered in the IANA IPPM 1061 METRICS REGISTRY as described in initial version of the registry 1062 [RFC4148]. However, areas for improvement of this registry have been 1063 identified, and the registry structure has to be revisited when there 1064 is consensus to do so. 1066 Therefore, the metrics in this draft may be considered for 1067 registration in the future, and no IANA Action is requested at this 1068 time. 1070 10. Acknowlegements 1072 A long time ago, in a galaxy far, far away (Minneapolis), Will Leland 1073 suggested the simple and elegant Type-P-Finite-One-way-Delay concept. 1074 Thanks Will. 1076 Yaakov Stein and Donald McLachlan also provided useful comments along 1077 the way. 1079 11. References 1080 11.1. Normative References 1082 [RFC2119] Bradner, S., "Key words for use in RFCs to Indicate 1083 Requirement Levels", BCP 14, RFC 2119, March 1997. 1085 [RFC2330] Paxson, V., Almes, G., Mahdavi, J., and M. Mathis, 1086 "Framework for IP Performance Metrics", RFC 2330, 1087 May 1998. 1089 [RFC2679] Almes, G., Kalidindi, S., and M. Zekauskas, "A One-way 1090 Delay Metric for IPPM", RFC 2679, September 1999. 1092 [RFC2680] Almes, G., Kalidindi, S., and M. Zekauskas, "A One-way 1093 Packet Loss Metric for IPPM", RFC 2680, September 1999. 1095 [RFC3393] Demichelis, C. and P. Chimento, "IP Packet Delay Variation 1096 Metric for IP Performance Metrics (IPPM)", RFC 3393, 1097 November 2002. 1099 [RFC3432] Raisanen, V., Grotefeld, G., and A. Morton, "Network 1100 performance measurement with periodic streams", RFC 3432, 1101 November 2002. 1103 [RFC4148] Stephan, E., "IP Performance Metrics (IPPM) Metrics 1104 Registry", BCP 108, RFC 4148, August 2005. 1106 [RFC5835] Morton, A. and S. Van den Berghe, "Framework for Metric 1107 Composition", RFC 5835, April 2010. 1109 11.2. Informative References 1111 [RFC5474] Duffield, N., Chiou, D., Claise, B., Greenberg, A., 1112 Grossglauser, M., and J. Rexford, "A Framework for Packet 1113 Selection and Reporting", RFC 5474, March 2009. 1115 [RFC5644] Stephan, E., Liang, L., and A. Morton, "IP Performance 1116 Metrics (IPPM): Spatial and Multicast", RFC 5644, 1117 October 2009. 1119 [Stats] McGraw-Hill NY NY, "Introduction to the Theory of 1120 Statistics, 3rd Edition,", 1974. 1122 [Y.1540] ITU-T Recommendation Y.1540, "Internet protocol data 1123 communication service - IP packet transfer and 1124 availability performance parameters", November 2007. 1126 [Y.1541] ITU-T Recommendation Y.1541, "Network Performance 1127 Objectives for IP-based Services", February 2006. 1129 Index 1131 ? 1132 ??? 14 1134 Authors' Addresses 1136 Al Morton 1137 AT&T Labs 1138 200 Laurel Avenue South 1139 Middletown,, NJ 07748 1140 USA 1142 Phone: +1 732 420 1571 1143 Fax: +1 732 368 1192 1144 Email: acmorton@att.com 1145 URI: http://home.comcast.net/~acmacm/ 1147 Emile Stephan 1148 France Telecom Division R&D 1149 2 avenue Pierre Marzin 1150 Lannion, F-22307 1151 France 1153 Phone: 1154 Fax: +33 2 96 05 18 52 1155 Email: emile.stephan@orange-ftgroup.com 1156 URI: