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Internet Drafts are working doc- 12 uments of the Internet Engineering Task Force (IETF), its areas, and 13 its working groups. Note that other groups may also distribute work- 14 ing documents as Internet Drafts. 16 Internet Drafts are draft documents valid for a maximum of six 17 months, and may be updated, replaced, or obsoleted by other documents 18 at any time. It is inappropriate to use Internet Drafts as reference 19 material or to cite them other than as ``work in progress''. 21 To learn the current status of any Internet Draft, please check the 22 ``1id-abstracts.txt'' listing contained in the Internet Drafts shadow 23 directories on ftp.is.co.za (Africa), nic.nordu.net (Europe), 24 munnari.oz.au (Pacific Rim), ds.internic.net (US East Coast), or 25 ftp.isi.edu (US West Coast). 27 This memo provides information for the Internet community. This memo 28 does not specify an Internet standard of any kind. Distribution of 29 this memo is unlimited. 31 2. Abstract 33 This memo refers to a metric for variation in delay of packets across 34 Internet paths. The metric is based on statistics of the difference 35 in One-Way-Delay of consecutive packets. This particular definition 36 of variation is called "Instantaneous Packet Delay Variation (ipdv)". 38 The metric is valid for measurements between two hosts both in the 39 case that they have synchronized clocks and in the case that they are 40 not synchronized. In the second case it allows an evaluation of the 41 reciprocal skew. Measurements performed on both directions (Two-ways 42 measurements) allow a better estimation of clock differences. The 43 precision that can be obtained is evaluated. 45 I-D Ipdv Metric November 1998 47 3. Introduction 49 This memo takes as a reference the Draft-ietf "One-Way-Delay metric for 50 IPPM" that it is supposed to be known. Part of the text in this memo is 51 directly taken from that Draft. 53 This memo defines a metric for variation in delay of packets that flow 54 from one host to another one through an IP path. Since the metric is 55 related to a variation, different definitions are possible according 56 to what the variation is measured against. 58 NOTE: The terminology used in this Draft will be re-visited as soon as 59 a terminology document will be available. 60 So far the following is considered: 61 - The term Jitter is derived from the well known definition given for 62 transmission of electrical pulses associated to a clock, and it seems 63 to be able to describe variations with respect to an expected arrival 64 time. 65 - Each entity adopted as a reference for variation measurements defines 66 a specific metric. Each metric describes a specific aspect or effect 67 of the behavior of the System Under Test (SUT). 68 - Among entities that can be adopted, as an example, it is possible to 69 consider a reference delay for the path, a reference delay for the Src 70 Dst pair, the Mean One-Way-Delay over a period of interest, the Delay 71 variation that can be derived considering the difference between the 72 actual and the expected arrival time, the difference between the 73 delay of a packet and the last measured similar delay. 75 3.1. Definition 77 A definition of the Instantaneous Packet Delay Variation (ipdv) can be 78 given for a pair of packets or for a packet inside a stream of packets. 80 For a pair of packets: 81 - The ipdv of a pair of IP packets, that are transmitted from the measu- 82 rement point MP1 to the measurement point MP2, is the difference 83 between the One-Way-Delay measured for the second packet and the One- 84 Way-Delay measured for the first packet of the pair. 86 For a stream of packets: 87 - The Instantaneous Packet Delay Variation of an IP packet, inside a 88 stream of packets, going from the measurement point MP1 to the measu- 89 rement point MP2, is the difference of the One-Way-Delay of that 90 packet and the One-Way-Delay of the preceding packet in the stream. 92 I-D Ipdv Metric November 1998 94 3.2. Motivation 96 A number of services that can be supported by IP are sensitive to the 97 regular delivery of packets and can be disturbed by instantaneous va- 98 riations in delay, while they are not disturbed by slow variations, 99 that can last a relatively long time. A specific metric for quick va- 100 riations is therefore desirable. Metrics that can be derived from the 101 analysis of statistics of ipdv can also be used, for example, for 102 buffer dimensioning, but this memo is not intended in that sense. 103 The scope of this metric is to provide a way for measurement of the 104 quality delivered by a path. 106 In addition, this type of metric is particularly robust with respect 107 differences and variations of the clocks of the two hosts. This allow 108 the use of the metric even if the two hosts that support the measure- 109 -ment points are not synchronized. In the latter case indications on 110 reciprocal skew of the clocks can be derived from the measurement and 111 corrections are possible. The related precision is often comparable 112 with the one that can be achieved with synchronized clocks, being of 113 the same order of magnitude of synchronization errors. This will 114 be discussed below. 116 3.3. General Issues Regarding Time 118 All what is contained in the paragraph 2.2. of the Draft ippm on One- 119 Way Delay metric (2.2. General Issues Regarding Time) applies also in 120 this case. 122 In addition, it is here considered that the reciprocal skew of the two 123 clocks can be decomposed into two parts: 124 * A fixed one, called in this context "skew", given, for example, by 125 tolerances in physical dimensions of crystals. 126 * A variable one, called in this context "drift", given, for example, 127 by changes in temperature or other conditions of operation. 128 Both of this components are part of the term "skew" as defined in the 129 referenced Draft and in the Framework document. 131 NOTE: The drift of a clock, as it is above defined over a long period 132 must have an average value that tends to zero while the period becomes 133 large since the frequency of the clock has a finite (and little) 134 range. In order to underline the order of magnitude of this effect,it 135 is considered that the maximum range of drift for commercial crystals 136 is about 50 part per million (ppm). Since it is mainly connected with 137 variations in operating temperature (from 0 to 70 degrees Celsius), it 138 is expected that a host will have a nearly constant temperature during 139 its operation period, and variations in temperature, even if quick, 140 could be less than one Celsius per second, and range in the order of 142 I-D Ipdv Metric November 1998 144 few degrees. The total range of the drift is usually related to varia- 145 -tions from 0 to 70 Celsius. These are important points for evaluation 146 of precision of ipdv measurements, as it will see below. 