Network Working Group                                      A. Jayasumana
Request for Comments: 5236                     Colorado State University
Category: Informational                                       N. Piratla
                                                   Deutsche Telekom Labs
                                                                T. Banka
                                               Colorado State University
                                                                 A. Bare
                                                              R. Whitner
                                              Agilent Technologies, Inc.
                                                               June 2008
                   Improved Packet Reordering Metrics

Status of This Memo


This memo provides information for the Internet community. It does not specify an Internet standard of any kind. Distribution of this memo is unlimited.




The content of this RFC was at one time considered by the IETF, and therefore it may resemble a current IETF work in progress or a published IETF work. The IETF standard for reordering metrics is RFC 4737. The metrics in this document were not adopted for inclusion in RFC 4737. This RFC is not a candidate for any level of Internet Standard. The IETF disclaims any knowledge of the fitness of this RFC for any purpose and in particular notes that the decision to publish is not based on IETF review for such things as security, congestion control, or inappropriate interaction with deployed protocols. The RFC Editor has chosen to publish this document at its discretion. Readers of this RFC should exercise caution in evaluating its value for implementation and deployment. See RFC 3932 for more information.

このRFCの内容は、IETFによって考慮一度だったので、それが進行または公開されたIETF仕事で現在IETFの作業に似ていてもよいです。並べ替えメトリックのIETF標準このRFCはインターネットStandardのどんなレベルの候補ではないこの文書に記載されているメトリックはRFC 4737.に含めるために採用されなかったRFC 4737.です。 IETFは、いかなる目的のためにと、公開する決定が展開されたプロトコルとセキュリティ、輻輳制御、または不適切な相互作用のようなもののためにIETFレビューに基づいていない特定のノートに、このRFCのフィットネスの知識を負いません。 RFC Editorはその裁量でこの文書を公開することを選択しました。このRFCの読者は実現と展開のためにその値を評価する際に警戒する必要があります。詳細については、RFC 3932を参照してください。



This document presents two improved metrics for packet reordering, namely, Reorder Density (RD) and Reorder Buffer-occupancy Density (RBD). A threshold is used to clearly define when a packet is considered lost, to bound computational complexity at O(N), and to keep the memory requirement for evaluation independent of N, where N is the length of the packet sequence. RD is a comprehensive metric that captures the characteristics of reordering, while RBD evaluates the sequences from the point of view of recovery from reordering.

この文書では、パケットの並べ替え、すなわち、並べ替え密度(RD)と並べ替えバッファ占有密度(RBD)のための2つの改良されたメトリックを提示します。閾値は、パケットが失われたと考えられる場合、明らかにO(N)に結合した計算の複雑さを定義するために、Nはパケットシーケンスの長さNの評価のための独立したメモリ要件を維持するために使用されます。 RDは、RBDの並べ替えからの回復の観点からの配列を評価しながら、並べ替えの特性を捉え、総合評価指標です。

These metrics are simple to compute yet comprehensive in their characterization of packet reordering. The measures are robust and orthogonal to packet loss and duplication.


Table of Contents


   1. Introduction and Motivation .....................................3
   2. Attributes of Packet Reordering Metrics .........................4
   3. Reorder Density and Reorder Buffer-Occupancy Density ............7
      3.1. Receive Index (RI) .........................................8
      3.2. Out-of-Order Packet ........................................9
      3.3. Displacement (D) ...........................................9
      3.4. Displacement Threshold (DT) ................................9
      3.5. Displacement Frequency (FD) ...............................10
      3.6. Reorder Density (RD) ......................................10
      3.7. Expected Packet (E) .......................................10
      3.8. Buffer Occupancy (B) ......................................10
      3.9. Buffer-Occupancy Threshold (BT) ...........................11
      3.10. Buffer-Occupancy Frequency (FB) ..........................11
      3.11. Reorder Buffer-Occupancy Density (RBD) ...................11
   4. Representation of Packet Reordering and Reorder Density ........11
   5. Selection of DT ................................................12
   6. Detection of Lost and Duplicate Packets ........................13
   7. Algorithms to Evaluate RD and RBD ..............................14
      7.1. Algorithm for RD ..........................................14
      7.2. Algorithm for RBD .........................................16
   8. Examples .......................................................17
   9. Characteristics Derivable from RD and RBD ......................21
   10. Comparison with Other Metrics .................................22
   11. Security Considerations .......................................22
   12. References ....................................................22
      12.1. Normative References .....................................22
      12.2. Informative References ...................................22
   13. Contributors ..................................................24
1. Introduction and Motivation

Packet reordering is a phenomenon that occurs in Internet Protocol (IP) networks. Major causes of packet reordering include, but are not limited to, packet striping at layers 2 and 3 [Ben99] [Jai03], priority scheduling (e.g., Diffserv), and route fluttering [Pax97] [Boh03]. Reordering leads to degradation of the performance of many applications [Ben99] [Bla02] [Lao02]. Increased link speeds [Bar04], increased parallelism within routers and switches, Quality-of-Service (QoS) support, and load balancing among links all point to increased packet reordering in future networks.

パケットの並べ替えは、インターネットプロトコル(IP)ネットワークで発生する現象です。パケットの並べ替えの主な原因としては、[Pax97] [Boh03]ひらひら層2及び3 [Ben99] [Jai03]、優先スケジューリング(例えば、Diffservの)、及び経路でパケットストライピング、これらに限定されません。並べ替えは、多くのアプリケーション[Ben99] [Bla02] [Lao02]の性能の低下につながります。リンク速度[Bar04]、ルータとスイッチ内の並列性を高める、サービス品質(QoS)のサポートを増加し、将来のネットワークで並べ替えが増加パケットへのリンクの中のすべてのポイントをロード・バランシング。

Effective metrics for reordering are required to measure and quantify reordering. A good metric or a set of metrics capturing the nature of reordering can be expected to provide insight into the reordering phenomenon in networks. It may be possible to use such metrics to predict the effects of reordering on applications that are sensitive to packet reordering, and perhaps even to compensate for reordering. A metric for reordered packets may also help evaluate network protocols and implementations with respect to their impact on packet reordering.


The percentage of out-of-order packets is often used as a metric for characterizing reordering. However, this metric is vague and lacking in detail. Further, there is no uniform definition for the degree of reordering of an arrived packet [Ban02] [Pi05a]. For example, consider the two packet sequences (1, 3, 4, 2, 5) and (1, 4, 3, 2, 5). It is possible to interpret the reordering of packets in these sequences differently. For example,

アウトオブオーダーパケットのパーセンテージは、しばしば並べ替えを特徴付けるための測定基準として使用されます。しかし、このメトリックは曖昧であり、詳細に欠けています。さらに、到着したパケット[Ban02] [Pi05a]の並べ替えの度には均一な定義は存在しません。例えば、2つのパケットのシーケンスを考える(1、3、4、2、5)、(1、4、3、2、5)。異なったこれらの配列にパケットの並べ替えを解釈することが可能です。例えば、

(i) Packets 2, 3, and 4 are out of order in both cases.


(ii) Only packet 2 is out of order in the first sequence, while packets 2 and 3 are out of order in the second.


(iii) Packets 3 and 4 are out of order in both the sequences.


(iv) Packets 2, 3, and 4 are out of order in the first sequence, while packets 4 and 2 are out of order in the second sequence.

パケット4及びA 2は第二の配列における順序から外れている間(IV)パケット2,3、および4は、第一の配列順序から外れています。

In essence, the percentage of out-of-order packets as a metric of reordering is subject to interpretation and cannot capture the reordering unambiguously and hence, accurately.


Other metrics attempt to overcome this ambiguity by defining only the late packets or only the early packets as being reordered. However, measuring reordering based only on late or only on early packets is not always effective. Consider, for example, the sequence (1, 20, 2,


3, ..., 19, 21, 22, ...); the only anomaly is that packet 20 is delivered immediately after packet 1. A metric based only on lateness will indicate a high degree of reordering, even though in this example it is a single packet arriving ahead of others. Similarly, a metric based only on earliness does not accurately capture reordering caused by a late arriving packet. A complete reorder metric must account for both earliness and lateness, and it must be able to differentiate between the two. The inability to capture both the earliness and the lateness precludes a metric from being useful for estimating end-to-end reordering based on reordering in constituent subnets.


The sensitivity to packet reordering can vary significantly from one application to the other. Consider again the packet sequence (1, 3, 4, 2, 5). If buffers are available to store packets 3 and 4 while waiting for packet 2, an application can recover from reordering. However, with certain real-time applications, the out-of-order arrival of packet 2 may render it useless. While one can argue that a good packet reordering measurement scheme should capture application-specific effects, a counter argument can also be made that packet reordering should be measured strictly with respect to the order of delivery, independent of the application.

パケット並べ替えに対する感度は、他の1つのアプリケーションから大きく異なります。再び、パケットシーケンス(1、3、4、2、5)を考えます。バッファは、パケット2を待っている間にパケット3と4を格納するために利用可能な場合、アプリケーションは、並べ替えから回復することができます。しかし、特定のリアルタイムアプリケーションで、パケット2のアウトオブオーダー到着は、それは無用です。 1は、測定スキームを並べ替えの良いパケットは、アプリケーション固有の効果を捉えるべきであると主張することができますが、カウンターの引数は、パケットの並べ替えは、アプリケーションとは独立して、配信の順序に関して厳密に測定する必要があることを行うことができます。

Many different packet reordering metrics have been suggested. For example, the standards-track document RFC 4737 [RFC4737] defines 11 metrics for packet reordering, including lateness-based percentage metrics, reordering extent metrics, and N-reordering.

多くの異なるパケット並べ替えメトリックが提案されています。例えば、標準トラック文書RFC 4737 [RFC4737]は遅れベースの百分率メトリック、並べ替え範囲メトリクス、及びN-並べ替えを含むパケットの並べ替えのための11のメトリクスを定義します。

Section 2 of this document discusses the desirable attributes of any packet reordering metric. Section 3 introduces two additional packet reorder metrics: Reorder Density (RD) and Reorder Buffer-occupancy Density (RBD), which we claim are superior to the others [Pi07]. In particular, RD possesses all the desirable attributes, while other metrics fall significantly short in several of these attributes. RBD is unique in measuring reordering in terms of the system resources needed for recovery from packet reordering. Both RD and RBD have a computation complexity O(N), where N is the length of the packet sequence, and they can therefore be used for real-time online monitoring.

このドキュメントのセクション2は、メトリック並べ替え任意のパケットの望ましい属性について説明します。並べ替え密度(RD)と並べ替えバッファ占有密度(RBD)、我々は他の[Pi07]に優れていると主張:セクション3は、2つの追加パケットのリオーダー指標を導入します。他のメトリックは、これらの属性のいくつかに大きく及ばないながら具体的には、RDは、すべての望ましい属性を持っています。 RBDは、パケットの並べ替えからの回復のために必要なシステムリソースの面で並べ替えを測定でユニークです。両方のRDとRBDのNは、パケットシーケンスの長さであり、計算の複雑さO(N)を有し、したがって、それらはリアルタイムのオンライン監視に使用することができます。

2. Attributes of Packet Reordering Metrics

The first and foremost requirement of a packet reordering metric is its ability to capture the amount and extent of reordering in a sequence of packets. The fact that a measure varies with reordering of packets in a stream does not make it a good metric. In [Ben99], the authors have identified desirable features of a reordering metric. This list encloses the foremost requirements stated above: simplicity, low sensitivity to packet loss, ability to combine reorder measures from two networks, minimal value for in-order data, and independence of data size. These features are explained below in detail, along with additional desired features. Note, the ability to combine reorder measures from two networks is added to broaden applicability, and data size independence is discussed under evaluation complexity. However, data size independence could also refer to the final measure, as in percentage reordering or even a normalized representation.

メトリック並び替え、パケットのまず第一の要件は、パケットのシーケンスで並べ替えの量および程度を捕捉する能力です。尺度は、ストリーム内のパケットの並べ替えに応じて変化するという事実は、それは良いメトリックことはありません。 [Ben99]では、著者は、並べ替えメトリックの望ましい特徴を同定しました。シンプル、パケット損失、二つのネットワークからの追加注文措置を組み合わせる能力、インオーダーデータの最小値、およびデータサイズの独立性に対して低感度:このリストには、上記第一の要件を囲みます。これらの機能は、追加の所望の特徴とともに、以下に詳細に説明します。注、二つのネットワークからの追加注文措置を組み合わせる能力は、適用可能性を広げるために追加され、データサイズの独立性は、評価の複雑さの下で議論されています。しかしながら、データサイズ独立もパーセンテージ並べ替えあるいは正規表現のように、最終的な測定値を参照することができます。

a) Simplicity


An ideal metric is one that is simple to understand and evaluate, and yet informative, i.e., able to provide a complete picture of reordering. Percentage of packets reordered is the simplest singleton metric; but the ambiguity in its definition, as discussed earlier, and its failure to carry the extent of reordering make it less informative. On the other hand, keeping track of the displacements of each and every packet without compressing the data will contain all the information about reordering, but it is not simple to evaluate or use.


A simpler metric may be preferred in some cases even though it does not capture reordering completely, while other cases may demand a more complex, yet complete metric.


In striving to strike a balance, the lateness-based metrics consider only the late packets as reordered, and earliness-based metrics only the early packets as reordered. However, a metric based only on earliness or only on lateness captures only a part of the information associated with reordering. In contrast, a metric capturing both early and late arrivals provides a complete picture of reordering in a sequence.


b) Low Sensitivity to Packet Loss and Duplication


A reorder metric should treat only an out-of-order packet as reordered, i.e., if a packet is lost during transit, then this should not result in its following packets, which arrive in order, being classified as out of order. Consider the sequence (1, 3, 4, 5, 6). If packet 2 has been lost, the sequence should not be considered to contain any out-of-order packets. Similarly, if multiple copies of a packet (duplicates) are delivered, this must not result in a packet being classified as out of order, as long as one copy arrives in the proper position. For example, sequence (1, 2, 3, 2, 4, 5) has no reordering. The lost and duplicate packet counts may be tracked using metrics specifically intended to measure those, e.g., percentage of lost packets, and percentage of duplicate packets.


c) Low Evaluation Complexity


Memory and time complexities associated with evaluating a metric play a vital role in implementation and real-time measurements. Spatial/memory complexity corresponds to the amount of buffers required for the overall measurement process, whereas time/computation complexity refers to the number of computation steps involved in computing the amount of reordering in a sequence. On-the-fly evaluation of the metric for large streams of packets requires the computational complexity to be O(N), where N denotes the number of received packets, used for the reordering measure. This allows the metric to be updated in constant-time as each packet arrives. In the absence of a threshold defining losses or the number of sequence numbers to buffer for detection of duplicates, the worst-case complexity of loss and duplication detection will increase with N. The rate of increase will depend, among other things, on the value of N and the implementation of the duplicate detection scheme.


d) Robustness


Reorder measurements should be robust against different network phenomena and peculiarities in measurement or sequences such as a very late arrival of a duplicate packet, or even a rogue packet due to an error or sequence number wraparound. The impact due to an event associated with a single or a small number of packets should have a sense of proportionality on the reorder measure. Consider, for example, the arrival sequence: (1, 5430, 2, 3, 4, 5, ...) where packet 5430 appears to be very early; it may be due to either sequence rollover in test streams or some unknown reason.


e) Broad Applicability


A framework for IP performance metrics [RFC2330] states: "The metrics must aid users and providers in understanding the performance they experience or provide".


