Network Working Group~~C.Demichelis~~C. Demichelis INTERNET-DRAFTCSELT~~expires May~~Expiration Date: December 1999 P. Chimento CTIT June1999 Instantaneous Packet Delay Variation Metric for IPPM~~<draft-ietf-ippm-ipdv-02.txt>~~<draft-ietf-ippm-ipdv-03.txt>1. Status of this Memo This document is an~~Internet Draft. Internet Drafts~~Internet-Draft and is in full conformance with | all provisions of Section 10 of RFC2026. Internet-Draftsare working~~doc- uments~~documentsof the Internet Engineering Task Force (IETF), its areas, and its working groups. Note that other groups may also distribute~~work- ing~~workingdocuments as~~Internet~~Internet-Drafts.~~Internet Drafts~~Internet-Draftsare draft documents valid for a maximum of six~~months,~~monthsand may be updated, replaced, or obsoleted by other documents at any time. It is inappropriate to use~~Internet Drafts~~Internet-Draftsas reference material or to cite them other than as~~``work~~"workin~~progress''. To learn the~~progress." The list ofcurrent~~status~~Internet-Drafts can be accessed at | http://www.ietf.org/ietf/1id-abstracts.txt | The listof~~any Internet Draft, please check the ``1id-abstracts.txt'' listing contained in the Internet Drafts~~Internet-Draftshadow directories~~on ftp.is.co.za (Africa), nic.nordu.net (Europe), munnari.oz.au (Pacific Rim), ds.internic.net (US East Coast), or ftp.isi.edu (US West Coast).~~can be accessed at | http://www.ietf.org/shadow.htmlThis memo provides information for the Internet community. This memo does not specify an Internet standard of any kind. Distribution of this memo is unlimited. 2. Abstract This memo refers to a metric for variation in delay of packets across Internet paths. The metric is based on statistics of the difference in One-Way-Delay of consecutive packets. This particular definition of variation is called "Instantaneous Packet Delay Variation (ipdv)". The metric is valid for measurements between two hosts both in the case that they have synchronized clocks and in the case that they are not synchronized. In the second case it allows an evaluation of the reciprocal skew. Measurements performed on both directions~~(Two-ways~~(Two-waymeasurements) allow a better estimation of clock differences. The precision that can be obtained is evaluated.~~I-D Ipdv Metric November 1998~~3. Introduction This memo takes as a reference the Draft-ietf "One-Way-Delay metric|for IPPM"~~that it is supposed to be known.~~[1].Part of the text in this memo is directly taken from that Draft. This memo defines a metric for variation in delay of packets that flow from one host to another one through an IP path. Since the metric is related to a variation, different definitions are possible according to what the variation is measured against.~~NOTE: The terminology used in this Draft will be re-visited as soon as a terminology document will be available. So far the following is considered: -~~"Jitter" commonly has two meanings:The~~term Jitter~~first meaningis~~derived from~~the~~well known definition given for transmission~~| variationof~~electrical pulses associated to~~a~~clock, and it seems to be able to describe variations~~signalwith respect to~~an expected~~some clock signal, where the |arrival~~time. - Each entity adopted as a reference for variation measurements defines a specific metric. Each metric describes a specific aspect or effect~~timeof the~~behavior~~signal is expected to coincide with the arrival |of the~~System Under Test (SUT). - Among entities that can be adopted, as an example, it is possible~~clock signal. The second meaning hasto~~consider a reference delay for~~do withthe~~path,~~variation | ofametric (e.g. delay) with respect to somereferencemetric (e.g. | averagedelay~~for the Src Dst pair, the Mean One-Way-Delay over a period~~or minimum delay). The formof~~interest, the Delay variation~~"jitter"that~~can be derived considering the difference between the actual and~~we talk | about here has to do almost exclusively withthe~~expected arrival time,~~second meaning, | rather thanthe~~difference between~~first. Seethe~~delay of a packet and~~section onthe~~last measured similar delay.~~relationship with other | standards.3.1. Definition A definition of the Instantaneous Packet Delay Variation (ipdv) can be given for a pair of packets or for a packet inside a stream of packets. For a pair of packets:~~-~~+The ipdv of a pair of IP packets, that are transmitted from the~~measu- rement~~measurementpoint MP1 to the measurement point MP2, is the difference between the One-Way-Delay measured for the second packet and the~~One- Way-Delay~~One-Way-Delaymeasured for the first packet of the pair. For a stream of packets:~~-~~+The Instantaneous Packet Delay Variation of an IP packet, inside a stream of packets, going from the measurement point MP1 to the~~measu- rement~~measurementpoint MP2, is the difference of the One-Way-Delay of that packet and the One-Way-Delay of the preceding packet in the stream.~~I-D Ipdv Metric November 1998~~3.2. Motivation A number of services that can be supported by IP are sensitive to the regular delivery of packets and can be disturbed by instantaneous~~va- riations~~variationsin delay, while they are not disturbed by slow variations, that can last a relatively long time. A specific metric for quick~~va- riations~~variationsis therefore desirable. Metrics that can be derived from the analysis of statistics of ipdv can also be used, for example, for|buffer~~dimensioning, but this memo is not intended in that sense.~~dimensioning.The scope of this metric is to provide a way for measurement of the quality delivered by a path. In addition, this type of metric is particularly robust with respect differences and variations of the clocks of the two hosts. This~~allow~~allowsthe use of the metric even if the two hosts that support the~~measure- -ment~~measurementpoints are not synchronized. In the latter case indications~~on~~ofreciprocal skew of the clocks can be derived from the measurement and corrections are possible. The related precision is often comparable with the one that can be achieved with synchronized clocks, being of the same order of magnitude of synchronization errors. This will be discussed below. 3.3. General Issues Regarding Time~~All what is~~Everythingcontained in the~~paragraph~~Section2.2. of~~the Draft ippm on One- Way Delay metric (2.2. General Issues Regarding Time)~~[2]applies also in this|case. In addition,~~it is~~we assumehere~~considered~~that the reciprocal skew of the two clocks can be decomposed into two parts:~~*~~+A fixed one, called in this context "skew", given, for example, by tolerances in physical dimensions of crystals.~~*~~+A variable one, called in this context "drift", given, for example, by changes in temperature or other conditions of operation. Both of~~this~~thesecomponents are part of the term "skew" as defined in the referenced Draft and in the Framework document. NOTE: The drift of a clock, as it is above defined over a long period must have an average value that tends to zero while the period becomes large since the frequency of the clock has a finite (and~~little)~~small)range. In order to underline the order of magnitude of this effect,it is considered that the maximum range of drift for commercial crystals is about 50 part per million (ppm). Since it is mainly connected with variations in operating temperature (from 0 to 70 degrees Celsius), it is expected that a host will have a nearly constant temperature during its operation period, and variations in temperature, even if quick, could be less than one Celsius per second, and range in the order of~~I-D Ipdv Metric November 1998~~few degrees. The total range of the drift is usually related to~~varia- -tions~~variationsfrom 0 to 70 Celsius. These are important points for evaluation of precision of ipdv measurements, as~~it~~will~~see~~be seenbelow. 4. Structure of this memo The metric will be defined as applicable to a stream of packets that flow from a source host to a destination host (one-way ipdv). The~~ini- tial~~initialassumption is that source and destination hosts have synchronized clocks. The definition of a singleton of one-way ipdv metric is first~~consi- -dered,~~considered,and then a definition of samples for ipdv will be given. Then the case of application to~~not synchronized~~non-synchronizedhosts will be~~dis- cussed,~~discussed,and the precision will be compared with the one of~~the previous case.~~synchronized clocks.A bidirectional ipdv metric will be defined, as well as the methodology for error corrections. This will not be a~~two-ways~~two-waymetric, but a "paired" one-way in opposite directions. Some statistics describing the IP path's behavior will be proposed.~~In the Appendix A a more detailed analysis is reported of the ipdv theory and of the characteristics of ipdv distribution.~~5. A singleton definition of a One-way ipdv metric|This definition makes use of the corresponding definition of type-P-~~One-Way-Delay, that is supposed to be known.~~One-Way-Delay metric [2].This section makes use of those parts of the One-Way-Delay Draft that directly apply to the One-Way-ipdv metric, or makes direct references to that Draft. 5.1. Metric name Type-P-One-way-ipdv 5.2. Metric parameters +~~Scr,~~Src,the IP address of a host + Dst, the IP address of a host + T1, a time + T2, a time. It is explicitly noted that also the difference T2-T1 is a parameter of the measurement though this is already implicit, since the times T1 and T2 exactly define the time conditions in which the measurement takes place.~~I-D Ipdv Metric November 1998 + Path,~~Note thatthe~~path from Src to Dst; in cases where there~~packet lengthis~~only one path from Src to Dst, this optional~~an implicitparameter~~can be omitted. {Comment: the presence of path is motivated by cases such as with Merit's NetNow setup, in which a Src on one NAP can reach a Dst on another NAP by either~~of~~several different backbone networks. Generally,~~both the | Type-P-One-way-delay metric and the Type-P-One-way-ipdv metric, since |this~~optional parameter is useful only when several dif- -ferent routes are possible from Src~~contributesto~~Dst. Using~~the~~loose source route IP option is avoided since it would often artificially worsen~~overall one-way delay. We assume thatthe~~performance observed, and since it might not be supported along some paths.