148 4. Structure of this memo 150 The metric will be defined as applicable to a stream of packets that 151 flow from a source host to a destination host (one-way ipdv). The ini- 152 tial assumption is that source and destination hosts have synchronized 153 clocks. 154 The definition of a singleton of one-way ipdv metric is first consi- 155 -dered, and then a definition of samples for ipdv will be given. 157 Then the case of application to not synchronized hosts will be dis- 158 cussed, and the precision will be compared with the one of the previous 159 case. 161 A bidirectional ipdv metric will be defined, as well as the methodology 162 for error corrections. This will not be a two-ways metric, but a 163 "paired" one-way in opposite directions. Some statistics describing the 164 IP path's behavior will be proposed. 166 In the Appendix A a more detailed analysis is reported of the ipdv 167 theory and of the characteristics of ipdv distribution. 169 5. A singleton definition of a One-way ipdv metric 171 This definition makes use of the corresponding definition of type-P- 172 One-Way-Delay, that is supposed to be known. This section makes use 173 of those parts of the One-Way-Delay Draft that directly apply to the 174 One-Way-ipdv metric, or makes direct references to that Draft. 176 5.1. Metric name 178 Type-P-One-way-ipdv 180 5.2. Metric parameters 182 + Scr, the IP address of a host 183 + Dst, the IP address of a host 184 + T1, a time 185 + T2, a time. It is explicitly noted that also the difference T2-T1 186 is a parameter of the measurement though this is already implicit, 187 since the times T1 and T2 exactly define the time conditions in which 188 the measurement takes place. 190 I-D Ipdv Metric November 1998 192 + Path, the path from Src to Dst; in cases where there is only one 193 path from Src to Dst, this optional parameter can be omitted. 194 {Comment: the presence of path is motivated by cases such as with 195 Merit's NetNow setup, in which a Src on one NAP can reach a Dst on 196 another NAP by either of several different backbone networks. 197 Generally, this optional parameter is useful only when several dif- 198 -ferent routes are possible from Src to Dst. Using the loose source 199 route IP option is avoided since it would often artificially worsen 200 the performance observed, and since it might not be supported along 201 some paths.} 203 5.2. Metric unit 205 The value of a Type-P-One-way-ipdv is either a real number of seconds 206 (positive, zero or negative) or an undefined number of seconds. 208 5.3. Definition 210 Type-P-One-way-ipdv is defined for two (consecutive) packets from Src 211 to Dst, as the difference between the value of the type-P-One-way- 212 delay from Src to Dst at T2 [via path] and the value of the type-P- 213 One-Way-Delay from Src to Dst at T1 [via path]. T1 is the wire-time 214 at which Scr sent the first bit of the first packet, and T2 is the 215 wire-time at which Src sent the first bit of the second packet. This 216 metric is therefore ideally derived from the One-Way-Delay metric. 218 NOTE: The requirement of "consecutive" packets is not essential. The 219 measured value is anyway the difference in One-Way-Delay at the 220 times T1 and T2, which is meaningful by itself, as long as the 221 times T1 and T2 are such to describe the investigated charac- 222 -teristics. These times will be better defined later. 224 Therefore, for a real number ddT "The type-P-one-way-ipdv from Src to 225 Dst at T1, T2 [via path] is ddT" means that Src sent two consecutive 226 packets whose the first at wire-time T1 (first bit), and the second 227 wire-time T2 (first bit) and the packets were received by Dst at wire 228 -time dT1+T1 (last bit of the first packet), and, respectively, at 229 wire-time dT2+T2 (last bit of the second packet), and that dT2-dT1=ddT. 231 "The type-P-one-way-ipdv from Src to Dst at T1,T2 [via path] is unde- 232 fined" means that Src sent the first bit of a packet at T1 and the 233 first bit of a second packet at T2 and that Dst did not receive one 234 or both packets. 236 I-D Ipdv Metric November 1998 238 5.4. Discussion 240 Type-P-One-way-ipdv is a metric that makes use of the same measurement 241 methods provided for delay metrics. 243 The following practical issues have to be considered: 244 + Being a differential measurement, this metric is less sensitive 245 to clock synchronization problems. This issue will be more 246 carefully examined in section 6. of this memo. It is pointed 247 out that, if the reciprocal clock conditions change in time, 248 the accuracy of the measurement will depend on the time inter- 249 -val T2-T1 and the amount of possible errors will be discussed 250 below. 251 + A given methodology will have to include a way to determine whether a 252 delay value is infinite or whether it is merely very large (and 253 the packet is yet to arrive at Dst). 254 As noted by Mahdavi and Paxson, simple upper bounds (such as the 255 255 seconds theoretical upper bound on the lifetimes of IP 256 packets [Postel: RFC 791]) could be used, but good engineering, 257 including an understanding of packet lifetimes, will be nee- 258 -ded in practice. {Comment: Note that, for many applications of 259 these metrics, the harm in treating a large delay as infinite 260 might be zero or very small. A TCP data packet, for example, 261 that arrives only after several multiples of the RTT may as well 262 have been lost.} 263 + Usually a path is such that if the first packet is largely delayed, 264 it can "stop" the second packet of the pair and vary its delay. 265 This is not a problem for the definition since is, in any case, 266 part of the description of the path's behavior. 267 + As with other 'type-P' metrics, the value of the metric may de- 268 -pend on such properties of the packet as protocol,(UDP or TCP) 269 port number, size, and arrangement for special treatment (as 270 with IP precedence or with RSVP). 271 + If the packet is duplicated along the path (or paths!) so that 272 multiple non-corrupt copies arrive at the destination, then the 273 packet is counted as received, and the first copy to arrive 274 determines the packet's One-Way-Delay. 275 + If the packet is fragmented and if, for whatever reason, reas- 276 -sembly does not occur, then the packet will be deemed lost. 278 5.5. Methodologies 280 As with other Type-P-* metrics, the detailed methodology will depend 281 on the Type-P (e.g., protocol number, UDP/TCP port number, size, 282 precedence). 284 I-D Ipdv Metric November 1998 286 Generally, for a given Type-P, the methodology would proceed as fol- 287 lows: 289 + The need of synchronized clocks for Src and Dst will be discus- 290 -sed later. Here a methodology is supposed that is based on 291 synchronized clocks. 