JP2010193252A - System, method and program for packet transfer delay quartile monitoring threshold calculation - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a packet transfer delay quantile monitoring threshold calculation technology for calculating a monitoring threshold provided for a transfer delay quantile in accordance with a small number of sample measuring results while further reducing errors. <P>SOLUTION: A packet transfer delay quantile monitoring threshold calculation system comprises: an experience distribution function calculation means 101 for calculating an experience distribution function F1 from a sample set S obtained by pre-measurements; a density function calculation means 102 for calculating a density function F2 from the distribution function F1; a quantile density function calculation means 103 for calculating a density function F3 of a quantile (q) from the distribution function F1, the density function F2, the quantile (q) and a number (n) of samples in quantile calculation; a quantile distribution function calculation means 104 for calculating a distribution function F4 from the density function F3 of the quantile (q); and a threshold calculation means 105 for calculating an inverse function F4<SP>-1</SP>from the distribution function F4 of the quantile (q) and calculating an upper-limit threshold tu and a lower-limit threshold tl from a significant standard (a). <P>COPYRIGHT: (C)2010,JPO&INPIT

Description

  The present invention provides a small sample measurement with a monitoring threshold provided in a quantile of transfer delay for the purpose of detecting an abnormality of the packet transfer delay quantile before the quality to be provided to a user is deteriorated in a packet switching network. The present invention relates to a packet transfer delay quantile monitoring threshold value calculation system, a packet transfer delay quantile monitoring threshold value calculation method, and a program for calculating the same.

  2. Description of the Related Art In recent years, communication information networks such as IP networks that ensure quality represented by the next generation network (NGN) have become widespread.

  In a high-quality IP network, quality monitoring is necessary to detect an event as soon as possible and to quickly connect to a failure response. Also, when providing a delay-sensitive real-time application on an IP network, it is important to monitor packet transfer delay (hereinafter referred to as transfer delay), which is one of quality evaluation measures. When evaluating the transfer delay, generally the statistics (average value, quantile, etc.) of the transfer delay are used as an evaluation index (Non-patent Document 1).

  Then, normality is determined by comparing the evaluation index with a predetermined monitoring threshold. The monitoring threshold mainly includes a threshold for confirming that the evaluation index is within a range that is regularly assumed and a threshold for confirming that the quality to be provided to the user has not deteriorated. When the threshold value described later is used, an abnormality is detected when the quality to be provided to the user is reduced. On the other hand, when the above-described threshold value is used, the user may be able to detect the abnormality before experiencing quality deterioration. The present invention assumes a high-quality IP network, and uses a sample of transfer delay acquired in the past to detect an abnormality detection method that detects that the transfer delay is out of the expected range before the quality provided to the user decreases. set to target.

  In the abnormality detection method for detecting that the transfer delay is out of the assumed range, it is conceivable to set a significance level using the concept of statistical test and calculate a threshold value using a sample obtained from a prior measurement or the like. In that case, the threshold value calculation method differs depending on the statistic as an evaluation index. The average value is known as the central limit theorem that when the sample size is increased, the distribution of the average value approximately follows a normal distribution. For this reason, in the monitoring of the average value, there is a method of calculating a threshold value by assuming a normal distribution (Non-Patent Document 2, Non-Patent Document 3).

  However, in the case of quantiles (statistics used for calculating transfer delay fluctuations), the distribution of quantiles themselves is not a normal distribution (Non-patent Document 4). When calculating the threshold value of the transfer delay quantile, generally, a plurality of quantiles are obtained from samples obtained from prior measurements, etc., and the distribution of the quantiles themselves is estimated. The threshold is calculated based on the distribution of the order itself and the significance level.

  For example, when monitoring the 0.999 quantile of 10000 samples so that the significance level is 1%, generally obtain 100 samples of 0.999 quantile (acquire a total of 1000000 samples), and set the 0.01 quantile of 100 samples. The threshold is used. However, if the sample size is insufficient, the false detection rate when using the calculated threshold value deviates from the set significance level due to bias and variation. When threshold values having different significance levels and false detection rates are applied to monitoring, the following problems arise.