} 5.2.~~| packets sent for ipdv measurements are all of the same length. 5.3.Metric unit The value of a Type-P-One-way-ipdv is either a real number of seconds (positive, zero or negative) or an undefined number of seconds.~~5.3.~~5.4.Definition Type-P-One-way-ipdv is defined for two (consecutive) packets from Src to Dst, as the difference between the value of the type-P-One-way- delay from Src to Dst at T2 [via path] and the value of the type-P- One-Way-Delay from Src to Dst at T1 [via path]. T1 is the wire-time at which Scr sent the first bit of the first packet, and T2 is the wire-time at which Src sent the first bit of the second packet. This metric is therefore ideally derived from the One-Way-Delay metric. NOTE: The requirement of "consecutive" packets is not essential. The measured value is anyway the difference in One-Way-Delay at the times T1 and T2, which is meaningful by itself, as long as the times T1 and|T2~~are such to describe~~denotethe~~investigated charac- -teristics. These~~wiretimes~~will be better defined later.~~of the packets sent from Src to Dst.Therefore, for a real number ddT "The type-P-one-way-ipdv from Src to Dst at T1, T2 [via path] is ddT" means that Src sent two consecutive~~packets whose~~packets,the first at wire-time T1 (first bit), and the secondatwire-time T2 (first bit) and the packets were received by Dst at~~wire -time~~wire-timedT1+T1 (last bit of the first packet),~~and, respectively,~~andat wire-time dT2+T2 (last bit of the second packet), and that dT2-dT1=ddT. "The type-P-one-way-ipdv from Src to Dst at T1,T2 [via path] is~~unde- fined"~~undefined"means that Src sent the first bit of a packet at T1 and the first bit of a second packet at T2 and that Dst did not receive one or both packets.~~I-D Ipdv Metric November 1998 5.4.~~5.5.Discussion Type-P-One-way-ipdv is a metric that makes use of the same measurement methods provided for delay metrics. The following practical issues have to be considered: + Being a differential measurement, this metric is less sensitive to clock synchronization problems. This issue will be more carefully examined in section~~6.~~7of this memo. It is pointed out that, if the reciprocal clock conditions change in time, the accuracy of the measurement will depend on the time~~inter- -val~~intervalT2-T1 and the~~amount~~magnitudeof possible errors will be discussed below. + A given methodology will have to include a way to determine whether a delay value is infinite or whether it is merely very large (and the packet is yet to arrive at Dst). As noted by Mahdavi and Paxson, simple upper bounds (such as the 255 seconds theoretical upper bound on the lifetimes of IP packets [Postel: RFC 791]) could be used, but good engineering, including an understanding of packet lifetimes, will be~~nee- -ded~~neededin practice. {Comment: Note that, for many applications of these metrics, the harm in treating a large delay as infinite might be zero or very small. A TCP data packet, for example, that arrives only after several multiples of the RTT may as well have been lost.} +~~Usually a path is such that if~~As with other 'type-P' metrics,the~~first packet is largely delayed, it can "stop"~~value ofthe~~second packet~~metric may depend on such propertiesof the~~pair and vary its delay. This is not a problem for the definition since is, in any case, part of the description of the path's behavior. + As with other 'type-P' metrics, the value of the metric may de- -pend on such properties of the packet as protocol,(UDP or TCP) port number, size,~~packet as protocol,(UDP or TCP) port number, size,and arrangement for special treatment (as with IP precedence or with RSVP). + If the packet is duplicated along the path (or paths!) so that multiple non-corrupt copies arrive at the destination, then the packet is counted as received, and the first copy to arrive determines the packet's One-Way-Delay. + If the packet is fragmented and if, for whatever reason,~~reas- -sembly~~reassemblydoes not occur, then the packet will be deemed lost.~~5.5.~~5.6.Methodologies As with other Type-P-* metrics, the detailed methodology will depend on the Type-P (e.g., protocol number, UDP/TCP port number, size, precedence).~~I-D Ipdv Metric November 1998~~Generally, for a given Type-P, the methodology would proceed as~~fol- lows:~~follows:+ The need of synchronized clocks for Src and Dst will be~~discus- -sed~~discussedlater. Here a methodology is supposed that is based on synchronized clocks. + At the Src host, select Src and Dst IP addresses, and form two test packets of Type-P with these addresses. Any 'padding'~~por- -tion~~portionof the packet needed only to make the test packet a given size should be filled with randomized bits to avoid a situation in which the measured delay is lower than it would otherwise be due to compression techniques along the path. +~~Optionally, select a specific path and arrange for Src to send the packets to that path. {Comment: This could be done, for example, by installing a temporary host-route for Dst in Src's routing table.} +~~At the Dst host, arrange to receive the packets. + At the Src host, place a timestamp in the~~prepared~~first Type-P packet, and send it towards Dst [via path]. + If the packet arrives within a reasonable period of time, take a timestamp as soon as possible upon the receipt of the packet. By subtracting the two timestamps, an estimate of One-Way-Delay can be computed. + Record this first delay value. + At the Src host, place a timestamp in the~~prepared~~second Type-P packet, and send it towards Dst [via path]. + If the packet arrives within a reasonable period of time, take a timestamp as soon as possible upon the receipt of the packet. By subtracting the two timestamps, an estimate of One-Way-Delay can be computed. + By subtracting the second value of One-Way-Delay from the first value the ipdv value of the pair of packets is obtained. + If one or both packets fail to arrive within a reasonable period of time, the ipdv is taken to be undefined.~~5.6.~~5.7.Errors and Uncertainties In the singleton metric of ipdv, factors that affect the measurement are the same that can affect the One-Way-Delay measurement, even if, in this case, the influence is different. The Framework document[1]provides general guidance on this point, but we note here the following specifics related to delay metrics: + Errors/uncertainties due to uncertainties in the clocks of the Src and Dst hosts. + Errors/uncertainties due to the difference between 'wire time' and 'host time'.~~I-D Ipdv Metric November 1998~~Each of these~~type of~~errors~~are~~isdiscussed in more detail in the next paragraphs.~~5.6.1.~~5.7.1.Errors/Uncertainties related to Clocks If, as a first approximation, the error that affects the first~~measu- rement~~measurementof One-Way-Delay were the same of the one affecting the second measurement, they will cancel each other when calculating ipdv. The residual error related to clocks is the difference of the~~said~~errors that are supposed to change from the time T1, at which the first measurement is performed, to the time T2 at which the second~~measure-~~measurement is performed. Synchronization, skew, accuracy and resolution are here considered with the following notes: + Errors in synchronization between source and destination clocks contribute to errors in both of the delay measurements required for calculating ipdv. + If the synchronization error affecting the One-Way-Delay measurement is Tsync, and it is a linear function of time, through the skew value "sk", at time T1 the error will be Tsync1 and at time T2 the error will be Tsync2. The ipdv measurement will be affected by the error: Tsync2-Tsync1 = sk x (T2 - T1) depending on skew and T2-T1. To minimize this error it is~~pos- sible~~possibleto reduce the time interval T2-T1, but this could limit the generality of the metric. Methods for evaluating the synchronization error will be~~discus- sed~~discussedbelow, since they come from a statistic over a significant sample. If the measurement conditions do not allow~~to neglect~~neglectingthe drift,~~supposed as~~assumedlinear in the interval T2-T1, and having a value of "dr" expressed in ppm / sec., the ipdv error will become: Tsync2-Tsync1 = sk x (T2 - T1) + [dr x (T2-T1) x (T2-T1)] / 2~~It has to be noted that the presence of drift~~Driftvaries the skew value in the time. The limits in which the skew can vary are anyway limited and~~little,~~small,so that a given drift cannot act indefinitely. Section 7 and Appendix A provide more information on this point. + As far as accuracy and resolution are concerned, what is noted in the~~above referenced~~Draft on One-Way-Delay~~at~~[2] insection 3.7.1, applies also in this case, with the further consideration, about resolution, that in this case the uncertainty introduced is two times the one of a single delay measurement. Errors introduced by these effects are often larger than the ones introduced by the drift.~~I-D Ipdv Metric November 1998 5.6.2.~~5.7.2.Errors/uncertainties related to Wire-time vs Host-time The content of sec. 3.7.2 of~~the above referenced Draft~~[2]applies also in this case, with the following further consideration: The difference between Host-time and Wire-time can be in general~~de- composed~~decomposedinto two components,~~whose~~of whichone is constant and the other is~~variable around zero.~~variable.Only the variable components will produce~~measu- rement~~measurementerrors, while the constant one will be canceled while~~calcu- lating~~calculatingipdv. 6. Definitions for Samples of One-way ipdv Starting from the definition of the singleton metric of one-way ipdv,~~some ways of building~~| we definea sample of such~~singletons are here described. In particular two "discontinuous" samples and one "continuous" sample are defined, and the last one is proposed, being the most suitable for describing the aspect of the path's behavior underlined in the motiva- tion.~~singletons.In the following, the two|packets needed for a singleton measurement will be called a "pair".