Rather than being a mere value or a set of values that changes with the reordering of packets in a stream, a reorder metric should be useful for a variety of purposes. An application or a transport protocol implementation, for example, may be able to use the reordering information to allocate resources to recover from reordering. A metric may be useful for TCP flow control, buffer resource allocation for recovery from reordering and/or network diagnosis.


The ability to combine the reorder metrics of constituent subnets to measure the end-to-end reordering would be an extremely useful property. In the absence of this property, no amount of individual network measurements, short of measuring the reordering for the pair of endpoints of interest, would be useful in predicting the end-to-end reordering.


The ability to provide different types of information based on monitoring or diagnostic needs also broadens the applicability of a metric. Examples of applicable information for reordering may include parameters such as the percentage of reordered packets that resulted in fast retransmissions in TCP, or the percentage of utilization of the reorder recovery buffer.


3. Reorder Density and Reorder Buffer-Occupancy Density

In this memo, we define two discrete density functions, Reorder Density (RD) and Reorder Buffer-occupancy Density (RBD), that capture the nature of reordering in a packet stream. These two metrics can be used individually or collectively to characterize the reordering in a packet stream. Also presented are algorithms for real-time evaluation of these metrics for an incoming packet stream.


RD is defined as the distribution of displacements of packets from their original positions, normalized with respect to the number of packets. An early packet corresponds to a negative displacement and a late packet to a positive displacement. A threshold on displacement is used to keep the computation within bounds. The choice of threshold value depends on the measurement uses and constraints, such as whether duplicate packets are accounted for when evaluating these displacements (discussed in Section 5).


The ability of RD to capture the nature and properties of reordering in a comprehensive manner has been demonstrated in [Pi05a], [Pi05b], [Pi05c], and [Pi07]. The RD observed at the output port of a subnet when the input is an in-order packet stream can be viewed as a "reorder response" of a network, a concept somewhat similar to the "system response" or "impulse response" used in traditional system theory. For a subnet under stationary conditions, RD is the probability density of the packet displacement. RD measured on individual subnets can be combined, using the convolution operation, to predict the end-to-end reorder characteristics of the network formed by the cascade of subnets under a fairly broad set of conditions [Pi05b]. RD also shows significant promise as a tool for analytical modeling of reordering, as demonstrated with a load-balancing scenario in [Pi06]. Use of a threshold to define the condition under which a packet is considered lost makes the metric robust, efficient, and adaptable for different network and stream characteristics.

総合的に並べ替えの性質及び特性を捕捉するRDの能力は[Pi05a]で証明されている、[Pi05b]、[Pi05c]、および[Pi07]。入力における次のパケットストリームがネットワークの「リオーダー応答」で使用される「システム応答」又は「インパルス応答」にやや類似概念と見なすことができる場合にRDは、サブネットの出力ポートで観測しました伝統的なシステム理論。定常条件下サブネットに、RDは、パケット変位の確率密度です。個々のサブネット上で測定RD条件のかなり広いセットの下でサブネットのカスケードによって形成されるネットワークのエンドツーエンドのリオーダー特性を予測するために、畳み込み演算を使用して、組み合わせることができる[Pi05b]。 RDはまた、[Pi06]でのロードバランシングのシナリオで示されたように、並べ替えの分析モデリングのためのツールとして重要な約束を示しています。パケットが失われたと考えられる条件を定義するためのしきい値の使用は、メトリック、堅牢で効率的、かつ異なるネットワークに適応し、ストリームの特性になります。

RBD is the normalized histogram of the occupancy of a hypothetical buffer that would allow the recovery from out-of-order delivery of packets. If an arriving packet is early, it is added to a hypothetical buffer until it can be released in order [Ban02]. The occupancy of this buffer, after each arrival, is used as the measure of reordering. A threshold, used to declare a packet as lost, keeps the complexity of computation within bounds. The threshold may be selected based on application requirements in situations where the late arrival of a packet makes it useless, e.g., a real-time application. In [Ban02], this metric was called RD and buffer occupancy was known as displacement.

RBDは、パケットのアウトオブオーダーの配信からの回復を可能にする仮想的なバッファの占有の正規化ヒストグラムです。到着したパケットが早期であれば、それは[Ban02]の順序で解放できるようになるまで、それは仮想的なバッファに追加されます。このバッファの占有率は、各到着後、並べ替えの尺度として使用されます。失われたとしてパケットを宣言するために使用される閾値は、範囲内の計算の複雑さを維持します。しきい値は、パケットの到着が遅れるが、例えば、それは無用リアルタイムアプリケーションを作る状況でアプリケーションの要件に基づいて選択することができます。 【Ban02】において、このメトリックは、RDと呼ばれ、占有バッファた変位として知られていました。

RD and RBD are simple, yet useful, metrics for measurement and evaluation of reordering. These metrics are robust against many peculiarities, such as those discussed previously, and have a computational complexity of O(N), where N is the received sequence size. RD is orthogonal to loss and duplication, whereas RBD is orthogonal to duplication.

RDとRBDは、並べ替えの測定および評価のための評価指標、シンプルでありながら便利です。これらの指標は、先に述べたもののような多くの特殊性、に対してロバストであり、Nは、受信されたシーケンスのサイズはO(N)の計算の複雑さを有します。 RBDは、複製に直交する一方、RDは、損失と複製と直交しています。

A detailed comparison of these and other proposed metrics for reordering is presented in [Pi07].


The following terms are used to formally define RD, RBD, and the measurement algorithms. The wraparound of sequence numbers is not addressed in this document explicitly, but with the use of modulo-N arithmetic, all claims made here remain valid in the presence of wraparound.


3.1. Receive Index (RI)
3.1. 受信インデックス(RI)

Consider a sequence of packets (1, 2, ..., N) transmitted over a network. A receive index RI (1, 2, ...), is a value assigned to a packet as it arrives at its destination, according to the order of arrival. A receive index is not assigned to duplicate packets, and the receive index value skips the value corresponding to a lost packet. (The detection of loss and duplication for this purpose is described in Section 6.) In the absence of reordering, the sequence number of the packet and the receive index are the same for each packet.


RI is used to compute earliness and lateness of an arriving packet. Below are two examples of received sequences with receive index values for a sequence of 5 packets (1, 2, 3, 4, 5) arriving out of order:

RIは、到着したパケットの早さと遅れを計算するために使用されます。 5つのパケットの配列のインデックス値を受信して​​以下受け取った配列の2つの例は、(1、2、3、4、5)順不同で到着します。

Example 1: Arrived sequence: 2 1 4 5 3 receive index: 1 2 3 4 5

実施例1:到着順序:1 2 3 4 5 2 1 4 5 3インデックスを受け取ります

Example 2: Arrived sequence: 1 4 3 5 3 receive index: 1 3 4 5 -

実施例2:到着順序:1 4 3 5 3は、インデックスを受信:1 2 3 4 5 -

In Example 1, there is no loss or duplication. In Example 2, the packet with sequence number 2 is lost. Thus, 2 is not assigned as an RI. Packet 3 is duplicated; thus, the second copy is not assigned an RI.


3.2. Out-of-Order Packet
3.2. アウトオブオーダーパケット

When the sequence number of a packet is not equal to the RI assigned to it, it is considered to be an out-of-order packet. Duplicates for which an RI is not defined are ignored.