1) When the false detection rate is large with respect to the significance level, there are more events that exceed the threshold than expected, and there is a possibility that extra operating costs may occur despite being normal in nature.

2) When the false detection rate is small with respect to the significance level, there are fewer events that exceed the threshold than expected, and there is a possibility of missing an abnormality that should be captured. Therefore, it is necessary to calculate a threshold value that is less problematic, that is, the false detection rate is closer to the significance level.

ITU-T Rec. Y.1541, `` Network Performance Objectives for IP-Based Services, '' May 2002 I. Miloucheva, E. Muller, and A. Anzaloni, A practical approach to forecast quality of service parameter considering outliers, International Workshop on Inter-domain Performance and Simulation (IPS), 2003. Satoshi Imai, Akiko Okamura, Hitoshi Ueno, Akira Nakago, “Adaptive Real-Time Change Detection Method Based on Monitoring Data: Application to Proactive VoIP Voice Quality Monitoring,” IEICE Technical Report, NS2005-165, pp 29-32, 2004. Sadanori Konishi, Yoshimichi Ochi, Hirohiro Omori, “Method of Computational Statistics -Bootstrap / EM Algorithm / MCMC-”, Asakura Shoten, 2008.

  As described above, in the packet switching network, the monitoring threshold provided in the transfer delay quantile for the purpose of detecting an abnormality in the packet transfer delay quantile before the quality to be provided to the user is deteriorated, When calculating using the calculation method, there is a problem that the false detection rate when using the calculated threshold value deviates from the set significance level due to bias and variation.

  Therefore, in view of the above problems, the present invention provides a packet transfer delay quantile monitoring threshold value calculation system and a packet transfer delay component for calculating a monitor threshold value provided for a transfer delay quantile with less sample measurement results and less error. It is an object of the present invention to provide a rank monitoring threshold value calculation method and a program therefor.

In order to achieve the above object, the present invention has the following configuration.
a) A packet transfer delay quantile monitoring threshold value calculating system for calculating a packet transfer delay quantile monitoring threshold value in an information communication network according to the present invention includes a distribution function and a density function of the packet transfer delay mother distribution as F and f, respectively. And the distribution function and density function of the population distribution estimated from the sample set S are F1 and F2, respectively, and the distribution function and density function of the q quantile in the population distribution estimated from the sample set S are F4 and F3, respectively. An empirical distribution function F1 calculating means for calculating an empirical distribution function F1 of the population distribution estimated from the sample set S from the sample set S obtained by prior measurement, and a sample set from the distribution function F1 of the population distribution estimated from the sample set S Density function F2 calculating means for calculating the density function F2 of the population distribution estimated from S, and the distribution of the population distribution estimated from the sample set S In the population distribution estimated from the sample set S from the distribution function F1, the density function F2 of the population distribution estimated from the sample set S, the quantile q in the population distribution estimated from the sample set S, and the number of samples n at the time of quantile calculation The quantile density function F3 calculating means for calculating the q quantile density function F3 and the q distribution in the population distribution estimated from the sample set S from the q quantile density function F3 in the population distribution estimated from the sample set S. A quantile distribution function F4 calculating means for calculating a quantile distribution function F4;
Calculating an inverse function F4 ^-1 from its distribution function F4 of q quantile in mother distribution estimated from the sample set S, the upper threshold tu from significant level a, having a threshold value t calculating means for calculating a lower threshold tl It is characterized by.

b) The empirical distribution function F1 calculating means calculates the distribution function F1 as an empirical distribution function of the sample set S by the following (Equation 1).

c) Further, the density function F2 calculating means calculates the density function F2 by the following (Equation 2).

なお、v=(v1=0，v2，・・・，vr)は、サンプル集合Ｓから重複値を取り除いて要素０を追加したＳ′を昇順にソートした数列である。

Note that v = (v1 = 0, v2,..., Vr) is a number sequence obtained by sorting S ′ in which an element 0 is added by removing duplicate values from the sample set S in ascending order.

d) Further, the quantile density function F3 calculating means calculates the density function F3 by the following (Equation 3).