292 + At the Src host, select Src and Dst IP addresses, and form two 293 test packets of Type-P with these addresses. Any 'padding' por- 294 -tion of the packet needed only to make the test packet a given 295 size should be filled with randomized bits to avoid a situation 296 in which the measured delay is lower than it would otherwise 297 be due to compression techniques along the path. 298 + Optionally, select a specific path and arrange for Src to send 299 the packets to that path. {Comment: This could be done, for 300 example, by installing a temporary host-route for Dst in Src's 301 routing table.} 302 + At the Dst host, arrange to receive the packets. 303 + At the Src host, place a timestamp in the prepared first 304 Type-P packet, and send it towards Dst [via path]. 305 + If the packet arrives within a reasonable period of time, take a 306 timestamp as soon as possible upon the receipt of the packet. By 307 subtracting the two timestamps, an estimate of One-Way-Delay can 308 be computed. 309 + Record this first delay value. 310 + At the Src host, place a timestamp in the prepared second 311 Type-P packet, and send it towards Dst [via path]. 312 + If the packet arrives within a reasonable period of time, take a 313 timestamp as soon as possible upon the receipt of the packet. By 314 subtracting the two timestamps, an estimate of One-Way-Delay can 315 be computed. 316 + By subtracting the second value of One-Way-Delay from the first value 317 the ipdv value of the pair of packets is obtained. 318 + If one or both packets fail to arrive within a reasonable period 319 of time, the ipdv is taken to be undefined. 321 5.6. Errors and Uncertainties 323 In the singleton metric of ipdv, factors that affect the measurement 324 are the same that can affect the One-Way-Delay measurement, even if, 325 in this case, the influence is different. 327 The Framework document provides general guidance on this point, but 328 we note here the following specifics related to delay metrics: 329 + Errors/uncertainties due to uncertainties in the clocks of the 330 Src and Dst hosts. 331 + Errors/uncertainties due to the difference between 'wire time' 332 and 'host time'. 334 I-D Ipdv Metric November 1998 336 Each of these type of errors are discussed in more detail in the next 337 paragraphs. 339 5.6.1. Errors/Uncertainties related to Clocks 341 If, as a first approximation, the error that affects the first measu- 342 rement of One-Way-Delay were the same of the one affecting the second 343 measurement, they will cancel each other when calculating ipdv. The 344 residual error related to clocks is the difference of the said errors 345 that are supposed to change from the time T1, at which the first 346 measurement is performed, to the time T2 at which the second measure- 348 ment is performed. Synchronization, skew, accuracy and resolution are 349 here considered with the following notes: 350 + Errors in synchronization between source and destination clocks 351 contribute to errors in both of the delay measurements required 352 for calculating ipdv. 353 + If the synchronization error affecting the One-Way-Delay measurement 354 is Tsync, and it is a linear function of time, through the skew 355 value "sk", at time T1 the error will be Tsync1 and at time T2 356 the error will be Tsync2. The ipdv measurement will be affected 357 by the error: 358 Tsync2-Tsync1 = sk x (T2 - T1) 359 depending on skew and T2-T1. To minimize this error it is pos- 360 sible to reduce the time interval T2-T1, but this could limit 361 the generality of the metric. 362 Methods for evaluating the synchronization error will be discus- 363 sed below, since they come from a statistic over a significant 364 sample. 365 If the measurement conditions do not allow to neglect the drift, 366 supposed as linear in the interval T2-T1, and having a value of 367 "dr" expressed in ppm / sec., the ipdv error will become: 368 Tsync2-Tsync1 = sk x (T2 - T1) + [dr x (T2-T1) x (T2-T1)] / 2 369 It has to be noted that the presence of drift varies the skew 370 value in the time. The limits in which the skew can vary are 371 anyway limited and little, so that a given drift cannot act 372 indefinitely. Section 7 and Appendix A provide more information 373 on this point. 374 + As far as accuracy and resolution are concerned, what is noted 375 in the above referenced Draft on One-Way-Delay at section 3.7.1, 376 applies also in this case, with the further consideration, about 377 resolution, that in this case the uncertainty introduced is two 378 times the one of a single delay measurement. Errors introduced 379 by these effects are often larger than the ones introduced by 380 the drift. 382 I-D Ipdv Metric November 1998 384 5.6.2. Errors/uncertainties related to Wire-time vs Host-time 386 The content of sec. 3.7.2 of the above referenced Draft applies also 387 in this case, with the following further consideration: 388 The difference between Host-time and Wire-time can be in general de- 389 composed into two components, whose one is constant and the other is 390 variable around zero. Only the variable components will produce measu- 391 rement errors, while the constant one will be canceled while calcu- 392 lating ipdv. 394 6. Definitions for Samples of One-way ipdv 396 Starting from the definition of the singleton metric of one-way ipdv, 398 some ways of building a sample of such singletons are here described. 399 In particular two "discontinuous" samples and one "continuous" sample 400 are defined, and the last one is proposed, being the most suitable for 401 describing the aspect of the path's behavior underlined in the motiva- 402 tion. 403 In the following, the two packets needed for a singleton measurement 404 will be called a "pair". 406 6.1. "Discontinuous" definitions 408 A general definition can be the following: 409 Given particular binding of the parameters Src, Dst, path, and 410 Type-P, a sample of values of parameters T1 and T2 is defined. 411 The means for defining the values of T1 is to select a beginning 412 time T0, a final time Tf, and an average rate lambda, then 413 define a pseudo-random Poisson arrival process of rate lambda, 414 whose values fall between T0 and Tf. The time interval between 415 successive values of T1 will then average 1/lambda. Another si- 416 milar, but independent, pseudo-random Poisson arrival process 417 based on T0', Tf' and lambda', will produce a series of t' 418 values. The time interval between successive t' values will then 419 average 1/lambda'. For each T1 value that has been obtained 420 by the first process, it is then possible to calculate the 421 successive T2 values as the successive T1 values plus the 422 successive intervals of t'. 424 The result is shown in figure 1. 