パケットのシーケンス番号がそれに割り当てられたRIと等しくない場合には、アウトオブオーダーパケットであると考えられます。 RIが定義されていない重複は無視されます。

3.3. Displacement (D)
3.3. 変位(D)

Displacement (D) of a packet is defined as the difference between RI and the sequence number of the packet, i.e., the displacement of packet i is RI[i] - i. Thus, a negative displacement indicates the earliness of a packet and a positive displacement the lateness. In example 3 below, an arrived sequence with displacements of each packet is illustrated.

変位パケットの(D)は、RIとパケットのシーケンス番号との間の差として定義される、すなわち、パケットの変位iがRIである[I] - 、I。従って、負の変位は、パケットの早さと正の変位遅れを示しています。下記の実施例3においては、各パケットの変位との到着順序が示されています。

Example 3: Arrived sequence: 1 4 3 5 3 8 7 6 receive index: 1 3 4 5 - 6 7 8 Displacement: 0 -1 1 0 - -2 0 2

実施例3:到着順序:1 4 3 5 3 8 7 6は、受信率:1 2 3 4 5 - 6 7 8変位:0 -1 1 0 - -2 0 2

3.4. Displacement Threshold (DT)
3.4. 変位しきい値(DT)

The displacement threshold is a threshold on the displacement of packets that allows the metric to classify a packet as lost or duplicate. Determining when to classify a packet as lost is difficult because there is no point in time at which a packet can definitely be classified as lost; the packet may still arrive after some arbitrarily long delay. However, from a practical point of view, a packet may be classified as lost if it has not arrived within a certain administratively defined displacement threshold, DT.


Similarly, to identify a duplicate packet, it is theoretically necessary to keep track of all the arrived (or missing) packets. Again, however, from a practical point of view, missing packets within a certain window of sequence numbers suffice. Thus, DT is used as a practical means for declaring a packet as lost or duplicated. DT makes the metric more robust, keeps the computational complexity for long sequences within O(N), and keeps storage requirements independent of N.

同様に、重複したパケットを識別するために、すべての到着(または欠落)パケットを追跡するために理論的に必要です。再び、しかし、実用的な観点、配列番号十分での特定のウィンドウ内の欠落パケットから。したがって、DTは、失われたまたは複製としてパケットを宣言するための実用的な手段として使用されます。 DTは、メトリックがより堅牢になりO(N)内の長いシーケンスのための計算の複雑さを保ち、そしてNの独立したストレージ要件を保ちます

If the DT selected is too small, reordered packets might be classified as lost. A large DT will increase both the size of memory required to keep track of sequence numbers and the length of computation time required to evaluate the metric. Indeed, it is possible to use two different thresholds for the two cases. The selection of DT is further discussed in Section 5.

選択されたDTが小さすぎると失われたとして、並べ替えパケットが分類される可能性があります。大DTは、シーケンス番号を追跡するために必要なメモリのサイズとメトリックを評価するために必要な計算時間の長さの両方が増加します。確かに、2例のための2つの異なるしきい値を使用することが可能です。 DTの選択はさらにセクション5に記載されています。

3.5. Displacement Frequency (FD)
3.5. 変位周波数(FD)

Displacement Frequency FD[k] is the number of arrived packets having a displacement of k, where k takes values from -DT to DT.

変位周波数Fd [k]は、kはDTに-DTから値を取るkの変位を有する到着パケットの数です。

3.6. Reorder Density (RD)
3.6. 並べ替え密度(RD)

RD is defined as the distribution of the Displacement Frequencies FD[k], normalized with respect to N', where N' is the length of the received sequence, ignoring lost and duplicate packets. N' is equal to the sum(FD[k]) for k in [-DT, DT].

RDが失わ無視し、パケットを複製し、受信されたシーケンスの長さNに対する変位周波数FD [k]の分布を、正規化された「Nは、」として定義されます。 Nは」[-DT、DT]におけるkの和(FD [K])に等しいです。

3.7. Expected Packet (E)
3.7. 予想されるパケット(E)

A packet with sequence number E is expected if E is the largest number such that all the packets with sequence numbers less than E have already arrived or have been determined to be lost.


3.8. Buffer Occupancy (B)
3.8. バッファ占有率(B)

An arrived packet with a sequence number greater than that of an expected packet is considered to be stored in a hypothetical buffer sufficiently long to permit recovery from reordering. At any packet arrival instant, the buffer occupancy is equal to the number of out-of-order packets in the buffer, including the newly arrived packet. One buffer location is assumed for each packet, although it is possible to extend the concept to the case where the number of bytes is used for buffer occupancy. For example, consider the sequence of packets (1, 2, 4, 5, 3) with expected order (1, 2, 3, 4, 5). When packet 4 arrives, the buffer occupancy is 1 because packet 4 arrived early. Similarly, the buffer occupancy becomes 2 when packet 5 arrives. When packet 3 arrives, recovery from reordering occurs and the buffer occupancy reduces to zero.


3.9. Buffer-Occupancy Threshold (BT)
3.9. バッファ占有しきい値(BT)

Buffer-occupancy threshold is a threshold on the maximum size of the hypothetical buffer that is used for recovery from reordering. As with the case of DT for RD, BT is used for loss and duplication classification for Reorder Buffer-occupancy Density (RBD) computation (see Section 3.11). BT provides robustness and limits the computational complexity of RBD.

バッファ占有しきい値は、並べ替えからの回復のために使用される仮想的なバッファの最大サイズに対する閾値です。 RDのためのDTの場合と同様に、BTがリオーダーバッファ占有密度(RBD)計算の損失と複製の分類のために使用される(セクション3.11を参照)。 BTは、堅牢性を提供し、RBDの計算の複雑さを制限します。

3.10. Buffer-Occupancy Frequency (FB)
3.10. バッファ占有周波数(FB)

At the arrival of each packet, the buffer occupancy may take any value, k, ranging from 0 to BT. The buffer occupancy frequency FB[k] is the number of arrival instances after which the occupancy takes the value of k.

各パケットの到着時に、バッファ占有率は0からBTまでの範囲の任意の値、Kをとることができます。バッファ占有周波数FB [k]は占有率がkの値をとり、その後到着インスタンスの数です。

3.11. Reorder Buffer-Occupancy Density (RBD)
3.11. バッファ占有密度(RBD)を並べ替えます

Reorder buffer-occupancy density is the buffer occupancy frequencies normalized by the total number of non-duplicate packets, i.e., RBD[k] = FB[k]/N' where N' is the length of the received sequence, ignoring excessively delayed (deemed lost) and duplicate packets. N' is also the sum(FB[k]) for all k such that k belongs to [0, BT].

バッファ占有密度の順序を変更することは、非重複パケットの総数によって正規化バッファ占有周波数、すなわち、RBD [K] = FB [K] / N「Nは、ここ」受信シーケンスの長さであり、過度に(遅延無視します失われたとみなされる)、パケットを複製します。 N」は、kは[0、BT]に属しているように、全てのkについての和(FB [K])です。

4. Representation of Packet Reordering and Reorder Density

Consider a sequence of packets (1, 2, ..., N). Let the RI assigned to packet m be "the sequence number m plus an offset dm", i.e.,


RI = m + dm; D = dm

= M + DM TO。 D = DM

A reorder event of packet m is represented by r(m, dm). When dm is not equal to zero, a reorder event is said to have occurred. A packet is late if dm > 0 and early if dm < 0. Thus, packet reordering of a sequence of packets is completely represented by the union of reorder events, R, referred to as the reorder set:

パケットmのリオーダーイベントがR(M、DM)で表されます。 DMがゼロに等しくない場合、リオーダーイベントが発生したと言われています。パケットはDM> 0であれば後半であり、DM <0このように、パケットのシーケンスのパケットの並び替えを完全にリオーダーイベントの集合によって表される初期の場合、Rは、リオーダ・セットと呼ばれます。

R = {r(m,dm)| dm not equal to 0 for all m}

R = {R(M、DM)| }すべてのmについて0に等しくないDM

If there is no reordering in a packet sequence, then R is the null set.