~~6.1. "Discontinuous" definitions~~|A~~general definition can be~~stream of test packets is generated wherethe~~following:~~second packet of a | pair is, at the same time, the first packet of the next pair. | +Given particular binding of the parameters Src,~~Dst, path,~~Dstand Type-P, a|sample of values of~~parameters~~parameterT1~~and T2~~is defined.~~The means for defining~~To definethe values|of~~T1 is to~~T1,select a beginning time T0, a final time Tf, and an average|rate lambda, then define a pseudo-random Poisson arrival process|of rate lambda, whose values fall between T0 and Tf. The time|interval between successive values of T1 will then average|1/lambda.~~Another si- milar, but independent, pseudo-random Poisson arrival process based on T0', Tf' and lambda', will produce a series of t' values. The time interval between successive t' values will then average 1/lambda'. For each~~From the second value on,T1 value~~that has been obtained by~~ofthe~~first process, it is then possible to calculate the successive~~pair n | coincides withT2~~values as the successive T1 values plus the successive intervals~~of~~t'. The result is shown in figure 1. This general definition is likely go give problems, if no limits are considered for the obtained values. For example,~~the~~emission time of~~pair n-1, andthe first packet of~~a pair, could fall before the emission time of~~pair n | coincides withthe second packet of the~~preceding pair. Probably this could be acceptable (provided that there are means to recognize pairs -e.g. I-D Ipdv~~pair n-1. | 6.1.Metric~~November 1998 use of sequence numbers-), but~~name Type-P-One-way-ipdv-stream 6.2. Parameters + Src,the~~concept itself of ipdv would be,at least, slightly changed. A way for avoiding this type~~IP addressof~~philosophical problems can be to give some rules on~~a host + Dst,the~~values~~IP address of a host +T0,a time +Tf,a time +lambda,~~T0', Tf', lambda', without changing the meaning~~a rate in reciprocal seconds 6.3. Metric Units: A sequenceof~~the metric. |<- average interval 1/lambda ->| | | |<- av.int. | |<- av.int. | |1/lambda'->| | 1/lambda'->| _____|___________|___________________|_____________|________ pair i pair i+1 Figure 1 As~~triads whose elements are: + T, a time + Ti, a time interval. + dT a real number oran~~example, it could be~~undefined number of seconds 6.4. Definition A pseudo-random Poisson process isdefinedsuchthat~~the~~it begins at or before T0, with average arrival rate lambda, and ends at or after Tf. Those time values T(i) greater than or equal to T0 and less than or equal to Tf are then selected. Starting from time T0, at each pair of times T(i), T(i+1) of thisprocessa value of Type-P-One-way-ipdv is obtained. The valueof~~sorting~~the~~interval between pairs starts after~~sample isthesequence made up of the resulting <time, time interval, ipdv> triple, where the timeinterval~~between packets in a pair~~is~~expired, obtaining~~given by T(i+1)-T(i). Each time T(i), excludingthe~~result~~first and the last, is therefore at the same time the the second time of pair i and the first timeofpair i+1. The result is shown infigure~~2: |<--- av. int.......| ..........................| 1/lambda --->| | | |<- av.int. | |<- av.int. | |1/lambda'->| | 1/lambda'->| _____|___________|___________________|_____________|________~~3 |T(i-2) |T(i-1) |T(i) |T(i+1) _____|__________|___________________|__________|________ pair i-1pair i pair i+1 Figure~~2 Still other problems can be envisaged with these two definitions which are described in some more detail in Appendix A. 6.2. A "continuous" definition A way for naturally avoiding the previous problems and producing~~3 6.5. Discussion Note first that, sincea~~testing environment closer to actual scenarios~~pseudo-random number sequenceis~~to adopt~~employed,the~~follo- wing "continuous" definition. A continuous stream~~sequenceof~~test packets can be supposed, where~~times, and hencethe~~second packet~~valueof~~a pair is, at the same time,~~the~~first packet~~sample, is not fully specified. Pseudo-random number generatorsofgood quality will be needed to achievethe~~next pair. Therefore the preceding definitions become: + Given particular binding~~desired qualities. The sample is defined in termsofa Poisson process both to avoidthe~~parameters Src, Dst, path,~~effects of self-synchronizationand~~Type-P,~~also capturea sample~~of values of parameter T1~~thatis~~defined. The means for defining the values~~statistically as unbiased as possible. {Comment: there is,of~~T1 is~~course, no claim that real Internet traffic arrives accordingto~~select a beginning time T0, a final time Tf, and an average rate lambda, then define~~a~~pseudo-random~~Poisson arrival~~process of rate lambda, I-D Ipdv Metric November 1998 whose values fall between T0 and Tf. The time interval between successive values of T1 will then average 1/lambda. From the second value on, T1 value of the pair n coincides with T2 of~~process.} 6.6. Methodology Since packets can be lost or duplicated or can arrive in a different order thanthe~~pair n-1, and~~order sent, in order to recognizethe~~first packet~~pairsof~~pair n coincides~~test packets, they should be markedwith~~the second packet of the pair n-1.~~a sequence number.Forduplicated packets onlythe~~moment, in the following, this last definition will~~first received copy shouldbe~~con- sidered. Further refinement is required and is for further discussion. 6.3. Metric name Type-P-One-way-ipdv-stream 6.4. Parameters + Src, the IP address of~~considered. Ifa~~host + Dst, the IP address~~packet is lost, two valuesof~~a host + Path, the path* from Src to Dst; in cases where there~~ipdv will be undefined, since each packetis~~only one path from Src~~commonto~~Dst, this optional parameter~~two pairs. Steps for measurementcan be~~omitted~~the following:+~~T0,~~Starting fromagiventime~~+ Tf,~~T, Src generatesa~~time + lambda,~~test packet as fora~~rate~~singleton metrics, insertsin~~reciprocal seconds 6.5. Metric Units: A sequence of triads whose elements are: + T,~~the packetasequence number and the transmission time stamp Tx, then sorts thetimeTi at which the next packet has to be sent.+~~Ti, a~~Attime~~interval.~~Ti, Src repeats the previous step, unless T(i) > Tf.+~~dT~~On reception of the first packet, or the first packet aftera~~real~~sequencenumber~~or an undefined~~error, Dst records sequencenumber~~of seconds 6.6. Definition A pseudo-random Poisson process is defined such~~and transmission timestampthat~~it begins at or before T0, with average arrival rate lambda, and ends at or after Tf. Those time values Ti greater than or equal to T0 and less than or equal to Tf~~are~~then selected. Starting from time T, at each pair of times T(i), T(i+1)of this process a value of Type-P-One-way-ipdv is obtained. The value of~~contained inthe~~sample is~~packet andthe~~sequence made up~~reception time Rx as "old values". + On receptionof the~~resulting <time, time interval, ipdv> triad, where~~other packets Dst verifiesthe~~time interval~~seuqence number and if itis~~given~~correct,by~~T(i+1)-T(i). Each obtained time T(i), excluding~~usingthe~~first~~"old values"and the~~last,~~newly received ones, a value of ipdvis~~therefore at~~computed. Then Dst recordsthenew sequence number, transmit and receive timestamps as "old values". 6.7. Errors and uncertainties Thesame~~time~~considerations apply that have been made aboutthesingleton metric. An additional error can be introduced bythe~~second time of pair i~~pseudo-random Poisson process as focused in [2]. Further considerations will be made in section 7,and~~the first time~~in Appendix A. 6.8. Distributionof~~pair i+1.~~One-way-ipdv values |The~~result is shown in figure 3 |T(i-2) |T(i-1) |T(i) |T(i+1) _____|__________|___________________|__________|________ pair i-1 pair i pair i+1 Figure 3 I-D Ipdv Metric November 1998 6.7. Discussion Note first that, since a pseudo-random number sequence is employed, the sequence~~one-way-ipdv values are limited by virtueof~~times,~~the fact that there | are upperand~~hence~~lower bounds on the one-way-delay values. Specifically, | one-way-delay is upper bounded bythe value~~of~~chosen asthe~~sample,~~maximum | beyond which a packetis~~not fully specified. Pseudo-random number generators of good quality will be needed to achieve the desired qualities. The sample~~counted as lost. Itis~~defined in terms of a Poisson process both to avoid the effects of self-synchronization~~lower bounded by | propagation, transmissionand~~also capture a sample~~nodal transit delays assumingthat~~is statistically as unbiased as possible. {Comment:~~|there~~is, of course,~~areno~~claim~~queues or variable nodal delays in the path. Denote the | upper bound of one-way-delay by U and the lower bound by L and we see |that~~real Internet traffic arrives according to a Poisson arrival process.} 6.8. Methodology Since packets~~one-way-ipdvcan~~be lost~~only take on values in the (open) interval (L- | U, U-L). | In any finite interval, the one-way-delay can vary monotonically | (non-increasingor~~duplicated~~non-decreasing)orof course itcan~~arrive~~varyin~~a different order with respect the one of emission,~~both | directionsin~~order to recognize~~the~~pairs of test packets, they should be marked with a Sequence Number or make use~~interval, within the limitsof~~any other tool suitable to~~the~~scope. For duplicated packets only~~half-open | interval [L,U). Accordingly, within that interval,the~~first received copy should be considered. If a pac- ket is lost, two~~one-way-ipdv |values~~of ipdv will~~canbe~~undefined, since each packet, in~~positive, negative, or a mixture (including 0). | Sincethe~~supposed "continuous" definition,~~range of valuesis~~common to two pairs. Steps~~limited, the one-way-ipdv cannot | increase or decrease indefinitely. Suppose,for~~measurement can be~~example, thatthe~~following: + Starting from a given time T, Src generates~~| ipdv hasa~~test packet as for~~positive 'run' (i.e.a~~singleton metrics, inserts~~long sequence of positive values). | At some pointinthis 'run',the~~packet a Sequence Number and the transmission Time Stamp Tx,then sorts~~positive values must approach 0 (or | become negative) ifthe~~time Ti at which~~one-way-delay remains finite. Otherwise,the~~next packet has to~~| one-way-delay bounds wouldbe~~sent. + At time Ti, Src repeats the previous step, unless T(i) > Tf. + On reception of the first packet, or the first packet after~~violated. If sucha~~SN error, Dst records SN and Tx timestamp that~~run were to | continue infinitely long, the sample mean (assuming no packetsare~~contained in~~| lost) would approach 0 (becausethe~~packet and~~one-way-ipdv values must approach | 0). Note, however, that this says nothing aboutthe~~reception time Rx as "old values". + On reception~~shapeof the~~other packets Dst verifies the SN and if~~| distribution, or whetherit is~~correct, by using the "old values" and~~symmetric. Note further that over | significant intervals, depending onthe~~newly received ones, a value~~widthof~~ipdv is computed. Then Dst records~~the~~new SN, Tx and Rx timestamps as "old values". 