426 This general definition is likely go give problems, if no limits are 427 considered for the obtained values. For example, the emission 428 time of the first packet of a pair, could fall before the emission 429 time of the second packet of the preceding pair. Probably this could 430 be acceptable (provided that there are means to recognize pairs -e.g. 432 I-D Ipdv Metric November 1998 434 use of sequence numbers-), but the concept itself of ipdv would be,at 435 least, slightly changed. A way for avoiding this type of philosophical 436 problems can be to give some rules on the values T0, Tf, lambda, 437 T0', Tf', lambda', without changing the meaning of the metric. 439 |<- average interval 1/lambda ->| 440 | | 441 |<- av.int. | |<- av.int. | 442 |1/lambda'->| | 1/lambda'->| 443 _____|___________|___________________|_____________|________ 444 pair i pair i+1 445 Figure 1 447 As an example, it could be defined that the process of sorting the 448 interval between pairs starts after the interval between packets in a 449 pair is expired, obtaining the result of figure 2: 451 |<--- av. int.......| 452 ..........................| 1/lambda --->| 453 | | 454 |<- av.int. | |<- av.int. | 455 |1/lambda'->| | 1/lambda'->| 456 _____|___________|___________________|_____________|________ 457 pair i pair i+1 458 Figure 2 460 Still other problems can be envisaged with these two definitions which 461 are described in some more detail in Appendix A. 463 6.2. A "continuous" definition 465 A way for naturally avoiding the previous problems and producing a 466 testing environment closer to actual scenarios is to adopt the follo- 467 wing "continuous" definition. 468 A continuous stream of test packets can be supposed, where the second 469 packet of a pair is, at the same time, the first packet of the next 470 pair. Therefore the preceding definitions become: 472 + Given particular binding of the parameters Src, Dst, path, and 473 Type-P, a sample of values of parameter T1 is defined. 474 The means for defining the values of T1 is to select a beginning 475 time T0, a final time Tf, and an average rate lambda, then 476 define a pseudo-random Poisson arrival process of rate lambda, 478 I-D Ipdv Metric November 1998 480 whose values fall between T0 and Tf. The time interval between 481 successive values of T1 will then average 1/lambda. From the 482 second value on, T1 value of the pair n coincides with T2 of 483 the pair n-1, and the first packet of pair n coincides with the 484 second packet of the pair n-1. 485 For the moment, in the following, this last definition will be con- 486 sidered. Further refinement is required and is for further discussion. 488 6.3. Metric name 490 Type-P-One-way-ipdv-stream 492 6.4. Parameters 493 + Src, the IP address of a host 494 + Dst, the IP address of a host 496 + Path, the path* from Src to Dst; in cases where there is only 497 one path from Src to Dst, this optional parameter can be omitted 498 + T0, a time 499 + Tf, a time 500 + lambda, a rate in reciprocal seconds 502 6.5. Metric Units: 504 A sequence of triads whose elements are: 505 + T, a time 506 + Ti, a time interval. 507 + dT a real number or an undefined number of seconds 509 6.6. Definition 511 A pseudo-random Poisson process is defined such that it begins at or 512 before T0, with average arrival rate lambda, and ends at or after Tf. 513 Those time values Ti greater than or equal to T0 and less than or 514 equal to Tf are then selected. Starting from time T, at each pair of 515 times T(i), T(i+1)of this process a value of Type-P-One-way-ipdv is 516 obtained. The value of the sample is the sequence made up of the 517 resulting triad, where the time interval 518 is given by T(i+1)-T(i). Each obtained time T(i), excluding the first 519 and the last, is therefore at the same time the the second time of 520 pair i and the first time of pair i+1. The result is shown in figure 3 522 |T(i-2) |T(i-1) |T(i) |T(i+1) 523 _____|__________|___________________|__________|________ 524 pair i-1 pair i pair i+1 526 Figure 3 528 I-D Ipdv Metric November 1998 530 6.7. Discussion 532 Note first that, since a pseudo-random number sequence is employed, 533 the sequence of times, and hence the value of the sample, is not 534 fully specified. Pseudo-random number generators of good quality 535 will be needed to achieve the desired qualities. 537 The sample is defined in terms of a Poisson process both to avoid the 538 effects of self-synchronization and also capture a sample that is 539 statistically as unbiased as possible. {Comment: there is, of 540 course, no claim that real Internet traffic arrives according to a 541 Poisson arrival process.} 543 6.8. Methodology 545 Since packets can be lost or duplicated or can arrive in a different 546 order with respect the one of emission, in order to recognize the 547 pairs of test packets, they should be marked with a Sequence Number 548 or make use of any other tool suitable to the scope. For duplicated 549 packets only the first received copy should be considered. If a pac- 550 ket is lost, two values of ipdv will be undefined, since each packet, 551 in the supposed "continuous" definition, is common to two pairs. 553 Steps for measurement can be the following: 554 + Starting from a given time T, Src generates a test packet as for 555 a singleton metrics, inserts in the packet a Sequence Number 556 and the transmission Time Stamp Tx,then sorts the time Ti at 557 which the next packet has to be sent. 558 + At time Ti, Src repeats the previous step, unless T(i) > Tf. 559 + On reception of the first packet, or the first packet after a SN 560 error, Dst records SN and Tx timestamp that are contained in 561 the packet and the reception time Rx as "old values". 562 + On reception of the other packets Dst verifies the SN and if it is 563 correct, by using the "old values" and the newly received ones, 564 a value of ipdv is computed. Then Dst records the new SN, Tx 565 and Rx timestamps as "old values". 567 6.9. Errors and uncertainties 569 The same considerations apply that have been made about the single- 570 ton metric. An additional error can be introduced by the pseudo-ran- 571 dom Poisson process as focused in the above referenced Draft. 572 Further considerations will be made in section 7, and in Appendix A. 574 6.10 Some statistics for One-way-ipdv 576 Some statistics are here considered, that can provide useful informa- 577 -tion in analyzing the behavior of the packets flowing from Src to Dst 579 I-D Ipdv Metric November 1998 581 These statistics are given having in mind a practical use of them. The 582 focus is on the instantaneous behavior of the connection, while buffer 583 dimensioning is not in the scope of this document. 584 Other statistics can be defined if needed. 