（ただし、m=(n-1)q+1）

(However, m = (n-1) q + 1)

e) Further, the quantile density function F3 calculating means uses the density function F3 by using the distribution function F1, the density function F2, the sample number n at the time of calculating the quantile, and the specified quantile q. And
F3 = exp (((m-1) log (F1 (x))) + log (F2 (x)) + ((nm) log (1-F1 (x)))-log (B (m, n- m + 1)))
(However, m = (n-1) q + 1)
It is calculated as follows.

f) The quantile distribution function F4 calculating means calculates the distribution function F4 by the following (Equation 4).

g) The threshold value t calculating means calculates the inverse function F4 ^-1 from the distribution function F4, and calculates the upper limit threshold value tu and the lower limit threshold value tl by the following (Equation 5) using the significance level a. To do.

h) The packet transfer delay quantile monitoring threshold value calculation method for calculating the packet transfer delay quantile monitoring threshold value in the information communication network according to the present invention includes an empirical distribution function and a density function of the population distribution estimated from the sample set S. When the quantile distribution function and the quantile density function of the q quantile in the population distribution estimated from the sample set S are F1 and F2, respectively, and F4 and F3, respectively, the sample set S obtained by the prior measurement is used. An empirical distribution function F1 calculation procedure for calculating the distribution function F1 of the population distribution estimated from the sample set S, and a density function F2 of the population distribution estimated from the sample set S from the empirical distribution function F1 of the population distribution estimated from the sample set S The density function F2 calculation procedure to be calculated, the empirical distribution function F1 of the population distribution estimated from the sample set S, and the population distribution estimated from the sample set S Quantile that calculates density function F3 of q quantile in the population distribution estimated from sample set S from degree function F2, quantile q in population distribution estimated from sample set S, and quantile calculation sample number n Number density function F3 calculation procedure and quantile for calculating q quantile distribution function F4 in population distribution estimated from sample set S from q quantile density function F3 in population distribution estimated from sample set S a distribution function F4 calculation procedure calculates the inverse function F4 ^-1 from its distribution function F4 of q quantile in mother distribution estimated from the sample set S, is calculated upper threshold tu, a lower threshold tl from significance level a threshold and a t calculation procedure.

i) Further, the distribution function F1 is calculated by the above (Equation 1) by the distribution function F1 calculation procedure, the density function F2 is calculated by the (Equation 2) by the density function F2 calculation procedure, The quantile density function F3 is calculated from the above-described quantile density function F3 by the above (Equation 3) (where m = (n-1) q + 1) or F3 = exp (((m-1) log. (F1 (x))) + log (F2 (x)) + ((nm) log (1-F1 (x)))-log (B (m, n-m + 1))) (where m = (n-1) q + 1), the quantile distribution function F4 is calculated by the above-described (Numerical expression 4) by the quantile distribution function F4 calculation procedure, and the threshold (t) calculation procedure is performed by calculating the inverse function F4 ^-1 from the quantile distribution function F4, the upper threshold tu and lower threshold tl, and calculates the above equation (5) with significance level a.

j) The program according to the present invention is a computer which stores an empirical distribution function F1 calculation means, a density function F2 calculation means, a quantile in the packet transfer delay quantile monitoring threshold value calculation system according to any one of the above a) to g). This is a program for functioning as number density function F3 calculating means, quantile distribution function F4 calculating means, and threshold t calculating means.

  According to the present invention, the monitoring threshold provided in the quantile of packet transfer delay in the information communication network can be calculated with less error with a small sample measurement result.

It is a figure which shows the block configuration and input / output of the packet transfer delay quantile monitoring threshold value calculation system 100 for monitoring the packet transfer delay quantile according to the present invention. It is a figure which shows the relationship between the input and output to each means of the packet transfer delay quantile monitoring threshold value calculation system for monitoring the packet transfer delay quantile according to the present invention. 6 is a flowchart for explaining an embodiment of a packet transfer delay quantile monitoring threshold value calculation method for monitoring a packet transfer delay quantile according to the present invention.