Examples 4 and 5 illustrate the reorder set:


Example 4. No losses or duplicates


Arrived Sequence 1 2 3 5 4 6 receive index (RI) 1 2 3 4 5 6 Displacement (D) 0 0 0 -1 1 0 R = {(4,1), (5,-1)}

到着したシーケンス1 2 3 5 4 6は、インデックス(RI)を受ける1 2 3 4 5 6変位(D)0 0 0 -1 1 0 R = {(4,1)、(5、-1)}

Example 5. Packet 4 is lost and 2 is duplicated


Arrived Sequence 1 2 5 3 6 2 receive index (RI) 1 2 3 5 6 - Displacement (D) 0 0 -2 2 0 - R = {(3, 2), (5, -2)}

変位(D)0 0 -2 2 0 - - 到着シーケンス1 2 5 3 6 2 1 2 3 5 6指数(RI)受信R = {(3、2)、(5、-2)}

RD is defined as the discrete density of the frequency of packets with respect to their displacements, i.e., the lateness and earliness from the original position. Let S[k] denote the set of reorder events in R with displacement equal to k. That is:

RDは、それらの変位、元の位置から、すなわち、遅れや早に対してパケットの周波数の離散的密度として定義されます。 S [k]はkに等しい変位にRにおけるリオーダ・イベントの集合を示すものとします。あれは:

S[k]= {r(m, dm)| dm = k}

S [K] = {R(M、DM)| DM = K}

Let |S[k]| be the cardinality of set S[k]. Thus, RD[k] is defined as |S[k]| normalized with respect to the total number of received packets (N'). Note that N' does not include duplicate or lost packets.

してみましょう| S [k]は|集合S [k]の基数です。したがって、RD [k]はのように定義される| S [K] |受信したパケット(N ')の合計数に対して正規化しました。 N「の重複または失われたパケットが含まれていないことに注意してください。

RD[k] = |S[k]| / N' for k not equal to zero

RD [K] = | S [k]は|ゼロに等しくないkの/ N」

RD[0] corresponds to the packets for which RI is the same as the sequence number:

RD [0] RIシーケンス番号と同じであるため、パケットに対応します:

RD[0] = 1 - sum(|S[k]| / N')

RD [0] = 1 - 和(| S [K] | / N ')

As defined previously, FD[k] is the measure that keeps track of |S[k]|.

| S [k]は|先に定義したように、FD [k]はを追跡する尺度です。

5. Selection of DT
DT 5.選択

Although assigning a threshold for determining lost and duplicate packets might appear to introduce error into the reorder metrics, in practice this need not be the case. Applications, protocols, and the network itself operate within finite resource constraints that introduce practical limits beyond which the choice of certain values becomes irrelevant. If the operational nature of an application is such that a DT can be defined, then using DT in the computation of reorder metrics will not invalidate nor limit the effectiveness of the metrics, i.e., increasing DT does not provide any benefit. In the case of TCP, the maximum transmit and receive window sizes impose a natural limit on the useful value of DT. Sequence number wraparound may provide a useful upper bound for DT in some instances.

失われたと重複パケットを決定するためのしきい値を割り当てること実際には、リオーダーメトリクスにエラーを導入するように見えるかもしれないがある必要はありません。アプリケーション、プロトコル、およびネットワーク自体が特定の値の選択は無関係になり、それを超える実質的な制限を導入し、有限資源の制約内で動作します。アプリケーションの動作の性質はDTを定義することができるようなものである場合、リオーダ・メトリックの計算にDTを使用すること、すなわち、DTの増加は何らかの利益を提供しない、メトリックの有効性を無効にも制限しません。 TCPの場合には、最大送信および受信ウィンドウサイズは、DTの有用な値の自然の制限を課します。シーケンス番号のラップアラウンドは、いくつかの事例ではDTのために有益な上限を提供することができます。

If there are no operational constraints imposed by factors as described above, or if one is purely interested in a more complete picture of reordering, then DT can be made as large as required. If DT is equal to the length of the packet sequence (worst case scenario), a complete picture of reordering is seen. Any metric that does not rely on a threshold to declare a packet as lost implicitly makes one of two assumptions: a) A missing packet is not considered lost until the end of the sequence, or b) the packet is considered lost until it arrives. The former corresponds to the case where DT is set to the length of the sequence. The latter leads to many problems related to complexity and robustness.

上述した、または1つの並べ替えのより完全な像に純粋関心がある場合、その後、DTは、必要に応じて同じ大きさにすることができるような因子によって課されるいかなる動作制約が存在しない場合。 DTは、パケットシーケンス(最悪の場合)の長さに等しい場合、並べ替えの全体像が見られます。 a)の欠落パケットはシーケンスの最後まで失わ考慮されていない、またはそれが到着するまでb)は、パケットが失われたと考えられている:失われたように、パケットを宣言するために、閾値に依存しない任意のメトリックは、暗黙のうちに2つの仮定の一つになります。前者は、DTが配列の長さに設定されている場合に相当します。後者は、複雑さと堅牢性に関連する多くの問題につながります。

6. Detection of Lost and Duplicate Packets

In RD, a packet is considered lost if it is late beyond DT. Non-duplicate arriving packets do not have a copy in the buffer and do not have a sequence number less (earlier) than E. In RBD, a packet is considered lost if the buffer is filled to its threshold BT. A packet is considered a duplicate when the sequence number is less than the expected packet, or if the sequence number is already in the buffer.


Since RI skips the sequence number of a lost packet, the question arises as to how to assign an RI to subsequent packets that arrive before it is known that the packet is lost. This problem arises only when reorder metrics are calculated in real-time for an incoming sequence, and not with offline computations. This concern can be handled in one of two ways:


a) Go-back Method: RD is computed as packets arrive. When a packet is deemed lost, RI values are corrected and displacements are recomputed. The Go-back Method is only invoked when a packet is lost and recomputing RD involves at most DT packets.


b) Stay-back Method: RD evaluation lags the arriving packets so that the correct RI and E values can be assigned to each packet as it arrives. Here, RI is assigned to a packet only once, and the value assigned is guaranteed to be correct. In the worst case, the computation lags the arriving packet by DT. The lag associated with the Stay-back Method is incurred only when a packet is missing.


Another issue related to a metric and its implementation is the robustness against peculiarities that may occur in a sequence as discussed in Section 2. Consider, for example, the arrival sequence (1, 5430, 2, 3, 4, 5, ...). With RD, a sense of proportionality is easily maintained using the concept of threshold (DT), which limits the effects a rogue packet can have on the measurement results. In this example, when the displacement is greater than DT, rogue packet 5430 is discarded. In this way the impact due to the rogue packet is limited, at most, to DT packets, thus imposing a limit on the amount of error it can cause in the results. Note also that a threshold different from DT can be used for the same purpose. For example, a pre-specified threshold that limits the time a packet remains in the buffer can make RBD robust against rogue packets.