6.9. Errors and uncertainties The same considerations apply~~interval [L,U), |that~~have been made about~~the~~single- ton metric. An additional error can be introduced by the pseudo-ran- dom Poisson process as focused in the above referenced Draft. Further considerations will~~sample mean one-way-ipdv couldbe~~made in section 7, and in Appendix A. 6.10~~positive, negative or 0. 6.9.Some statistics for One-way-ipdv Some statistics are~~here considered, that~~suggested whichcan provide useful~~informa- -tion~~informationin|analyzing the behavior of the packets flowing from Src to~~Dst I-D Ipdv Metric November 1998 These statistics are given having in mind a practical use of them.~~Dst.The|focus is on the instantaneous behavior of the~~connection, while buffer dimensioning is not in the scope of this document.~~connection.Other|statistics can be defined if needed.~~6.10.1.~~6.9.1.Type-P-One-way-ipdv-inverse-percentile Given a Type-P-One-way-ipdv-Stream and a time threshold, that can be either positive or negative, the fraction of all the ipdv values in the Stream less than or equal to the threshold, if the threshold is positive, or greater or equal to the threshold if the threshold is~~ne- gative.~~negative.For many real-time services that require a regular delivery of the packets, this statistics can give the amount of packets received beyond acceptable limits.~~6.10.2 Type-P-One-way-ipdv-standard-deviation Given a Type-P-One-way-ipdv-Stream, the distribution of ipdv values is considered~~6.9.2. Type-P-One-way-ipdv-jitter | This metric was defined in [7]andis simplythe~~Standard Deviation can be calculated as an indication of regularity~~absolute valueof~~delivery. For practical purposes it~~| the Type-P-One-way-ipdv. Thiscan be~~useful~~usedto~~define~~derivea~~total standard deviation, computed over~~number of | metrics. | 7. Discussion on clock synchronization This section gives some considerations aboutthe~~com- plete set of value, and a standard deviation computed over the sub- set of those values that do not exceed given positive and negative thresholds. This allows a more accurate description of the performan- ce experienced by packets. Details on the shape of the ipdv distribu- tion are given in Appendix A. 6.10.3 Type-P-One-way-ipdv-average This statistic should tend to a value of ZERO for a number of ipdv values that tend to infinite. The behavior of Type-P-One-way-ipdv- average, and its meaning, are issues for the next section 7. 7. Discussion on clock synchronization This section gives some considerations about the need~~needof having~~syn- chronized~~synchronizedclocks at Src and Dst. These considerations are given as a basis for discussion, they require further investigation. We start from the analysis of the mean value of the ipdv distribution related to a "continuous" sample. Some more detailed calculations are presented in Appendix A.~~I-D Ipdv Metric November 1998~~7.1.~~Mean value~~Effectsof~~ipdv distribution. If D(i) is~~synchronization errors We refer here tothe~~delay~~two components that can generate this typeof~~packet "i", and ipdv(i) is~~errors that arethe~~i-th value~~reciprocal "skew" and "drift"of~~ipdv in~~the~~distribution~~Src and Dst clocks. It is firstof~~a sample~~all noted that the variable component "drift" is physically limited and its effects can be interpreted by saying that the total reciprocal skewof~~"n" values, collected with~~the~~described methodology, we~~two clockscan~~write: ipdv(1) = D1 - D0 .......... ipdv(i) = D(i) - D(i-1) .......... ipdv(n) = D(n) - D(n-1) The mean~~vary, ranging from a min to a max.valuein the time. This typeof~~ipdv distribution will result~~variation takes place very slowly being mostly connected to variationsin~~E(ipdv) = (D(n) - D(0))/n If an actual~~temperature. We suppose to perform ameasurement~~is performed,~~between a Src and a Dstthat~~lasts~~havea~~period~~reciprocal, initial skewof~~time long enough to contain~~"ts1" anda~~number "n" sufficiently large and, supposing synchronized clocks,~~reciprocal driftsuch~~that~~that, afterthe~~network conditions (traffic) allow to find a D(n) not too different from D(0), e.g. a~~time~~of n x 24 hours, E(ipdv) will tend to zero, since~~Tthe~~difference D(n) - D(0) will remain finite and little. 7.2. Effects of~~total skew is "ts2". It is not herea~~varying traffic If~~limitation to consider that atthe~~mean values~~beginningof~~delay D~~time T the two clocks indicate the same time T0. In order to analyze the effects produced by this situation we suppose that packetsare~~changing inside~~transferred, from Src to Dst, witha~~given period~~constant delay D In this conditions the measured ipdv should always be zero, and what is actually measured is the error. An ipdv value is measured at the beginningof~~time, for example they are increasing due to~~time T with two packets havingan~~increment~~intervalof~~traffic, we can consider, as a first approximation, the~~Ti(1).Anotheripdv~~values as decom- posed into~~value is measured at the end of T withtwo~~components, one being instantaneous and another one as~~packetshaving a~~constant rate dD and corresponding~~time interval Ti(2). On our purposes other errors (like wire-time vs host-time) are not considered since they are not relevant in this analysis, being commontoallthe~~increment "per interval" of~~measurement methods. It is then possible to calculatethe~~mean value~~valuesof~~D.~~the Tx and Rx timestamps as they are seen by the two clocks, and the related two ipdv values.The~~mean~~first ipdvvalue~~of the distribution~~will~~be shifted of the~~be: ipdv1 = ts1*Ti(1) + ((ts2-ts1)/T)*Ti(1) The second ipdvvalue~~dD corresponding to~~will be: ipdv2 = ts2*Ti(2) +((ts2-ts1)/T)*Ti(2) The error is given bythe~~mean value~~effectof theskew during the timeintervalTi(i)between~~test packets. This will happen only during~~the~~monotonic variation,~~two packets of the pair,and~~is not~~a~~distortion, since it is~~second order term due tothe~~record~~variationofthat skew inthe~~instantaneous behavior. When the conditions will come back~~same interval. If, as in the most of practical cases, the drift can be considered closetozero, then ts1 = ts2, andthe~~initial ones,~~error is not depending onthe~~distribution will resume a mean value around zero. As for~~time at whichthe~~case of drift, also in this case a monotonic varia- -tion cannot take place indefinitely.~~measurement is done.In~~Appendix A a method~~addition, this type of error can be corrected as itis~~given for subdividing~~indicated inthe~~variation into these two components over short periods,~~next paragraph and discussedin~~order to have indications~~Appendix A. In any case the maximum erroron~~variations of traffic condi- -tions. 7.3. Effects of synchronization errors We refer here~~an ipdv value will correspondto the~~two components that can generate this type~~effectof~~errors that are~~themaximumreciprocal~~"skew" and "drift" of~~skew onthe~~Src~~maximum interval between packets. 7.2. Related precision This means that: + If the skew is constantand~~Dst clocks. It~~is~~first of~~= tsall~~noted that~~the~~variable component "drift" I-D Ipdv Metric November 1998~~ipdv(i) values are increased by the quantity Ti(i)*ts with respect the actual value. The mean ipdv value will therefore increased of the quantity E[Ti(i)]*ts, whichis~~physically limited and its effects~~measured. Also E[Ti(i)]can be~~interpreted by saying~~measured, and should be related to lambda. That meansthat the~~total reciprocal~~skew~~of the two clocks~~tscan~~vary, ranging from~~be calculated. If together with ipdv(i), also the corresponding Ti(i) are collected, for each ipdv(i) valuea~~min to~~correcting term is available, anda~~max. value in the time. This type~~sampleof~~variation takes place very slowly being mostly connected to variations in temperature. We suppose to perform a measurement between~~"corrected" c-ipdv(i) values is obtained, where c-ipdv(i) = ipdv(i) - Ti(i)*st. + Considering the total skew as subdivided intoa~~Src~~fixed partand a~~Dst that have a reciprocal, initial skew of "ts1"~~variable part (skewand~~a reciprocal drift such that, after~~drift),respectively, ts and + or - td, fromthe~~time T~~mean ipdv value andthe~~total~~mean emission interval the averageskewcan be derived in the period of interest (Appendix A). The preceding correction can then be applied. The maximum residual error on an ipdv valueis~~"ts2". It is not here a limitation to consider that~~given by the difference between the actual skewat the~~beginning of~~time~~T~~in whichthe~~two clocks indicate~~value has been measured and the average skew, multiplied bythe~~same~~time~~T0. In order to analyze~~interval betweenthe~~effects produced by this situation we suppose that~~packetsthat have generated that ipdv value. Considerations on the number of values in the sample affected by errorsare~~transferred, from Src to Dst, with a constant delay D In this conditions~~reported in Appendix A. + Ifthe~~measured ipdv should always be zero, and what~~duration of the measurementis~~actually measured~~such that itispossible to | consider thatthe~~error. An~~ipdv~~value~~(without skew)is~~measured at~~close to zero,the~~beginning of time T with two packets having an interval~~mean valueof~~Ti(1).Another~~theipdvdistribution will have thevalue~~is measured at~~ofthe~~end~~average skew multiplied by the mean valueof~~T with two packets having a time interval Ti(2). On our purposes other errors (like wire-time vs host-time) are not considered since they are not relevant in this analysis, being common to all~~the~~measurement methods. It is then possible~~emission interval, as supposed above. + We observe that the displacement dueto~~calculate~~the~~values~~skew does not change the shapeof the~~Tx and Rx time- stamps as they are seen by~~distribution, and, for examplethe~~two clocks, and~~Standard Deviation remainsthe~~related two ipdv values. The first ipdv value will be: ipdv1 = ts1*Ti(1) + ((ts2-ts1)/T)*Ti(1) The second ipdv value will be: ipdv2 = ts2*Ti(2) +((ts2-ts1)/T)*Ti(2) The error~~same. What introduces a distortionis~~given by~~the effect of the~~skew during~~drift, also whenthe~~time inter- val Ti(i) between~~mean value of this effect is zero atthe~~two packets~~endof the~~pair, and a second order term due~~measurement. The value of this distortion is limitedto the~~variation~~effectof~~that~~the totalskew~~in~~variation onthe~~same~~emissioninterval.