586 6.10.1. Type-P-One-way-ipdv-inverse-percentile 588 Given a Type-P-One-way-ipdv-Stream and a time threshold, that can be 589 either positive or negative, the fraction of all the ipdv values in 590 the Stream less than or equal to the threshold, if the threshold is 591 positive, or greater or equal to the threshold if the threshold is ne- 592 gative. 594 For many real-time services that require a regular delivery of the 595 packets, this statistics can give the amount of packets received 596 beyond acceptable limits. 598 6.10.2 Type-P-One-way-ipdv-standard-deviation 600 Given a Type-P-One-way-ipdv-Stream, the distribution of ipdv values 601 is considered and the Standard Deviation can be calculated as an 602 indication of regularity of delivery. For practical purposes it can be 603 useful to define a total standard deviation, computed over the com- 604 plete set of value, and a standard deviation computed over the sub- 605 set of those values that do not exceed given positive and negative 606 thresholds. This allows a more accurate description of the performan- 607 ce experienced by packets. Details on the shape of the ipdv distribu- 608 tion are given in Appendix A. 610 6.10.3 Type-P-One-way-ipdv-average 612 This statistic should tend to a value of ZERO for a number of ipdv 613 values that tend to infinite. The behavior of Type-P-One-way-ipdv- 614 average, and its meaning, are issues for the next section 7. 616 7. Discussion on clock synchronization 618 This section gives some considerations about the need of having syn- 619 chronized clocks at Src and Dst. These considerations are given as a 620 basis for discussion, they require further investigation. We start 621 from the analysis of the mean value of the ipdv distribution related 622 to a "continuous" sample. Some more detailed calculations are presented 623 in Appendix A. 625 I-D Ipdv Metric November 1998 627 7.1. Mean value of ipdv distribution. 629 If D(i) is the delay of packet "i", and ipdv(i) is the i-th value of 630 ipdv in the distribution of a sample of "n" values, collected with 631 the described methodology, we can write: 633 ipdv(1) = D1 - D0 634 .......... 635 ipdv(i) = D(i) - D(i-1) 636 .......... 637 ipdv(n) = D(n) - D(n-1) 639 The mean value of ipdv distribution will result in 641 E(ipdv) = (D(n) - D(0))/n 643 If an actual measurement is performed, that lasts a period of time 644 long enough to contain a number "n" sufficiently large and, supposing 645 synchronized clocks, such that the network conditions (traffic) allow 646 to find a D(n) not too different from D(0), e.g. a time of n x 24 647 hours, E(ipdv) will tend to zero, since the difference D(n) - D(0) will 648 remain finite and little. 650 7.2. Effects of a varying traffic 652 If the mean values of delay D are changing inside a given period of 653 time, for example they are increasing due to an increment of traffic, 654 we can consider, as a first approximation, the ipdv values as decom- 655 posed into two components, one being instantaneous and another one 656 as having a constant rate dD and corresponding to the increment "per 657 interval" of the mean value of D. The mean value of the distribution 658 will be shifted of the value dD corresponding to the mean value of 659 the interval between test packets. This will happen only during the 660 monotonic variation, and is not a distortion, since it is the record 661 of the instantaneous behavior. When the conditions will come back 662 to the initial ones, the distribution will resume a mean value around 663 zero. As for the case of drift, also in this case a monotonic varia- 664 -tion cannot take place indefinitely. In Appendix A a method is given 665 for subdividing the variation into these two components over short 666 periods, in order to have indications on variations of traffic condi- 667 -tions. 669 7.3. Effects of synchronization errors 671 We refer here to the two components that can generate this type of 672 errors that are the reciprocal "skew" and "drift" of the Src and Dst 673 clocks. It is first of all noted that the variable component "drift" 675 I-D Ipdv Metric November 1998 677 is physically limited and its effects can be interpreted by saying 678 that the total reciprocal skew of the two clocks can vary, ranging from 679 a min to a max. value in the time. This type of variation takes place 680 very slowly being mostly connected to variations in temperature. 682 We suppose to perform a measurement between a Src and a Dst that have 683 a reciprocal, initial skew of "ts1" and a reciprocal drift such that, 684 after the time T the total skew is "ts2". It is not here a limitation 685 to consider that at the beginning of time T the two clocks indicate 686 the same time T0. 688 In order to analyze the effects produced by this situation we suppose 689 that packets are transferred, from Src to Dst, with a constant delay D 690 In this conditions the measured ipdv should always be zero, and what 691 is actually measured is the error. 693 An ipdv value is measured at the beginning of time T with two packets 694 having an interval of Ti(1).Another ipdv value is measured at the end 695 of T with two packets having a time interval Ti(2). 697 On our purposes other errors (like wire-time vs host-time) are not 698 considered since they are not relevant in this analysis, being common 699 to all the measurement methods. 701 It is then possible to calculate the values of the Tx and Rx time- 702 stamps as they are seen by the two clocks, and the related two ipdv 703 values. 705 The first ipdv value will be: ipdv1 = ts1*Ti(1) + ((ts2-ts1)/T)*Ti(1) 706 The second ipdv value will be: ipdv2 = ts2*Ti(2) +((ts2-ts1)/T)*Ti(2) 708 The error is given by the effect of the skew during the time inter- 709 val Ti(i) between the two packets of the pair, and a second order 710 term due to the variation of that skew in the same interval. 712 If, as in the most of practical cases, the drift can be considered 713 close to zero, then ts1 = ts2, and the error is not depending on the 714 time at which the measurement is done. In addition, this type of 715 error can be corrected as it is indicated in the next paragraph and 716 discussed in Appendix A. 718 In any case the maximum error on an ipdv value will correspond to the 719 effect of the maximum reciprocal skew on the maximum interval between 720 packets. 722 I-D Ipdv Metric November 1998 724 7.4. Related precision 726 This means that: 727 1) + If the skew is constant and is = ts all the ipdv(i) values are 728 increased by the quantity Ti(i)*ts with respect the actual value. 