メトリックとその実施に関連する別の問題は、例えば、第2の検討に議論されるように配列中に発生する可能性が特色に対するロバスト性である、到着順(1、5430、2、3、4、5、... )。 RDと、比例感を容易に測定結果に不正なパケットを有することができる効果を制限閾値(DT)の概念を使用して維持されます。変位がDTよりも大きい場合、この例では、不正なパケット5430は破棄されます。このように、不正なパケットによる影響は、このように、それが結果に引き起こすことができる誤差の量に制限を課す、DTパケットに、せいぜい、限られています。 DT異なる閾値は、同じ目的のために使用することができることにも留意されたいです。例えば、パケットがバッファに残っている時間を制限する事前指定された閾値は、不正なパケットに対するRBDを堅牢にすることができます。

7. Algorithms to Evaluate RD and RBD

The algorithms to compute RD and RBD are given below. These algorithms are applicable for online computation of an incoming packet stream and provide an up-to-date metric for the packet stream read so far. For simplicity, the sequence numbers are considered to start from 1 and continue in increments of 1. Only the Stay-back Method of loss detection is presented here; hence, the RD values lag by a maximum of DT. The algorithm for the Go-back Method is given in [Bar04]. Perl scripts for these algorithms are posted in [Per04].


7.1. Algorithm for RD
7.1. RDのためのアルゴリズム
   Variables used:
    RI: receive index.
    S: Arrival under consideration for lateness/earliness computation.
    D: Lateness or earliness of the packet being processed: dm for m.
    FD[-DT..DT]: Frequency of lateness and earliness.
    window[1..DT+1]: List of incoming sequence numbers; FIFO buffer.
    buffer[1..DT]: Array to hold sequence numbers of early arrivals.
    window[] and buffer[] are empty at the beginning.

Step 1. Initialize:


Store first unique DT+1 sequence numbers in arriving order into window; RI = 1;

ウィンドウに順番に到着して最初のユニークDT + 1つのシーケンス番号を格納します。 RI = 1。

Step 2. Repeat (until window is empty):


If (window or buffer contains sequence number RI) { Move sequence number out of window to S # window is FIFO


D = RI - S; # compute displacement

D = RI - S。 #コンピュート変位

If (absolute(D) <= DT) # Apply threshold { FD[D]++; # Update frequency

(絶対値(D)<= DT)#がしきい値を適用する場合、{FD [D] ++; #更新頻度

If (buffer contains sequence number RI) Delete RI from buffer;


If (D < 0) # Early Arrival add S to empty slot in buffer; RI++; # Update RI value }

(D <0)#早着がバッファに空きスロットにSを追加した場合、 RI ++; #更新RI値}

         Else # Displacement beyond threshold.
            Discard S;
            # Note, an early arrival in window is moved to buffer if
            # its displacement is less or equal to DT.  Therefore, the
            # contents in buffer will have only possible RIs.  Thus,
            # clearing an RI as it is consumed prevents memory leaks
            # in buffer
         # Get next incoming non-duplicate sequence number, if any.
         newS = get_next_arrival(); # subroutine called*
         if (newS != null)
              add newS to window;
         if (window is empty) go to step 3;
      Else # RI not found.  Get next RI value.
         # Next RI is the minimum among window and buffer contents.
         m = minimum (minimum (window), minimum (buffer));
         If (RI < m)
            RI = m;

Step 3. Normalize FD to get RD;


# Get a new sequence number from packet stream, if any subroutine get_next_arrival() { do # get non-duplicate next arrival {


              newS = new sequence from arriving stream;
              if (newS == null) # End of packet stream
                 return null;
        } while (newS < RI or newS in buffer or newS in window);

return newS; }

ニュースを返します。 }

7.2. Algorithm for RBD
7.2. RBDのためのアルゴリズム
   Variables used:
   # E : Next expected sequence number.
   # S : Sequence number of the packet just arrived.
   # B : Current buffer occupancy.
   # BT: Buffer Occupancy threshold.
   # FB[i]: Frequency of buffer occupancy i  (0 <= i <= BT).
   # in_buffer(N) : True if the packet with sequence number N is
     already stored in the buffer.
1. Initialize E = 1, B = 0 and FB[i] = 0 for all values of i.
1.初期化E = 1、B = 0とFB、iの全ての値のための[I] = 0。
2. Do the following for each arrived packet.
          If (in_buffer(S) || S < E) /*Do nothing*/;
          /* Case a: S is a duplicate or excessively delayed packet.
          Discard the packet.*/
             If (S == E)
             /* Case b: Expected packet has arrived.*/
                E = E + 1;
                While (in_buffer(E))
                   B = B - 1; /* Free buffer occupied by E.*/
                   E = E + 1; /* Expect next packet.*/
                FB[B] = FB[B] + 1; /*Update frequency for buffer
                occupancy B.*/
             } /* End of If (S == E)*/
             ElseIf (S > E)
             /* Case c: Arrived packet has a sequence number higher
                than expected.*/
                If (B < BT)
                /* Store the arrived packet in a buffer.*/
                   B = B + 1;
                /* Expected packet is delayed beyond the BT.
                Treat it as lost.*/
                      E = E + 1;
                   Until (in_buffer(E) || E == S);
                   While (in_buffer(E) || E == S)
                      if (E != S) B = B - 1;
                      E = E + 1;
                 FB[B] = FB[B] + 1; /*Update frequency for buffer
                 occupancy B.*/
             } /* End of ElseIf (S > E)*/


3. Normalize FB[i] to obtain RBD[i], for all values of i using
3.ノーマライズFB [I] RBD [i]は、Iの全ての値に対して用い得ること
      RBD[i] = ----------------------------------
                  Sum(FB[j] for 0 <= j <= BT)
8. Examples

a. Scenario with no packet loss


Consider the sequence of packets (1, 4, 2, 5, 3, 6, 7, 8) with DT = BT = 4.

DT = BT = 4のパケット(1、4、2、5、3、6、7、8)のシーケンスを考えます。

Tables 1 and 2 show the computational steps when the RD algorithm is applied to the above sequence.


   Table 1: Late/Early-packet Frequency computation steps
   S         1     4     2     5     3     6   7    8
   RI        1     2     3     4     5     6   7    8
   D         0    -2     1    -1     2     0   0    0
   FD[D]     1     1     1     1     1     2   3    4
   (S, RI,D and FD[D] as described in Section 7.1)

The last row (FD[D]) represents the current frequency of occurrence of the displacement D, e.g., column 3 indicates FD[1] = 1 while column 4 indicates FD[-1] = 1. The final set of values for RD are shown in Table 2.

最後の行(FD [D])は、変位D、例えば発生の現在の周波数を表し、列4は、RDの値のFD [-1] = 1の最終的なセットを示しながら、カラム3は、FD [1] = 1を示しています表2に示します。

   Table 2: Reorder Density (RD)
     D       -2       -1      0     1       2
   FD[D]      1        1      4     1       1
   RD[D]     0.125   0.125   0.5   0.125   0.125
   (D,FD[D] and RD[D] as described in Section 7.1)

Tables 3 and 4 illustrate the computational steps for RBD for the same example.


   Table 3: Buffer occupancy frequencies (FB) computation steps
   S         1     4     2     5     3     6     7     8
   E         1     2     2     3     3     6     7     8
   B         0     1     1     2     0     0     0     0
   FB[B]     1     1     2     1     2     3     4     5
   (E,S,B and FB[B] as described in Section 7.2)
   Table 4: Reorder Buffer-occupancy Density
   B           0        1     2
   FB[B]       5        2     1
   RBD[B]     0.625   0.25  0.125
   (B,FB[B] and RBD[B] as discussed in Section 7.2)

Graphical representations of the densities are as follows:


                ^                            ^
                |                            |
                |                            _
    ^       0.5 _                   ^ 0.625 | |
    |          | |                  |       | |
               | |                          | |
   RD[D]       | |                RBD[B]    | | - o.25
          _  _ | | _  _ 0.125               | || | - 0.125
         | || || || || |                    | || || |
        --+--+--+--+--+--+-->             ---+--+--+--
         -2 -1  0  1  2                      0  1  2
                D  -->                        B -->

b. Scenario with packet loss


Consider a sequence of 6 packets (1, 2, 4, 5, 6, 7) with DT = BT = 3. Table 5 shows the computational steps when the RD algorithm is applied to the above sequence to obtain FD[D].