~~If,~~+ In what has been said, skew and drift have been consideredas~~in the most~~"reciprocal". In Appendix A it will be considered that eachof~~practical cases,~~thetwo clocks have a skew and adrift~~can be considered close to zero, then ts1 = ts2,~~with respect a "true time",andit will be observed thatthe~~error~~differenceis~~not depending on~~negligible with respectthe~~time at~~situation inwhichone ofthe~~measurement~~two clocksis~~done. In addition, this type of error can be corrected~~takenas~~it is indicated in the next paragraph and discussed in Appendix A. In any case~~the~~maximum error on an ipdv value will correspond to~~"true time". 8. Definition for a bidirectional ipdv metric We now consider thatthe~~effect~~actionof the~~maximum reciprocal~~skew on~~the maximum interval between packets. I-D Ipdv Metric November 1998 7.4. Related precision This means that: 1) + If the skew is constant and~~one directionis~~= ts all the ipdv(i) values are increased by~~the~~quantity Ti(i)*ts~~same,with~~respect~~opposite sign, ofthe~~actual value.~~action on the other direction.The~~mean ipdv value will therefore increased~~ideaofperforming atthe~~quantity E[Ti(i)]*ts, which is measured. Also E[Ti(i)] can be measured, and should be related to lambda. That means that the skew ts can be calculated. If together with ipdv(i), also~~same time two independent measurements inthe~~corresponding Ti(i) are collected, for each ipdv(i) value a correcting term~~two directionsis~~avai- -lable, and~~suggested by this fact. If, aftera~~sample~~long measurement, the variable conditionsof~~"corrected" c-ipdv(i) values is obtained, where c-ipdv(i) = ipdv(i) - Ti(i)*st. 2) + Considering~~the~~total skew as subdivided into a fixed part and~~system under test have reached the situation ofa~~variable part (skew and drift),respectively, ts and + or - td, from~~contribution close to zero tothe mean~~ipdv~~value~~and~~ofthe~~mean emission interval~~ipdv distribution, it is expected that only the action ofthe average skew~~can be derived in~~has modifiedthe~~period of interest (Appendix A). The preceding correction can then be applied. The maximum residual er- -ror~~measured mean value. It is therefore expected thaton~~an ipdv~~one direction thatvalue is~~given by the difference between the actual skew at the time in which~~equal and opposite tothe~~value has been~~onemeasured~~and~~inthe~~ave- -rage skew, multiplied by the time interval between the packets that have generated that ipdv value. Considerations on~~other direction. This fact offersthe~~number~~possibilityof~~values in the sample affected by errors are reported~~defining a theoretical reference measurement durationin~~Appendix A. 3) + If~~thefollowing way: The referenceduration of~~the~~a bidirectional ipdvmeasurementbetween an host E and an host Wisreached at time Tfsuch that~~it~~for each time T > Tf the expression ABS(E(ipdv E-W) - E(ipdv W-E))< epsilon, where epsilonis~~possible to~~what we canconsider~~that the effect of the items at points 7.1 and 7.2, are close to~~aszero,is always verified. This is one, but notthe~~mean value of~~only method for verifying thatthemeanipdv~~distribution will have~~value has reachedthe value of the average~~skew multiplied by~~reciprocal skew. At this point it is possible to evaluate the reciprocal skew. This will require the knowledge ofthe mean value of the~~emission interval, as supposed above. 4) + We observe~~intervals between consecutive packets,thatcan be calculated overthe~~displacement due to~~transmitted stream, by usingthe~~skew does~~collected time stamps. A bidirectional measurement can be definednot~~change~~only as twin one-way independent metrics that take place (nearly) atthe~~shape~~same time, but also as a two-way metric making use of packets looped back at one end. This metric, that can be objectoffurther study/Draft, would be able to measure alsothe~~distribution, and, for example~~Round Trip Delay and its variations. Problems will anyway arise onthe~~Standard Devi- ation remains~~characterization of emission intervals inthe~~same. What introduces a distortion is~~backward direction. They would be produced bythe~~effect~~combinationof the~~drift, also when~~original Poisson arrival process andthe~~mean value of this~~effect~~is zero at the end~~ofipdv onthe~~measurement. The value of~~forward direction. It has to be studied ifthis~~distortion~~sequence of intervalsis~~limited to~~still suitable forthe~~effect of~~measurement. also other possibilities can be envisaged for obtaining a proper backward sequence and still maintainthe~~total skew variation~~loopback concept. 9. Relationship to other standards | The ITU definitions are basedon~~the emission interval. 5) + In what has been said, skew and drift have been considered~~delay variationas~~reciprocal". In Appendix A it~~defined for ATM | cells [5]. Wewill~~be considered that each of~~discuss these briefly first and then discussthe| ITU's definition for IP packets [3]. | 9.1. 1-Point Cell Delay Variation | The ITU looks at cell delay variation fromtwo~~clocks have~~different points of | view. The first, called 1-point cell delay variation, is essentially |a~~skew and~~measure of howa~~drift with respect~~cell stream varies froma~~"true time", and it will be observed that the difference is negligible with respect~~stated cell rate (e.g. |the~~situation in which one of~~peak cell rate). The basic idea behindthe~~two clocks~~measurementis~~taken~~as| follows: The observer atthe~~"true time". I-D Ipdv Metric November 1998 8. Definition for~~measurement point notes cell arrival | times and clock ticks. The clock ticks ata~~bidirectional ipdv metric We now consider that the action of the skew~~constant rate, basedon~~one direction is the same, with opposite sign, of~~|the~~action on~~peak cell rate forthe~~other direction.~~cell stream.The~~idea of performing at~~difference betweenthe~~same time two independent measurements in~~| cell arrival times andthe~~two directions~~clock ticksis~~suggested by this fact. If, after a long measurement, the variable conditions of~~the~~system under test have reached the situation of~~1-point cell delay | variation. Ifa~~contribution close to zero to~~cell arrives later thanthe~~mean value of~~clock tick,the~~ipdv distribution, it is expected that only~~clock | "restarts" atthe~~action~~actual cell arrival time, and continues to tick at | a constant rate from that point. | The purposeof~~the average skew has modified the measured mean value. It~~this measureis~~therefore expected that on one direction that value~~to identify whatis~~equal~~called "cell | clumping"and~~opposite~~non-conforming cells. That is,toidenify cells that | violatethe~~one measured in the other direction. This fact offers~~leaky bucket parameters defined for that cell stream. | That is whythe~~possibility of defining~~clock skips whena~~theoretical reference measurement duration in~~cell is later thanthe~~following way: The reference duration~~normal | inter-cell time defined by the peak cell rate. It isof~~a bidirectional ipdv measurement between an host E~~much less | interest when cells are late than when they arrive too close | together. | 9.2. 2-Point Delay Variation, Cellsand~~an host W~~Packets | 2-Point cell delay variation, as defined in [5] is closer to what is | defined here. The basic idea behind this metricis~~reached at time Tf such~~that~~for~~two | measurement points, whose clocks are synchronized, observe a cell | stream and timestamp wheneach~~time T > Tf~~cell passes. The difference inthe~~expression ABS(E(ipdv E-W) - E(ipdv W-E))< epsilon, where epsilon~~| timestamps for a cellis~~what~~essentially the one-way delay. There is also | assumed to be a one-way cell delay for a reference cell whichwe~~can consider as zero,~~will | denote d0. The cell delay variation for the ith cellis~~always verified. This~~then di-d0. | Note that thisis~~one, but~~not~~the only method for verifying~~an absolute value, butthat the~~mean ipdv value has reached the value of~~cell delay | variation can be either positive or negative. [5] does not specify | how to choosethe~~average reciprocal skew. At this point it~~reference cell delay. | In [3] thereis~~possible~~an informative appendix describing packet delay | variation, which means that the material is not binding as a | standard. The definitions are very similarto~~evaluate~~[5] with "packet" | subsituting for "cell" in most places. One difference is that [3] | offers two ways to definethe~~reciprocal skew. This will require~~reference packet (withthe~~knowledge~~default | being the first): | + Take the delayof the~~mean value~~first packetof the~~intervals between consecutive packets, that can be calculated over~~sequence asthe~~trans- -mitted stream, by using~~| reference time. | + Takethe~~collected time stamps. A bidirectional measurement can be defined not only as twin~~averageone-way~~independent metrics that take place (nearly) at the same time, but also~~packet delayasthe reference time. | 9.3. Discussion | 9.3.1. Differences | Demichelis [4] points outa~~two-ways metric making use of packets looped back at one end. This metric, that can be object~~numberof~~further study/Draft, would be able to measure also the Round Trip Delay and its variations. Problems will anyway arise on~~problems withthe~~characterization of emission intervals~~2-point PDV | definitionin~~the backward direction. They would be produced