729 The mean ipdv value will therefore increased of the quantity 730 E[Ti(i)]*ts, which is measured. Also E[Ti(i)] can be measured, and 731 should be related to lambda. That means that the skew ts can be 732 calculated. If together with ipdv(i), also the corresponding Ti(i) 733 are collected, for each ipdv(i) value a correcting term is avai- 734 -lable, and a sample of "corrected" c-ipdv(i) values is obtained, 735 where c-ipdv(i) = ipdv(i) - Ti(i)*st. 736 2) + Considering the total skew as subdivided into a fixed part and a 737 variable part (skew and drift),respectively, ts and + or - td, 738 from the mean ipdv value and the mean emission interval the average 739 skew can be derived in the period of interest (Appendix A). The 740 preceding correction can then be applied. The maximum residual er- 741 -ror on an ipdv value is given by the difference between the actual 742 skew at the time in which the value has been measured and the ave- 743 -rage skew, multiplied by the time interval between the packets 744 that have generated that ipdv value. Considerations on the number 745 of values in the sample affected by errors are reported in 746 Appendix A. 747 3) + If the duration of the measurement is such that it is possible 748 to consider that the effect of the items at points 7.1 and 7.2, 749 are close to zero, the mean value of the ipdv distribution will 750 have the value of the average skew multiplied by the mean value of 751 the emission interval, as supposed above. 752 4) + We observe that the displacement due to the skew does not change 753 the shape of the distribution, and, for example the Standard Devi- 754 ation remains the same. What introduces a distortion is the effect 755 of the drift, also when the mean value of this effect is zero at 756 the end of the measurement. The value of this distortion is limited 757 to the effect of the total skew variation on the emission interval. 758 5) + In what has been said, skew and drift have been considered as 759 reciprocal". In Appendix A it will be considered that each of the 760 two clocks have a skew and a drift with respect a "true time", and 761 it will be observed that the difference is negligible with respect 762 the situation in which one of the two clocks is taken as the "true 763 time". 765 I-D Ipdv Metric November 1998 767 8. Definition for a bidirectional ipdv metric 769 We now consider that the action of the skew on one direction is the 770 same, with opposite sign, of the action on the other direction. The 771 idea of performing at the same time two independent measurements in 772 the two directions is suggested by this fact. 774 If, after a long measurement, the variable conditions of the system 775 under test have reached the situation of a contribution close to zero 776 to the mean value of the ipdv distribution, it is expected that only 777 the action of the average skew has modified the measured mean value. 778 It is therefore expected that on one direction that value is equal and 779 opposite to the one measured in the other direction. 781 This fact offers the possibility of defining a theoretical reference 782 measurement duration in the following way: 784 The reference duration of a bidirectional ipdv measurement between 785 an host E and an host W is reached at time Tf such that for each time 786 T > Tf the expression ABS(E(ipdv E-W) - E(ipdv W-E))< epsilon, where 787 epsilon is what we can consider as zero, is always verified. This is 788 one, but not the only method for verifying that the mean ipdv value 789 has reached the value of the average reciprocal skew. 791 At this point it is possible to evaluate the reciprocal skew. 792 This will require the knowledge of the mean value of the intervals 793 between consecutive packets, that can be calculated over the trans- 794 -mitted stream, by using the collected time stamps. 796 A bidirectional measurement can be defined not only as twin one-way 797 independent metrics that take place (nearly) at the same time, but 798 also as a two-ways metric making use of packets looped back at one 799 end. This metric, that can be object of further study/Draft, would be 800 able to measure also the Round Trip Delay and its variations. Problems 801 will anyway arise on the characterization of emission intervals in the 802 backward direction. They would be produced by the combination of the 803 original Poisson arrival process and the effect of ipdv on the forward 804 direction. It has to be studied if this sequence of intervals is still 805 suitable for the measurement. also other possibilities can be 806 envisaged for obtaining a proper backward sequence and still maintain 807 the loopback concept. 809 I-D Ipdv Metric November 1998 811 9. References 813 V.Paxon, G.Almes, J.Mahdavi, M.Mathis - "Framework for IP Performance 814 Metrics", Internet Draft Feb. 1998 816 G.Almes, S.Kalidindi - "A One-Way-Delay Metric for IPPM", Internet 817 Draft Nov. 1997 819 10. Author's Address 821 Carlo Demichelis 822 CSELT - Centro Studi E Laboratori Telecomunicazioni S.p.A 823 Via G. Reiss Romoli 274 824 10148 - TORINO 825 Italy 826 Phone +39 11 228 5057 827 Fax. +39 11 228 5069 829 I-D Ipdv Metric November 1998 831 APPENDIX A 833 This Appendix considers the scenario in which two hosts have clocks 834 that are both not synchronized. Between the two hosts, in an inde- 835 -pendent way and at the same time in both direction an ipdv measure- 836 -ment is performed according the methodology that is described in the 837 main body of this Draft. 838 This hypothetical scenario is only supposed for discussing the theory 839 and the characteristics of the ipdv metric and its results, without 840 considering implementation issues. 842 A.1 - Initial positions 844 The two hosts will be called West (W) and East (E). The two measure- 845 -ments start at the same time, while the end of the measurement it is 846 supposed to be decided by the results of the measurement itself. 848 At the beginning of the measurement the time declared by the West 849 clock is T0w, the time declared by the East clock is T0e, while the 850 true time is T0t. 852 The W-clock is affected by an absolute skew of skw ppm and the E-clock 853 by an absolute skew of skw ppm. 855 The W-clock is affected by an absolute drift ranging from -drw ppm to 856 +drw ppm, the E-clock by an absolute drift ranging from -dre ppm to 857 +dre ppm. 859 A.2 - Evaluation of skew and drift effects 861 In order to evaluate the effect of the drift on this type of metric, 862 it is necessary to consider the time in which the variation of the skew 863 takes place. We consider the two extreme cases in which the variation 864 takes place uniformly from the beginning to the end of the measurement 865 and the variation takes place suddenly at a generic time along the 866 measurement. Let TM be the measurement time. 868 A.2.1 - Mean ipdv value 870 Since the mean ipdv value, as it has been seen, is the difference of 871 the last delay minus the first, divided by the number of considered 872 values, we consider what, in the two cases, is measured for first and 873 last delay. 875 We call trueDf the true first Delay and trueDl the true last Delay. 