6つのパケット(1、2、4、5、6、7)RDアルゴリズムがFD [D]を得るために上記のシーケンスに適用されたときにDT = BT = 3、表5で計算手順を示すシーケンスを考えます。

   Table 5: Late/Early-packet Frequency computation steps
   S         1     2     4     5     6     7
   RI        1     2     4     5     6     7
   D         0     0     0     0     0     0
   FD[D]     1     2     3     4     5     6
   (S,RI,D and FD[D] as described in Section 7.1)

Table 6 illustrates the FB[B] for the above arrival sequence.

表6は、上記到来シーケンスのFB [B]を示しています。

   Table 6: Buffer occupancy computation steps
   S        1     2     4     5     6     7
   E        1     2     3     3     3     7
   B        0     0     1     2     3     0
   FB[B]    1     2     1     1     1     3
   (E,S,B and FB[B] as described in Section 7.2)

Graphical representations of RD and RBD for the above sequence are as follows.


                ^                        ^
                |                        |
          1.0   _                        |
      ^        | |                ^      |
      |        | |                | 0.5  _
               | |                      | |
    RD[D]      | |               RBD[B] | | _  _  _ 0.167
               | |                      | || || || |
           --+--+--+-->                --+--+--+--+-->
            -1  0  1                     0  1  2  3
                D  -->                      B -->

c. Scenario with duplicate packets


Consider a sequence of 6 packets (1, 3, 2, 3, 4, 5) with DT = 2. Table 7 shows the computational steps when the RD algorithm is applied to the above sequence to obtain FD[D].

RDアルゴリズムがFD [D]を得るために、上記配列に適用した場合の計算手順を示すDT = 2、表7と6つのパケット(1、3、2、3、4、5)のシーケンスを考えます。

   Table 7: Late/Early-packet Frequency computation steps
   S         1     3     2     3     4     5
   RI        1     2     3     -     4     5
   D         0    -1     1     -     0     0
   FD[D]     1     1     1     -     2     3
   (S, RI,D and FD[D] as described in Section 7.1)

Table 8 illustrates the FB[B] for the above arrival sequence.

表8は、上記の到着順ためFB [B]を示しています。

   Table 8: Buffer Occupancy Frequency computation steps
   S     1     3     2     3     4     5
   E     1     2     2     -     4     5
   B     0     1     0     -     0     0
   FB[B] 1     1     2     -     3     4
   (E,S,B and FB[B] as described in Section 7.2)

Graphical representations of RD and RBD for the above sequence are as follows:


                 ^                            ^
                 |                            |
     ^           |                   ^   0.8  _
     |       0.6 _                   |       | |
                | |                          | |
    RD[D]       | |                RBD[B]    | |
          0.2 _ | | _ 0.2                    | | _ 0.2
             | || || |                       | || |
         --+--+--+--+--+--+-->             ---+--+--+--
          -2 -1  0  1  2                      0  1  2
                 D  -->                        B -->
9. Characteristics Derivable from RD and RBD

Additional information may be extracted from RD and RBD depending on the specific applications. For example, in the case of resource allocation at a node to recover from reordering, the mean and variance of buffer occupancy can be derived from RBD. For example:


Mean occupancy of recovery buffer = sum(i*RBD[i] for 0 <= i <= BT)

回復バッファの占有率を平均=合計(私はRBDを* [i]を0 <私は= BTを<=)

The basic definition of RBD may be modified to count the buffer occupancy in bytes as opposed to packets when the actual buffer space is more important. Another alternative is to use time to update the buffer occupancy compared to updating it at every arrival instant.


The parameters that can be extracted from RD include the percentage of late (or early) packets, mean displacement of packets, and mean displacement of late (or early) packets [Ye06]. For example, the fraction of packets that arrive after three or more of their successors according to the order of transmission is given by Sum


[RD[i] for 3<=i<=DT]. RD also allows for extraction of parameters such as entropy of the reordered sequence, a measure of disorder in the sequence [Ye06]. Due to the probability mass function nature of RD, it is also a convenient measure for theoretical modeling and analysis of reordering, e.g., see [Pi06].

[RD [I] 3 <iが<= = DT]。 RDはまた、並べ替えシーケンスのエントロピー、配列[Ye06]における障害の指標としてのパラメータの抽出を可能にします。 RDの確率質量関数の性質のために、それは例えば、[Pi06]参照、また、並べ替えの理論的なモデリングと解析のための便利な尺度です。

10. Comparison with Other Metrics

RD and RBD are compared to other metrics of [RFC4737] in [Pi07].

RDとRBDは、[RFC4737] [Pi07]内の他の測定基準と比較されます。

11. Security Considerations

The security considerations listed in [RFC4737], [RFC3763], and [RFC4656] are extensive and directly applicable to the usage of these metrics; thus, they should be consulted for additional details.


12. References
12.1. Normative References
12.1. 引用規格

[RFC2330] Paxson, V., Almes, G., Mahdavi, J., and M. Mathis, "Framework for IP Performance Metrics", RFC 2330, May 1998.

[RFC2330]パクソン、V.、Almes、G.、Mahdavi、J.、およびM.マティス、 "IPパフォーマンス・メトリックのためのフレームワーク"、RFC 2330、1998年5月。

[Pi07] N. M. Piratla and A. P. Jayasumana, "Metrics for Packet Reordering - A Comparative Analysis," International Journal of Communication Systems (IJCS), Vol. 21/1, 2008, pp: 99-113.

通信システムの国際ジャーナル(IJCS)、集 - [Pi07] N. M. Piratla及びA. P. Jayasumana、 "比較分析、パケット並べ替えのためのメトリック"。 21/1、2008年、頁:99から113まで。

12.2. Informative References
12.2. 参考文献

[Ben99] J. C. R. Bennett, C. Partridge and N. Shectman, "Packet Reordering is Not Pathological Network Behavior," IEEE/ACM Trans. on Networking , Dec. 1999, pp.789-798.

[Ben99] J. C. R.ベネット、C.ヤマウズラおよびN. Shectmanは、 "パケット再順序付けは、病理学的ネットワーク動作ではありません、" IEEE / ACMトランス。ネットワーキング、1999年12月、pp.789-798に。

[Jai03] S. Jaiswal, G. Iannaccone, C. Diot, J. Kurose and D. Towsley, "Measurement and Classification of Out-of-sequence Packets in Tier-1 IP Backbone," Proc. IEEE INFOCOM, Mar. 2003, pp. 1199-1209.

【Jai03] S. Jaiswal、G. Iannaccone、C. Diot、J.黒瀬及びD. Towsley、 "ティア1のIPバックボーンにおけるアウトオブシーケンスパケットの測定と分類、" PROC。 IEEE INFOCOM、2003年3月、頁。1199年から1209年。

[Pax97] V.Paxson, "Measurements and Analysis of End-to-End Internet Dynamics," Ph.D. Dissertation, U.C. Berkeley, 1997,

[Pax97] V.Paxson、「測定およびエンドツーエンドのインターネットダイナミクスの分析、」博士論文、U.C.バークレー、1997、。

[Boh03] S. Bohacek, J. Hespanha, J. Lee, C. Lim and K.Obraczka, "TCP-PR: TCP for Persistent Packet Reordering," Proc. of the IEEE 23rdICDCS, May 2003, pp.222-231.

【Boh03] S. Bohacek、J. Hespanha、J.リー、C.イムとK.Obraczka、 "TCP-PR:永続パケットの並び替えのためにTCP、" PROC。 IEEE 23rdICDCS、2003年5月、pp.222-231の。

[Bla02] E. Blanton and M. Allman, "On Making TCP More Robust to Packet Reordering," ACM Computer Comm. Review, 32(1), Jan. 2002, pp.20-30.