by the combination~~[3]. Firstofall isthe~~original Poisson arrival process and the effect~~issueof~~ipdv on~~choosingthe~~forward direction. It has to be studied if~~| reference delay time. Ifthis~~sequence of intervals~~is~~still suitable for~~chosen arbitrarily, it becomes | uncertain how to comparethe~~measurement. also other possibilities~~measurements taken from two non- | overlapping periods. If it is chosen as an average, thatcanalsobe~~envisaged for obtaining~~|a~~proper backward sequence and still maintain~~problem, because over long periods of time in a network,the~~loopback concept. I-D Ipdv Metric November 1998 9. References V.Paxon, G.Almes, J.Mahdavi, M.Mathis - "Framework for IP Performance Metrics", Internet Draft <draft-ietf-ippm-framework-01.txt> Feb. 1998 G.Almes, S.Kalidindi - "A One-Way-Delay Metric for IPPM", Internet Draft <draft-ietf-ippm-delay-01.txt> Nov. 1997 10. Author's Address Carlo Demichelis <carlo.demichelis@cselt.it> CSELT - Centro Studi E Laboratori Telecomunicazioni S.p.A Via G. Reiss Romoli 274 10148 - TORINO Italy Phone +39 11 228 5057 Fax. +39 11 228 5069 I-D Ipdv Metric November 1998 APPENDIX~~| average one-way delay can vary widely.A~~This Appendix considers~~twenty-four hour average as |the~~scenario in which two hosts have clocks that are both not synchronized. Between~~reference time can seriously overestimatethe~~two hosts, in an inde- -pendent way and~~actual delay | variationat~~the same~~a giventime~~in both direction an ipdv measure- -ment is performed according the methodology that is described in the main body~~of~~this Draft. This hypothetical scenario is only supposed for discussing the theory and~~day becausethe~~characteristics of~~night-time hours, when |the~~ipdv metric and its results, without considering implementation issues. A.1 - Initial positions The two hosts will~~delay canbe~~called West (W) and East (E). The two measure- -ments start at~~expected to approachthe~~same~~propagation and nodetime,~~while~~| is included inthe~~end of~~average. Onthe~~measurement it~~other hand, thereis~~supposed~~no clear way |to~~be decided by the results of the measurement itself. At the beginning of the measurement~~partitionthe time~~declared by the West clock is T0w, the~~in order to find averages for certain periods | oftime~~declared by~~and computethe~~East clock~~delay variation with reference to these | averages. | Another problem pointed out in [4]is~~T0e, while~~the~~true time is T0t. The W-clock is affected by an absolute skew of skw ppm and~~fact that 2-point PDV | requires synchronized clocks, whereas in this document Demichelis | shows that synchronized clocks are not absolutely necessary for ipdv. | 9.3.2. Relationship betweenthe~~E-clock by an absolute skew of skw ppm.~~metrics |The~~W-clock~~ipdv metric described here and the 1-point cell delay variation | metric described in [5] do not really have much in common (see also | [4]). 1-point delay variationis~~affected by an absolute drift ranging from -drw ppm~~really intendedto~~+drw ppm,~~talk aboutthe~~E-clock by an absolute drift ranging from -dre ppm to +dre ppm. A.2 - Evaluation~~| relationshipof~~skew and drift effects In order~~cell arrival timesto~~evaluate the effect of the drift on this type of metric, it~~a given periodic event, and | consequentlyis~~necessary~~more closely relatedto~~consider the time in which~~the~~variation~~first definitionof~~the skew takes place. We consider the two extreme cases~~| "jitter" givenin~~which the~~Section 3 above. | 2-point delayvariation~~takes place uniformly from~~(actually,the~~beginning~~packet variant described in | [3]) is relatedtoipdv, and this relationship can be made precise as | follows: Suppose that an arbitrarily chosen packet is designated as |the~~end of~~reference packet forthe2-pointmeasurement andalso asthe~~variation takes place suddenly at a generic time along~~| start packet oftheipdvmeasurement.~~Let TM be the measurement time. A.2.1 - Mean~~Denote this packet by p(0). | Then givenipdv~~value Since~~measurements for a series of packets,the~~mean ipdv value, as it has been seen,~~2-point | delay variation for packet iisp(0) +the~~difference~~sum from k=1 to iof~~the last~~| ipdv(k). | Similarly, given a sequence of 2-pointdelay~~minus~~variation measurements | we can derivethe~~first, divided by~~ipdv measurement as follows: Denotethe~~number of considered values, we consider what, in the two cases, is measured~~2-point | delay variation measurementfor~~first and last delay. We call trueDf the true first Delay and trueDl~~packet i as v(i). Thenthe~~true last Delay. I-D Ipdv Metric November 1998 For~~ipdv value | forthe~~evaluation that we want to do, it~~pair of packets p(k-1), p(k)is~~not a limitation to con- -sider that they~~simply v(k)-v(k-1) [6]. | 9.3.3. Summary | As described above, thereare~~equal and have~~a~~value~~number of disadvantagesof~~trueD. We also consider as time 0~~the~~true time at which~~| 2-point packet delay variation approach. Further,the~~transmission of~~ipdv approach | described here is general enough to providethe~~first~~same information as | the 2-pointpacket~~starts from West toward East. In case~~delay variation measurements. Becauseof~~continuous drift we define a "drift per second" as: drpsW = 2*drw / TM~~this,and~~drpsE = 2*dre / TM along the measurement this will bring~~| because ofthe~~skew from a value of: skWmin = skw - drw ; skEmin = ske - dre to a value~~(possibly) looser clock synchronization requirements |of~~skWmax = skw + drw ; skEmax = ske + dre What is measured as first Delay is: measured first Rx time - measured first Tx time OffsetEast + trueD*[1 + skEmin + (1/2)*drpsE] - OffsetWest What is measured as last Delay is: measured last Rx time - measured last Tx time OffsetEast + (TM + trueD)*[1 + skEmin + (1/2)*2*dre] - - OffsetWest - TM*[1 + skWmin + (1/2)*2*drw]~~ipdv, we recommend the one-way-ipdv approach for the delay | variation measurement. | 10. Security Considerations |The~~difference between~~one-way-ipdv metric hasthe~~last~~same security properties as the one- | way-delay metric [2]. The packets contain no user information,and~~first Delay~~so | privacy of user datais~~therefore: TM*(skEmin - skWmin + dre - drw) - trueD*drpsE/(2*TM) if TM = 10 hours drpsE~~not a concern. Itis~~in the order of 50*10E-6 / 36000~~still possiblethat~~is about 10E-9 and the second term~~| there could be an attempt at a denialofservice attack by sending | many measurement packets intothe~~expression is~~network; there could also be | attempts to disrupt measurements by diverting packets or corrupting | them. | In general, legitimate measurements must have their parameters | selected carefullyin~~the~~order~~of 10E-14 for true delays~~to avoid interfering with normal traffic |in the~~order of 1 sec (negligible term). We consider that, with very good approximation: Mean emission interval (mti) = TM / number~~network. Such measurements should also be authorized and | authenticated in some way so that attacks can be identified and | intercepted. | 11. Acknowledgements | Thanks to Matt Zekauskas from Advanced and Ruediger Geib from | Deutsche Telekom for discussions relating to the contentsof~~ipdv values (N) Therefore: mean ipdv = (measured last Delay~~this | revised draft. | 12. References | [1] V.Paxon, G.Almes, J.Mahdavi, M.Mathis-~~measured first Delay) / N = = mti*(skEmin~~"Framework for IP | Performance Metrics", RFC 2330 Feb. 1998 | [2] G.Almes, S.Kalidindi-~~skWmin + dre~~"A One-Way-Delay Metric for IPPM", | Internet Draft <draft-ietf-ippm-delay-07.txt> May 1999 | [3] Draft New ITU-T Recommendation I.380 "Internet Protocol Data | Communication Service-~~drw) but we considered skEmin = ske~~IP Packet Transfer and Availability | Performance Parameters" | [4] Demichelis, Carlo-~~dre~~"Packet Delay Variation Comparison between | ITU-Tand~~skWmin = skw~~IETF Draft Definitions" March 1999 | [5] ITU-T Recommendation I.356 "B-ISDN ATM Layer Cell Transfer | Performance" | [6] e-mail exchanges with Ruediger Geib | [7] V. Jacobson, K. Nichols, K. Poduri - "An expedited forwarding | PHB", Internet Draft, November 1998 <draft-ietf-diffserv-phb- | ef-01.txt> | 13. Authors' Addresses | Carlo Demichelis <carlo.demichelis@cselt.it> CSELT-~~drw and therefore: mean ipdv = (meas.lastD~~Centro Studi E Laboratori Telecomunicazioni S.p.A Via G. Reiss Romoli 274 10148-~~meas.firstD) / mti*(reciprocal mean skew)~~TORINO Italy Phone +39 11 228 5057 Fax. +39 11 228 5069 Philip Chimento <chimento@ctit.utwente.nl> CTIT - Centre for Telematics and Information Technology University of Twente Postbox 217 7500 AE EnschedeThe~~previous procedure is now applied to~~Netherlands Phone +31 53 489 4331 FAX +31 53 489 4524 APPENDIX A This Appendix considersthe~~case~~scenarioin whichtwo hosts have clocks that are both not synchronized. Betweenthe~~total drift takes place~~two hosts,in~~a very short time. Some cases are possible,~~an independent wayand~~we consider~~atthe~~one~~same timein~~which at~~both direction an ipdv measurement is performed accordingthe~~beginning~~methodology that is described inthe~~West clock has skWmax~~main body of this Draft. This hypothetical scenario is only supposed for discussing the theoryand the~~East clock has skEmin, at time txW~~characteristics oftheipdv metric and its results, without considering implementation issues. 