  Hereinafter, a packet transfer delay quantile monitoring threshold value calculation system according to the present invention will be described in detail with reference to the drawings.

  FIG. 1 is a diagram showing a block configuration of a packet transfer delay quantile monitoring threshold value calculation system 100 for monitoring a packet transfer delay quantile according to the present invention, and an input unit 200 and an output unit 300.

  As shown in the figure, the packet transfer delay quantile monitoring threshold value calculation system 100 includes an empirical distribution function (F1) calculation means 101, a density function (F2) calculation means 102, and a quantile density function (F3) calculation. It comprises means 103, quantile distribution function (F4) calculating means 104, and threshold (t) calculating means 105.

  FIG. 2 is a diagram showing the relationship between input and output to each means of the packet transfer delay quantile monitoring threshold value calculation system according to the present invention.

  As shown in the figure, the empirical distribution function (F1) calculating means 101 inputs the sample measurement value set (Si) from the input unit 200 and outputs the empirical distribution function (F1).

  The density function (F2) calculating means 102 inputs the empirical distribution function (F1), calculates the density function (F2) therefrom, and outputs it.

  The quantile density function (F3) calculating means 103 inputs an empirical distribution function (F1), a density function (F2), a sample number (n) at the time of quantile calculation, and a specified quantile (p). From these, the quantile density function (F3) is calculated and output.

  The quantile distribution function (F4) calculating means 104 receives the quantile density function (F3), and calculates and outputs the quantile distribution function (F4) therefrom.

  The threshold (t) calculation means 105 receives the quantile distribution function (F4) and the significance level (a), calculates the threshold (t) therefrom, and outputs it to the output unit 300.

  FIG. 3 is a flowchart for explaining an embodiment of a packet transfer delay quantile monitoring threshold value calculation method for monitoring a packet transfer delay quantile according to the present invention.

  In the present invention, the q quantile Qq of n data sets S is defined as follows (Formula 6).

<Step S201>
The empirical distribution function (F1) calculating means 101 calculates the empirical distribution function F1 of the packet transfer delay from the result vector V0 of the sample measurement value set Si obtained by the prior measurement of the packet transfer delay, using the above (Equation 1). calculate. Here, “Indicator” is “1” when the condition (Si ≦ x) is met, and “0” when the condition is not met.

<Step S202>
The density function (F2) calculating means 102 estimates and calculates the packet transfer delay density function F2 from the packet transfer delay experience distribution function F1. Since the empirical distribution function F1 of packet transfer delay is a step function, the density function F2 of packet transfer delay is estimated and calculated from the above (Equation 2). Note that v = (v1 = 0, v2,..., Vr) is a numerical sequence obtained by sorting S ′ in which the duplicate value is removed from the sample set S and the element 0 is added in ascending order.

<Step S203>
The quantile density function (F3) calculating means 103 calculates the above (Equation 3) from the empirical distribution function F1, the density function F2 of the packet transfer delay, the sample number n at the time of calculating the quantile, and the specified quantile q. However, the density function F3 of the packet transfer delay quantile is estimated and calculated from m = (n−1) q + 1).

  First, the density function of the m-th order statistic when m = (n−1) q + 1 is a natural number is calculated, and then expanded to a real function using a beta function B. Since both the empirical distribution function F1 and the density function F2 of the packet transfer delay are step functions in which the discontinuous portions become the set S ′, the density function F3 of the packet transfer delay quantile also has the set S ′. Is a step function.

The quantile density function (F3) calculating means 103 designates the empirical distribution function F1 and density function F2 of the packet transfer delay and the number of samples n at the time of quantile calculation instead of calculating the above (Equation 3). Function using the quantile p
exp (((m-1) log (F1 (x))) + log (F2 (x)) + ((nm) log (1-F1 (x)))-log (B (m, n-m + 1)))
(However, m = (n-1) * q + 1)
May be calculated and used as the quantile density function F3. When calculating with a computer, using this equation reduces the calculation error.