877 I-D Ipdv Metric November 1998 879 For the evaluation that we want to do, it is not a limitation to con- 880 -sider that they are equal and have a value of trueD. We also consider 881 as time 0 the true time at which the transmission of the first packet 882 starts from West toward East. 884 In case of continuous drift we define a "drift per second" as: 885 drpsW = 2*drw / TM and drpsE = 2*dre / TM 886 along the measurement this will bring the skew from a value of: 887 skWmin = skw - drw ; skEmin = ske - dre 888 to a value of 889 skWmax = skw + drw ; skEmax = ske + dre 891 What is measured as first Delay is: 893 measured first Rx time - measured first Tx time 894 OffsetEast + trueD*[1 + skEmin + (1/2)*drpsE] - OffsetWest 896 What is measured as last Delay is: 898 measured last Rx time - measured last Tx time 899 OffsetEast + (TM + trueD)*[1 + skEmin + (1/2)*2*dre] - 900 - OffsetWest - TM*[1 + skWmin + (1/2)*2*drw] 902 The difference between the last and first Delay is therefore: 904 TM*(skEmin - skWmin + dre - drw) - trueD*drpsE/(2*TM) 906 if TM = 10 hours drpsE is in the order of 50*10E-6 / 36000 that is 907 about 10E-9 and the second term of the expression is in the order of 908 10E-14 for true delays in the order of 1 sec (negligible term). 909 We consider that, with very good approximation: 911 Mean emission interval (mti) = TM / number of ipdv values (N) 912 Therefore: 914 mean ipdv = (measured last Delay - measured first Delay) / N = 915 = mti*(skEmin - skWmin + dre - drw) 917 but we considered skEmin = ske - dre and skWmin = skw - drw 918 and therefore: 920 mean ipdv = (meas.lastD - meas.firstD) / mti*(reciprocal mean skew) 922 The previous procedure is now applied to the case in which the total 923 drift takes place in a very short time. Some cases are possible, and 924 we consider the one in which at the beginning the West clock has 925 skWmax and the East clock has skEmin, at time txW the West clock 926 assumes skWmin and at time txE the East clock assumes skEmax. 928 I-D Ipdv Metric November 1998 930 What is measured as first Delay is now: 932 measured first Rx time - measured first Tx time 933 OffsetEast + trueD*(1 + skEmin) - OffsetWest 935 What is measured as last Delay is: 937 measured last Rx time - measured last Tx time 938 + OffsetEast + txE*(1 + skEmin) + (TM - txE)*(1 + skEmax) + 939 + trueD*(1 + skEmax) - 940 - OffsetWest - txW*(1 + skWmax) - (TM - txW)*(1 + skWmin) 942 but the mean skew values will be: 944 mskw = [skWmax*txW + skWmin*(TM - txW)] / TM 945 mske = [skEmin*txE + skEmax*(TM - txE)] / TM 947 the difference between the two delays therefore is: 949 TM*(mske - mskw) + 2*trueD*dre 951 and the mean ipdv value will be: 953 mean ipdv = mti*(mske - mskw) + 2*mti*trueD*dre/TM 955 the second term of the second member in the previous hypotheses is in 956 the order of the nanosecond, and we neglect it. Also in this case, from 957 the mean ipdv value, and knowing the mean emission interval, the rela- 958 -tive skew of the clocks can be obtained. 960 More in general, independently on how the drift acts inside its limits, 961 we assert that always the mean ipdv value divided by the mean emission 962 interval produces the value of the mean reciprocal skew of the two 963 clocks, provided that the collected number of ipdv values is signi- 964 -ficant for the statistics. 966 A.2.2 - Errors and corrections 968 If the drift is always close to zero, it is possible to obtain the 969 true value of the reciprocal skew and correct all the ipdv values. Each 970 of them is associated to an emission interval ti between the two 971 packets that have produced the value itself. Then a better ipdv value 972 will be: 973 corr.ipdv(i) = meas.ipdv(i) - ti * skew 974 This is a better value but not exactly the true one, since we supposed 975 that both clocks are not synchronized to the true time. Two errors are 976 affecting the corrective terms which are: 978 I-D Ipdv Metric November 1998 980 + The reciprocal skew is measured as referred to the Src clock 981 + The interval ti is measured by the Src clock. 982 These are second order errors since the measured skew will be affected 983 by a "relative" error in the order of the Src skew, an the same is 984 for the error affecting the ti value. 986 If the drift is significant and it can range from the lower to the 987 upper limit of its field, the measured average of the skew will depend 988 on the type of variation. Some cases are considered that demonstrate 989 that actually the proposed correction is not so much effective in this 990 case. Only the fixed part of the total clock variation can be properly 991 corrected. 993 A.2.2.1 - Constant drift 995 The first case is the first one considered in the preceding paragraph, 996 where the drift is uniform. We suppose that a reciprocal skew is measu- 997 -red and used for correction. 999 At the beginning of the measurement the actual reciprocal skew is: 1001 init.skew = mean.skew - rel.max.drift 1003 and at the end the actual reciprocal skew is: 1005 final.skew = mean.skew + rel max.drift 1007 The correction is effective only in the central part of the measurement. 1008 At the beginning and at the end a residual error will affect the ipdv 1009 values whose value will be: 1011 ipdv(i).err = ti * rel.max.drift 1013 We underline here that the error is larger for large intervals ti and 1014 lower for short intervals ti. For intervals derived from a poissonian 1015 arrival process, there are many short intervals and few large intervals. 1016 We also note that a constant drift cannot last indefinitely, since there 1017 is a minimum and a maximum for the skew. 1019 A.2.2.2 - Step of drift 1021 In this case the error profile depends on the time at which the drift 1022 changes. If the change is near the beginning or near the end of the 1023 measurement, the calculated mean skew will be very close to the actual 1024 skew of the largest part of the measurement. On that part the correc- 1025 -tion will be effective, while over the remaining few values the error 1026 will be twice with respect the preceding case. 1028 I-D Ipdv Metric November 1998 1030 The worse condition is produced by a change in drift in the middle of 1031 the measurement. In this case the correction would be useful only if 1032 the drift was significantly less than the skew. 1034 A.3 - Comparison with a synchronized case 1036 In this section we consider a case in which the two hosts have synchro- 1037 -nized clocks, and the synchronization is obtained by setting the real 1038 time each second in each of the clocks. We optimistically suppose that 1039 this is done exactly (without any imprecision). On the clocks, anyway 1040 skew and drift continue to act. We refer to reciprocal skew and drift, 1041 having already seen that this is significant. We suppose to perform an 1042 ipdv measurement and we evaluate what is measured by the mean ipdv 1043 value and what is the error on the measured ipdv values. 