14. Initial positions The two hosts will be calledWest~~clock assumes skWmin~~(W)andEast (E). The two measurements startat~~time txE~~the~~East clock assumes skEmax. I-D Ipdv Metric November 1998 What is measured as first Delay is now: measured first Rx time - measured first Tx time OffsetEast + trueD*(1 + skEmin) - OffsetWest What~~same time, while the end of the measurement itis~~measured as last Delay is: measured last Rx time - measured last Tx time + OffsetEast + txE*(1 + skEmin) + (TM - txE)*(1 + skEmax) + + trueD*(1 + skEmax) - - OffsetWest - txW*(1 + skWmax) - (TM - txW)*(1 + skWmin) but~~supposed to be decided bythe~~mean skew values will be: mskw = [skWmax*txW + skWmin*(TM - txW)] / TM mske = [skEmin*txE + skEmax*(TM - txE)] / TM~~results ofthe~~difference between~~measurement itself. Atthe~~two delays therefore is: TM*(mske - mskw) + 2*trueD*dre~~beginning of the measurement the time declared by the West clock is T0w, the time declared by the East clock is T0e, while the true time is T0t. The W-clock is affected by an absolute skew of skw ppmand the~~mean ipdv value will be: mean ipdv = mti*(mske - mskw) + 2*mti*trueD*dre/TM~~E- clock by an absolute skew of skw ppm. The W-clock is affected by an absolute drift ranging from -drw ppm to +drw ppm,the~~second term~~E-clock by an absolute drift ranging from -dre ppm to +dre ppm. 14.1. Evaluationofskew and drift effects In order to evaluatethe~~second member in~~effect ofthe~~previous hypotheses~~drift on this type of metric, itisnecessary to consider the timeinwhichthe~~order~~variationof the~~nanosecond, and we neglect it. Also~~skew takes place. We consider the two extreme casesin~~this case, from~~whichthe~~mean ipdv value, and knowing~~variation takes place uniformly fromthe~~mean emission interval,~~beginning tothe~~rela- -tive skew~~endof the~~clocks can be obtained. More in general, independently on how~~measurement andthe~~drift acts inside its limits, we assert that always~~variation takes place suddenly at a generic time alongthe~~mean~~measurement. Let TM be the measurement time. 14.1.1. Meanipdv value~~divided by~~Sincethe mean~~emission interval produces the value of~~ipdv value, as it has been seen, isthe~~mean reciprocal skew~~differenceof the~~two clocks, provided that~~last delay minus the first, divided bythe~~collected~~number of~~ipdv values~~considered values, we consider what, in the two cases,is~~signi- -ficant~~measuredforfirst and last delay. We call trueDfthe~~statistics. A.2.2 - Errors~~true first Delayand~~corrections If~~trueDlthe~~drift is always close~~true last Delay. For the evaluation that we wantto~~zero,~~do,it is~~possible~~not a limitationto~~obtain the true~~consider that they are equal and have avalue oftrueD. We also consider as time 0the~~reciprocal skew and correct all~~true time at whichthe~~ipdv values. Each~~transmissionof~~them is associated to an emission interval ti between~~the~~two packets that have produced~~first packet starts from West toward East. In case of continuous drift we define a "drift per second" as: drpsW = 2*drw / TM and drpsE = 2*dre / TM alongthe~~value itself. Then~~measurement this will bring the skew froma~~better ipdv~~value~~will be: corr.ipdv(i)~~of: skWmin=~~meas.ipdv(i)~~skw-~~ti * skew This is~~drw ; skEmin = ske - dre toa~~better~~value~~but not exactly the true one, since we supposed that both clocks are not synchronized to the true time. Two errors are affecting the corrective terms which are: I-D Ipdv Metric November 1998~~of skWmax = skw + drw ; skEmax = ske + dre What is measured as first Delay is: measured first Rx time - measured first Tx time OffsetEast + trueD*[1 + skEmin + (1/2)*drpsE] - OffsetWest What is measured as last Delay is: measured last Rx time - measured last Tx time OffsetEast + (TM+trueD)*[1 + skEmin + (1/2)*2*dre] - - OffsetWest - TM*[1 + skWmin + (1/2)*2*drw]The~~reciprocal skew is measured as referred to~~difference betweenthe~~Src clock~~last and first Delay is therefore: TM*(skEmin - skWmin+~~The interval ti~~dre - drw) - trueD*drpsE/(2*TM) if TM = 10 hours drpsEis~~measured by the Src clock. These are second order errors since the measured skew will be affected by a "relative" error~~in the order of~~the Src skew, an the same is for the error affecting the ti value. If the drift~~50*10E-6 / 36000 thatis~~significant~~about 10E-9and~~it can range from the lower to the upper limit of its field, the measured average of the skew will depend on~~the~~type~~second termof~~variation. Some cases are considered that demonstrate that actually~~the~~proposed correction~~expressionis~~not so much effective~~in~~this case. Only~~the~~fixed part~~orderof~~the total clock variation can be properly corrected. A.2.2.1 - Constant drift The first case is the first one considered~~10E-14 for true delaysin the~~preceding paragraph, where the drift is uniform.~~order of 1 sec (negligible term).We~~suppose that a reciprocal skew is measu- -red and used for correction. At the beginning~~consider that, with very good approximation: Mean emission interval (mti) = TM / numberof~~the measurement the actual reciprocal skew is: init.skew~~ipdv values (N) Therefore: mean ipdv=~~mean.skew~~(measured last Delay-~~rel.max.drift~~measured first Delay) / N = = mti*(skEmin - skWmin + dre - drw) but we considered skEmin = ske - dreand~~at the end the actual reciprocal skew is: final.skew~~skWmin = skw - drw and therefore: mean ipdv=~~mean.skew + rel max.drift~~(meas.lastD - meas.firstD) / mti*(reciprocal mean skew)The~~correction~~previous procedureis~~effective only~~now applied to the caseinwhichthe~~central part of~~total drift takes place in a very short time. Some cases are possible, and we considerthe~~measurement. At~~one in which atthe beginningthe West clock has skWmaxand~~at~~the~~end a residual error will affect~~East clock has skEmin, at time txWthe~~ipdv values whose value will be: ipdv(i).err = ti * rel.max.drift We underline here that~~West clock assumes skWmin and at time txEthe~~error~~East clock assumes skEmax. Whatis~~larger for large intervals ti and lower for short intervals ti. For intervals derived from a poissonian arrival process, there are many short intervals and few large intervals. We also note that a constant drift cannot last indefinitely, since there~~measured as first Delayis~~a minimum and a maximum for the skew. A.2.2.2~~now: measured first Rx time-~~Step of drift In this case the error profile depends on the~~measured first Txtime~~at which the drift changes. If the change~~OffsetEast + trueD*(1 + skEmin) - OffsetWest Whatis~~near~~measured as last Delay is: measured last Rx time - measured last Tx time + OffsetEast + txE*(1 + skEmin) + (TM - txE)*(1 + skEmax) + + trueD*(1 + skEmax) - - OffsetWest - txW*(1 + skWmax) - (TM - txW)*(1 + skWmin) butthe~~beginning or near~~mean skew values will be: mskw = [skWmax*txW + skWmin*(TM - txW)] / TM mske = [skEmin*txE + skEmax*(TM - txE)] / TMthe~~end of~~difference betweenthe~~measurement,~~two delays therefore is: TM*(mske - mskw) + 2*trueD*dre andthe~~calculated~~mean~~skew~~ipdv valuewill~~be very close to the actual skew of~~be: mean ipdv = mti*(mske - mskw) + 2*mti*trueD*dre/TMthe~~largest part~~second termof the~~measurement. On that part the correc- -tion will be effective, while over the remaining few values the error will be twice with respect~~second member inthe~~preceding case. I-D Ipdv Metric November 1998 The worse condition~~previous hypothesesis~~produced by a change in drift~~in the~~middle~~orderof the~~measurement. In~~nanosecond, and we neglect it. Also inthis~~case~~case, fromthe~~correction would be useful only if~~mean ipdv value, and knowingthe~~drift was significantly less than~~mean emission interval,the~~skew. A.3 - Comparison with a synchronized case In this section we consider a case~~relative skew of the clocks can be obtained. Morein~~which~~general, independently on howthe~~two hosts have synchro- -nized clocks, and~~drift acts inside its limits, we assert that alwaysthe~~synchronization is obtained~~mean ipdv value dividedby~~setting~~the~~real time each second in each~~mean emission interval produces the valueof the~~clocks. We optimistically suppose~~mean reciprocal skew of the two clocks, providedthat~~this~~the collected number of ipdv valuesis~~done exactly (without any imprecision). On~~significant forthe~~clocks, anyway skew~~statistics. 14.1.2. Errorsandcorrections If thedrift~~continue to act. We refer to reciprocal skew and drift, having already seen that this~~is~~significant. We suppose~~always closeto~~perform an ipdv measurement and we evaluate what~~zero, itis~~measured by~~possible to obtainthe~~mean ipdv~~truevalue~~and what is~~ofthe~~error on~~reciprocal skew and correct allthe~~measured~~ipdv values.~~We notice, first of all, that nothing changes for ipdv values measured over intervals falling completely between two synchronization instants. In this case, the effect~~Eachof~~synchronization~~themis~~only to put~~associatedto~~zero~~an emission interval ti betweenthe~~offset,~~two packetsthat~~does not appear in~~have producedthe~~calculation of~~value itself. Then a betteripdv~~values. Something different happens if~~value will be: corr.ipdv(i) = meas.ipdv(i) - ti * skew This is a better value but not exactlythe~~synchronization instant (or more synchronization instants) falls inside~~true one, since we supposed that both clocks are not synchronized tothe~~interval. In this case~~true time. Two errors are affectingthe~~error can range from~~corrective terms which are:+The reciprocal skew is measured as referredto~~-~~the~~error related to one second interval, or, more in general, from~~Src clock+~~to - the error related to an~~Theinterval~~equal to~~ti is measured bythe~~synchronization period. The (few) large intervals~~Src clock. These are second order errors since the measured skewwill~~produce~~be affected bya~~limited~~"relative"error~~while~~inthe~~(many) short intervals will continue to produce errors~~orderof theSrc skew, an thesame~~order of magnitude of~~is forthe~~not synchronized case. Besides, even if~~error affecting the ti value. Ifthe drift is~~negligible,~~significant and it can range fromthe~~mean ipdv value is no more suitable~~lowerto~~calculate~~the~~skew, and it will be much more close to zero. Therefore it~~upper limit of its field, the measured average of the skew will depend on the type of variation. Some cases are considered that demonstrate that actually the proposed correctionis~~no more possible to correct~~not so much effective in this case. Onlythe~~distortion~~fixed partof the~~distribution. Finally, it~~total clock variation can be properly corrected. 14.1.3. Constant drift The first caseis~~necessary to add to these errors~~the~~unavoidable impre- cision of~~first one considered inthe~~synchronization process.