[Bla02] E.ブラントンとM.オールマン、「パケットの順序変更にTCPはより強固な作りで、」ACMコンピュータコム。レビュー、32(1)、2002年1月、pp.20-30。

[Lao02] M. Laor and L. Gendel, "The Effect of Packet Reordering in a Backbone Link on Application Throughput," IEEE Network, Sep./Oct. 2002, pp.28-36.

【Lao02] M. Laor及びL. Gendel、「アプリケーションスループットにバックボーンリンクにおけるパケット並べ替えの効果、」IEEEネットワーク、Sep./Oct。 2002年、pp.28-36。

[Bar04] A. A. Bare, "Measurement and Analysis of Packet Reordering Using Reorder Density," Masters Thesis, Department of Computer Science, Colorado State University, Fort Collins, Colorado, Fall 2004.

[Bar04] A. A.ベア、修士論文「パ​​ケットの測定と分析は、並べ替えの密度を、使用して並べ替え」、コンピュータサイエンス、コロラド州立大学、フォートコリンズ、コロラド州、省は2004年秋。

[Ban02] T. Banka, A. A. Bare, A. P. Jayasumana, "Metrics for Degree of Reordering in Packet Sequences", Proc. 27th IEEE Conference on Local Computer Networks, Tampa, FL, Nov. 2002, pp. 332-342.

【Ban02] T.挽歌、A. A.ベア、A. P. Jayasumana、 "パケットシーケンスに並べ替えの程度を指標"、PROC。第27回IEEEローカルコンピュータネットワーク上の会議、タンパ、FL、2002年11月、頁332から342まで。

[Pi05a] N. M. Piratla, "A Theoretical Foundation, Metrics and Modeling of Packet Reordering and Methodology of Delay Modeling using Inter-packet Gaps," Ph.D. Dissertation, Department of Electrical and Computer Engineering, Colorado State University, Fort Collins, CO, Fall 2005.

【Pi05a】N. M. Piratla、「理論的基礎、メトリックおよびパケットの並べ替えと遅延モデル化の手法のモデリングインターパケットギャップを使用して、」博士論文、電気およびコンピュータ工学科、コロラド州立大学、フォートコリンズ、COは、2005年秋。

[Pi05b] N. M. Piratla, A. P. Jayasumana and A. A. Bare, "RD: A Formal, Comprehensive Metric for Packet Reordering," Proc. 5th International IFIP-TC6 Networking Conference (Networking 2005), Waterloo, Canada, May 2-6, 2005, LNCS 3462, pp: 78-89.

【Pi05b】N. M. Piratla、A. P. JayasumanaおよびA. A.ベア、 "RD:パケット並べ替えのための正式な、総合メトリック、" PROC。第5回国際IFIP-TC6ネットワーク会議(ネットワーキング2005)、ウォータールー、カナダ、月2-6、2005、LNCS 3462、頁:78-89。

[Pi06] N. M. Piratla and A. P. Jayasumana, "Reordering of Packets due to Multipath Forwarding - An Analysis," Proc. IEE Intl. Conf. Communications ICC 2006, Istanbul, Turkey, Jun. 2006, pp:829-834.

[Pi06] N. M. Piratla及びA. P. Jayasumana、 "マルチパスによる転送にパケットの並び替え - 分析、" PROC。 IEE国際空港。 confに。コミュニケーションICC 2006、イスタンブール、トルコ、2006年6月、頁:829から834まで。

[Per04] Perl Scripts for RLED and RBD,, Last modified on Jul. 18, 2004.

RLEDとRBD、のための[Per04] Perlスクリプトは、最後の2004年7月18日に変更しました。

[Ye06] B. Ye, A. P. Jayasumana and N. Piratla, "On Monitoring of End-to-End Packet Reordering over the Internet," Proc. Int. Conf. on Networking and Services (ICNS'06), Santa Clara, CA, July 2006.

【Ye06] B.イェ、A. P. Jayasumana及びN. Piratla、「インターネット上でエンドツーエンドのパケット並べ替えの監視に、」PROC。 int型。 confに。ネットワーキング・サービス(ICNS'06)、カリフォルニア州サンタクララ、2006年7月に。

[RFC4737] Morton, A., Ciavattone, L., Ramachandran, G., Shalunov, S., and J. Perser, "Packet Reordering Metrics", RFC 4737, November 2006.

[RFC4737]モートン、A.、Ciavattone、L.、ラマチャンドラン、G.、Shalunov、S.、およびJ. Perser、 "パケット並べ替えメトリック"、RFC 4737、2006年11月。

[RFC3763] Shalunov, S. and B. Teitelbaum, "One-way Active Measurement Protocol (OWAMP) Requirements", RFC 3763, April 2004.

[RFC3763] Shalunov、S.及びB. Teitelbaum、 "ワンウェイアクティブな測定プロトコル(OWAMP)の要件"、RFC 3763、2004年4月。

[RFC4656] Shalunov, S., Teitelbaum, B., Karp, A., Boote, J., and M. Zekauskas, "A One-way Active Measurement Protocol (OWAMP)", RFC 4656, September 2006.

[RFC4656] Shalunov、S.、Teitelbaum、B.、カープ、A.、BOOTE、J.、およびM. Zekauskas、 "ワンウェイアクティブな測定プロトコル(OWAMP)"、RFC 4656、2006年9月。

[Pi05c] N. M. Piratla, A. P. Jayasumana and T. Banka, "On Reorder Density and its Application to Characterization of Packet Reordering," Proc. 30th IEEE Local Computer Networks Conference (LCN 2005), Sydney, Australia, Nov. 2005, pp:156-165.

【Pi05c】N. M. Piratla、A. P. Jayasumana及びT.バンカ、「並べ替えの密度及びパケット並べ替えの特性、への応用」PROC。 30日IEEEローカルコンピュータネットワーク会議(LCN 2005)、シドニー、オーストラリア、2005年11月、頁:156-165。

13. Contributors

Jerry McCollom Hewlett Packard, 3404 East Harmony Road Fort Collins, CO 80528, USA

ジェリーMcCollomヒューレット・パッカード、3404東ハーモニー道路フォートコリンズ、CO 80528、USA



Authors' Addresses


Anura P. Jayasumana Computer Networking Research Laboratory Department of Electrical and Computer Engineering 1373 Colorado State University, Fort Collins, CO 80523, USA

電気およびコンピュータ工学1373コロラド州立大学、フォートコリンズ、CO 80523、USAのAnura P. Jayasumanaコンピュータネットワーク研究所部門



Nischal M. Piratla Deutsche Telekom Laboratories Ernst-Reuter-Platz 7 D-10587 Berlin, Germany

Nischal M. Piratlaドイツテレコム研究所エルンスト・ロイタープラッツ7 D-10587ベルリン、ドイツ



Tarun Banka Computer Networking Research Laboratory Department of Electrical and Computer Engineering 1373 Colorado State University Fort Collins, CO 80523, USA

電気およびコンピュータ工学1373コロラド州立大学フォートコリンズ、CO 80523、USAのタルン挽歌コンピュータネットワーク研究所部門



Abhijit A. Bare Agilent Technologies, Inc. 900 South Taft Ave. Loveland, CO 80537, USA

Abhijit A.ベアアジレント・テクノロジー株式会社900南タフトアベニュー。ラブランド、CO 80537、USA



Rick Whitner Agilent Technologies, Inc. 900 South Taft Ave. Loveland, CO 80537, USA

リックWhitnerアジレント・テクノロジー株式会社900南タフトアベニュー。ラブランド、CO 80537、USA



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