1045 We notice, first of all, that nothing changes for ipdv values measured 1046 over intervals falling completely between two synchronization instants. 1047 In this case, the effect of synchronization is only to put to zero the 1048 offset, that does not appear in the calculation of ipdv values. 1050 Something different happens if the synchronization instant (or more 1051 synchronization instants) falls inside the interval. In this case the 1052 error can range from + to - the error related to one second interval, 1053 or, more in general, from + to - the error related to an interval equal 1054 to the synchronization period. The (few) large intervals will produce 1055 a limited error while the (many) short intervals will continue to 1056 produce errors of the same order of magnitude of the not synchronized 1057 case. 1059 Besides, even if the drift is negligible, the mean ipdv value is no 1060 more suitable to calculate the skew, and it will be much more close to 1061 zero. Therefore it is no more possible to correct the distortion of the 1062 distribution. 1064 Finally, it is necessary to add to these errors the unavoidable impre- 1065 cision of the synchronization process. We have to consider that the 1066 magnitude of errors introduced by skew and drift is in the order of 1067 tenth of microseconds. Not always the complete synchronization process 1068 has a better precision. 1070 A.4 - Bidirectional measurement and components of ipdv 1072 Three terms have been described that can displace the mean ipdv value 1073 from zero. They are: 1075 I-D Ipdv Metric November 1998 1077 - The total skew, already discussed above, that always acts in an equal 1078 way and opposite direction over the two directions between West and 1079 East hosts. 1080 - The effect of varying traffic that can increase or decrease along 1081 limited periods, the average value of the One-Way-Delay. The metric 1082 above presented supposes that the measurement period is large enough 1083 for considering this effect as tending to zero. 1084 It is explicitly noted that the effect will produce a zero effect 1085 only on the mean ipdv value, while the effect on values ipdv(i) is 1086 always present. This is not a distortion of the distribution, since 1087 is part of the variation that is measured. This effect is different, 1088 and usually concordant, on the two directions. 1089 - The difference between first and last instantaneous values of the 1090 delay variation, that tends to zero when the number of collected 1091 ipdv values becomes large. 1093 In order to isolate the last two effects, we consider here a measurement 1094 over a long period (e.g. 24 hours)where the drift is negligible, and 1095 the effect of the skew has been corrected. 1097 A.4.1 - Slow variation in a given period 1099 The packets of the stream can be represented on a system of cartesian 1100 orthogonal axes with transmission time on x-axis and reception time on 1101 y-axis, by points localized by transmission and reception time of each 1102 packet. Considering an arbitrary period of time Tper, which will be a 1103 parameter of this procedure, it can be taken as a sliding window over 1104 the sample and for each position of this window, established by suc- 1105 -cessive packets, the segment of straight line is calculated that best 1106 approximate the points, by means of a linear regression method. 1108 The slope of this segment will be one if along the period the delay 1109 has not changed, and different from one if that delay has increased (>1) 1110 or decreased (<1). For each position of the window it is therefore 1111 possible to find a value of "slow delay variation" with Tper as a 1112 parameter. This will give an indication on variations produced by 1113 different traffic conditions along the measurement period. This item 1114 can be subject for further study. 1116 At the same time this procedure offers a criterion for reducing the 1117 error introduced in the calculation of the mean ipdv by the instanta- 1118 -neous component of the difference between last and first delay. 1119 Supposing that the timestamps, on which the metric is based, are 1120 collected and then processed, if the method of the sliding window is 1121 applied at the beginning and at the end of the collected sample, it 1122 is possible to avoid starting and ending the measurement on values 1123 possibly too different from the average (points too far away from the 1124 calculated straight line). 1126 I-D Ipdv Metric November 1998 1128 A.5 - Symmetry of an ipdv distribution and emission intervals 1130 It is demonstrated that, if the packets of the test sequence are pro- 1131 pagated in an independent way, in the sense that none of them is 1132 influenced by the preceding packets (large emission intervals), the ipdv 1133 distribution will be perfectly symmetrical. If the variation of the 1134 delay is such that some packets is delayed by the preceding one (ideal- 1135 -ly queued to it in a buffer), the related ipdv value generated will 1136 have a lower limit, that will be the negative value of the emission 1137 interval minus the time required for transmitting the packet from the 1138 buffer. If the intervals were constant, this would correspond to a well 1139 defined value, that would allow to measure the bandwidth of the bottle- 1140 -neck provided by the output of that buffer. Since the intervals are 1141 derived from a poissonian arrival process, this limit is not a fixed 1142 one, and is not immediately evident of the ipdv distribution. 1144 Another effect of this interference among packets is that also the 1145 packet following the queued one will produce a lower ipdv value since 1146 it will "gain" the time of latency in the buffer of the previous one. 1148 The total effect is that the ipdv values will tend to concentrate on 1149 the negative side of the distribution, with some limitation on the 1150 negative maximum values. In other words, the negative side of the 1151 distribution will be shorter than the positive one, but containing more 1152 values. Nothing changes for the meaning of the mean ipdv value. 1154 This asymmetry is not a distortion, since represents the actual propa- 1155 -gation characteristics. For the supposed type of intervals, the dis- 1156 -tribution is always asymmetrical, since always are present intervals 1157 lower than the delay variability, and the degree of asymmetry will 1158 change with the level of interference. 1160 The relationship between asymmetry and the combination of average emis- 1161 -sion interval and available bandwidth can be investigated and could 1162 provide information about the level of congestion of the network