~~preceding paragraph, where the drift is uniform.We~~have to consider~~supposethata reciprocal skew is measured and used for correction. Atthe~~magnitude~~beginningof~~errors introduced by~~the measurement the actual reciprocalskewis: init.skew = mean.skew - rel.max.driftand~~drift~~at the end the actual reciprocal skew is: final.skew = mean.skew + rel max.drift The correctioniseffective onlyin the~~order of tenth~~central partof~~microseconds. Not always~~the~~complete synchronization process has a better precision. A.4 - Bidirectional measurement~~measurement. At the beginningand~~components of ipdv Three terms have been described that can displace~~at the end a residual error will affectthe~~mean~~ipdvvalues whosevalue~~from zero. They are: I-D Ipdv Metric November 1998 - The total skew, already discussed above,~~will be: ipdv(i).err = ti * rel.max.drift We underline herethat~~always acts in an equal way and opposite direction over~~the~~two directions between West~~error is larger for large intervals tiand~~East hosts. - The effect of varying traffic that can increase or decrease along limited periods, the average value of the One-Way-Delay. The metric above presented supposes~~lower for short intervals ti. For intervals derived from a poissonian arrival process, there are many short intervals and few large intervals. We also notethat~~the measurement period~~a constant drift cannot last indefinitely, since thereis~~large enough~~a minimum and a maximumfor~~considering~~the skew. 14.1.4. Step of drift Inthis~~effect as tending to zero. It is explicitly noted that~~casethe~~effect will produce a zero effect only~~error profile dependson the~~mean ipdv value, while~~time at whichthe~~effect on values ipdv(i) is always present. This is not a distortion of~~drift changes. Ifthe~~distribution, since~~changeis~~part of~~nearthe~~variation that is measured. This effect is different, and usually concordant, on~~beginning or nearthe~~two directions. - The difference between first and last instantaneous values~~endof the~~delay variation, that tends~~measurement, the calculated mean skew will be very closeto~~zero when~~the~~number~~actual skewof~~collected ipdv values becomes large. In order to isolate~~the~~last two effects, we consider here a measurement over a long period (e.g. 24 hours)where~~largest part ofthe~~drift is negligible, and~~measurement. On that partthe~~effect of~~correction will be effective, while overthe~~skew has been corrected. A.4.1 - Slow variation in a given period The packets of~~remaining few valuesthe~~stream can~~error willbe~~represented on a system of cartesian orthogonal axes~~twicewith~~transmission time on x-axis and reception time on y-axis, by points localized~~respect the preceding case. The worse condition is producedby~~transmission and reception time of each packet. Considering an arbitrary period~~a change in drift in the middleof~~time Tper, which will~~the measurement. In this case the correction wouldbeuseful only if the drift was significantly less than the skew. 14.2. Comparison witha~~parameter of~~synchronized case Inthis~~procedure, it can be taken as~~section we considera~~sliding window over~~case in whichthe~~sample~~two hosts have synchronized clocks,and~~for~~the synchronization is obtained by setting the real time each second ineach~~position~~ofthe clocks. We optimistically suppose thatthis~~window, established~~is done exactly (without any imprecision). On the clocks, anyway skew and drift continue to act. We refer to reciprocal skew and drift, having already seen that this is significant. We suppose to perform an ipdv measurement and we evaluate what is measuredby~~suc- -cessive packets,~~the~~segment of straight line~~mean ipdv value and whatis~~calculated that best approximate~~the~~points, by means of a linear regression method. The slope~~error on the measured ipdv values. We notice, firstofall, that nothing changes for ipdv values measured over intervals falling completely between two synchronization instants. Inthis~~segment will be one if along the period~~case,the~~delay has not changed, and different from one if that delay has increased (>1) or decreased (<1). For each position~~effectof~~the window it~~synchronizationis~~therefore possible~~onlyto~~find a value~~put to zero the offset, that does not appear in the calculationof~~"slow delay variation" with Tper as a parameter. This will give an indication on variations produced by~~ipdv values. Somethingdifferent~~traffic conditions along~~happens ifthe~~measurement period. This item can be subject for further study. At~~synchronization instant (or more synchronization instants) falls insidethe~~same time~~interval. Inthis~~procedure offers a criterion for reducing~~case the error can range from + to -the error~~introduced~~related to one second interval, or, moreingeneral, from + to -the~~calculation of~~error related to an interval equal tothe~~mean ipdv by~~synchronization period. The (few) large intervals will produce a limited error whilethe~~instanta- -neous component~~(many) short intervals will continue to produce errorsof the~~difference between last and first delay. Supposing that the timestamps, on which~~same order of magnitude ofthe~~metric is based, are collected and then processed,~~not synchronized case. Besides, evenif the~~method of~~drift is negligible,the~~sliding window~~mean ipdv valueis~~applied at~~no more suitable to calculatethe~~beginning~~skew,and~~at~~it will be much more close to zero. Therefore it is no more possible to correctthe~~end~~distortionof the~~collected sample,~~distribution. Finally,it is~~possible~~necessaryto~~avoid starting and ending~~add to these errorsthe~~measurement on values possibly too different from~~unavoidable imprecision ofthe~~average (points too far away from~~synchronization process. We have to consider thatthe~~calculated straight line). I-D Ipdv Metric November 1998 A.5 - Symmetry~~magnitudeof~~an ipdv distribution~~errors introduced by skewand~~emission intervals It~~driftis~~demonstrated that, if~~inthe~~packets~~orderoftenth of microseconds. Not alwaysthe~~test sequence are pro- pagated~~complete synchronization process has a better precision. 14.3. Bidirectional measurement and components of ipdv Three terms have been described that can displace the mean ipdv value from zero. They are: + The total skew, already discussed above, that always actsin an~~independent way, in~~equal way and opposite direction over the two directions between West and East hosts. + The effect of varying traffic that can increase or decrease along limited periods, the average value ofthe~~sense~~One-Way-Delay. The metric above presented supposesthat~~none of them~~the measurement periodis~~influenced by~~large enough for considering this effect as tending to zero. It is explicitly noted thatthe~~preceding packets (large emission intervals),~~effect will produce a zero effect only onthemeanipdv~~distribution will be perfectly symmetrical. If~~value, whilethe~~variation~~effect on values ipdv(i) is always present. This is not a distortionof the~~delay~~distribution, sinceis~~such~~part of the variationthat~~some packets~~is~~delayed by~~measured. This effect is different, and usually concordant, onthe~~preceding one (ideal- -ly queued to it in a buffer),~~two directions. + The difference between first and last instantaneous values ofthe~~related ipdv value generated will have a lower limit,~~delay variation,that~~will be~~tends to zero whenthe~~negative value~~numberofcollected ipdv values becomes large. In order to isolatethe~~emission interval minus the time required for transmitting~~last two effects, we consider here a measurement over a long period (e.g. 24 hours)wherethe~~packet from~~drift is negligible, andthe~~buffer. If~~effect ofthe~~intervals were constant, this would correspond to~~skew has been corrected. 14.4. Slow variation ina~~well defined value, that would allow to measure the bandwidth~~given period The packetsof the~~bottle- -neck provided~~stream can be represented on a system of cartesian orthogonal axes with transmission time on x-axis and reception time on y-axis,by~~the output~~points localized by transmission and reception timeof~~that buffer. Since the intervals are derived from~~each packet. Considering an arbitrary period of time Tper, which will bea~~poissonian arrival process,~~parameter ofthis~~limit is not~~procedure, it can be taken asa~~fixed one,~~sliding window over the sampleand~~is not immediately evident~~for each positionofthis window, established by successive packets,the~~ipdv distribution. Another effect~~segmentof~~this interference among packets~~straight lineiscalculatedthat~~also the packet following~~best approximatethe~~queued one will produce~~points, by means ofa~~lower ipdv value since it~~linear regression method. The slope of this segmentwill~~"gain"~~be one if alongthe~~time of latency in~~periodthe~~buffer~~delay has not changed, and different from one if that delay has increased (>1) or decreased (<1). For each positionof the~~previous one. The total effect~~window itis~~that the ipdv values will tend~~therefore possibleto~~concentrate on the negative side~~find a valueof~~the distribution,~~"slow delay variation"with~~some limitation~~Tper as a parameter. This will give an indicationonvariations produced by different traffic conditions alongthe~~negative maximum values. In other words, the negative side of the distribution will~~measurement period. This item canbe~~shorter than~~subject for further study. Atthe~~positive one, but containing more values. Nothing changes~~same time this procedure offers a criterionforreducingthe~~meaning~~error introduced in the calculationof the mean ipdv~~value. This asymmetry is not a distortion, since represents the actual propa- -gation characteristics. For~~bythe~~supposed type~~instantaneous componentof~~intervals,~~the~~dis- -tribution~~difference between last and first delay. Supposing that the timestamps, on which the metricis~~always asymmetrical, since always~~based,are~~present intervals lower than the delay variability,~~collectedandthen processed, ifthe~~degree~~methodof~~asymmetry will change with~~the~~level of interference. The relationship between asymmetry~~sliding window is applied at the beginningandatthe~~combination~~endof~~average emis- -sion interval and available bandwidth can be investigated~~the collected sample, it is possible to avoid startingand~~could provide information about~~endingthe~~level of congestion of~~measurement on values possibly too different from the average (points too far away fromthe~~network~~calculated straight line). | Expiration date: December, 1999