<Step S204>
The quantile distribution function (F4) calculating means 104 integrates the quantile density function F3 according to the above (Equation 4) from the packet transfer delay quantile density function F3, and distributes the packet transfer delay quantile. The function F4 is estimated and calculated. At this time, since the quantile density function F3 is a step function, a function that performs piecewise quadrature with a discontinuous point as a dividing point is referred to as a quantile distribution function F4.

<Step S205>
Threshold (t) calculation means 105 calculates an inverse function F4 ^-1 from its packet transfer delay quantile distribution function F4, to calculate the upper threshold tu and lower limit threshold tl with significance level a. Considering that the quantile density function F3 is a step function and that the quantile distribution function F4 is a monotonically increasing function, the upper limit threshold tu and the lower limit threshold tl are calculated by the above (Equation 5).

  As a result of performing the Monte Carlo simulation by the computer for the packet transfer delay quantile monitoring threshold value calculation method according to the present invention, it is possible to calculate a threshold value closer to the true value compared to the conventional method, and to monitor using the calculated threshold value. When done, it was found that a significance level close to the target could be achieved.

  It should be noted that the empirical distribution function (F1) calculation means 101, the density function (F2) calculation means 102, the quantile density function (F3) calculation means 103, the minutes in the packet transfer delay quantile monitoring threshold value calculation system 100 according to the present invention. The order distribution function (F4) calculation means 104 and the threshold (t) calculation means 105 use the hardware resources such as a CPU and a memory constituting the packet transfer delay quantile monitoring threshold value calculation system 100 for each of the above means. This is realized by executing the corresponding program.

  The programs corresponding to the above means can be distributed to the market via a recording medium such as FD, CD-ROM, DVD, or a network such as the Internet.

100: Monitoring system for packet transfer delay quantile 101: Empirical distribution function (F1) calculating means 102: Density function (F2) calculating means 103: Quantile density function (F3) calculating means 104: Quantile distribution function ( F4) Calculation means 105: Threshold value (t) calculation means 200: Input unit 300: Output unit

Claims (10)

A packet transfer delay quantile monitoring threshold value calculation system for calculating a packet transfer delay quantile monitoring threshold value in an information communication network,
When the distribution function and density function of the population distribution estimated from the sample set S are F1 and F2, respectively, and the distribution function and density function of the q quantile in the population distribution estimated from the sample set S are respectively F4 and F3,
Empirical distribution function F1 calculating means for calculating an empirical distribution function F1 of the population distribution estimated from the sample set S from the sample set S obtained by the prior measurement;
A density function F2 calculating means for calculating a density function F2 of the population distribution estimated from the sample set S from a distribution function F1 of the population distribution estimated from the sample set S;
From the distribution function F1 of the population distribution estimated from the sample set S, the density function F2 of the population distribution estimated from the sample set S, the quantile q in the population distribution estimated from the sample set S, and the sample number n at the time of quantile calculation, Quantile density function F3 calculating means for calculating the q quantile density function F3 in the population distribution estimated from the sample set S;
A quantile distribution function F4 calculating means for calculating a q quantile distribution function F4 in the population distribution estimated from the sample set S from a q quantile density function F3 in the population distribution estimated from the sample set S;
Calculating an inverse function F4 ^-1 from its distribution function F4 of q quantile in mother distribution estimated from the sample set S, the upper threshold tu from significant level a, having a threshold value t calculating means for calculating a lower threshold tl And a packet transfer delay quantile monitoring threshold value calculation system. 2. The packet transfer delay quantile monitoring threshold calculation according to claim 1, wherein the experience distribution function F1 calculating means calculates the distribution function F1 as an experience distribution function of the sample set S by the following (Equation 1). system.

3. The packet transfer delay quantile monitoring threshold value calculation system according to claim 1, wherein the density function F2 calculation means calculates the density function F2 by the following (Equation 2).

Note that v = (v1 = 0, v2,..., Vr) is a number sequence obtained by sorting S ′ in which an element 0 is added by removing duplicate values from the sample set S in ascending order. 4. The packet transfer delay quantile monitoring threshold value calculation according to claim 1, wherein the quantile density function F3 calculation means calculates the density function F3 by the following (Expression 3). system.

(However, m = (n-1) q + 1) The quantile density function F3 calculating means uses the density function F3, the distribution function F1, the density function F2, the sample number n at the time of quantile calculation, and the specified quantile q.
F3 = exp (((m-1) log (F1 (x))) + log (F2 (x)) + ((nm) log (1-F1 (x)))-log (B (m, n- m + 1)))
(However, m = (n-1) q + 1)
The packet transfer delay quantile monitoring threshold value calculation system according to any one of claims 1 to 3, wherein 5. The packet transfer delay quantile monitoring threshold calculation according to claim 1, wherein the quantile distribution function F4 calculating means calculates the distribution function F4 by the following (Equation 4). system.

The threshold value t calculating means calculates the inverse function F4 ^-1 from the distribution function F4, and calculates the upper limit threshold value tu and the lower limit threshold value tl using the significance level a by the following (Equation 5). Item 7. The packet transfer delay quantile monitoring threshold value calculation system according to any one of Items 1 to 6.

A packet transfer delay quantile monitoring threshold calculation method for calculating a packet transfer delay quantile monitoring threshold in an information communication network,
The empirical distribution function and density function of the population distribution estimated from the sample set S are F1 and F2, respectively. The quantile distribution function and quantile density function of the q quantile in the population distribution estimated from the sample set S are F4 and F4, respectively. And F3,
An empirical distribution function F1 calculation procedure for calculating the distribution function F1 of the population distribution estimated from the sample set S from the sample set S obtained by the prior measurement;
A density function F2 calculation procedure for calculating a population distribution density function F2 estimated from the sample set S from a population distribution experience distribution function F1 estimated from the sample set S;
Based on the empirical distribution function F1 of the population distribution estimated from the sample set S, the density function F2 of the population distribution estimated from the sample set S, the quantile q in the population distribution estimated from the sample set S, and the sample number n at the time of quantile calculation A quantile density function F3 calculating procedure for calculating a q quantile density function F3 in the population distribution estimated from the sample set S;
A quantile distribution function F4 calculation procedure for calculating a q quantile distribution function F4 in the population distribution estimated from the sample set S from a q quantile density function F3 in the population distribution estimated from the sample set S;
Calculating an inverse function F4 ^-1 from its distribution function F4 of q quantile in mother distribution estimated from the sample set S, a threshold t calculation procedure for calculating the upper threshold tu, a lower threshold tl from significance level a,
A packet transfer delay quantile monitoring threshold value calculation method comprising: The distribution function F1 is calculated by the following (Equation 6) by the distribution function F1 calculation procedure, the density function F2 is calculated by the following (Equation 7) by the density function F2 calculation procedure, and the quantile density By the function F3 calculation procedure, the quantile density function F3 is expressed by the following (Equation 8) (where m = (n-1) q + 1) or F3 = exp (((m-1) log (F1 (x ))) + log (F2 (x)) + ((nm) log (1-F1 (x)))-log (B (m, n-m + 1))) (where m = (n-1 ) q + 1), the quantile distribution function F4 is calculated by the following (Equation 9) by the quantile distribution function F4 calculation procedure, and the quantile number is calculated by the threshold (t) calculation procedure. 9. The packet transfer delay amount according to claim 8, wherein the inverse function F4 ^-1 is calculated from the distribution function F4, and the upper limit threshold tu and the lower limit threshold tl are calculated by the following (Equation 10) using the significance level a. Order monitoring threshold value calculation method.

  An empirical distribution function F1 calculation means, a density function F2 calculation means, a quantile density function F3 calculation means, a quantile number in the packet transfer delay quantile monitoring threshold value calculation system according to any one of claims 1 to 7. A program for functioning as distribution function F4 calculating means and threshold t calculating means.

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