JP4933475B2 - BAND MANAGEMENT PROGRAM, BAND MANAGEMENT DEVICE, AND BAND MANAGEMENT METHOD - Google Patents

Description

  The present invention relates to a bandwidth management program, a bandwidth management device, and a bandwidth management method.

  2. Description of the Related Art Conventionally, in order to realize smooth operation of an IP network, in a relay device installed at a relay point of a line constituting an IP network, such as a switch or a router that outputs a packet input from an input line to an output line Band management based on an allowable delay time required from an application used by a user is performed.

  The delay time generated in the relay device is determined from the amount of traffic input from the input line to the relay device and the bandwidth based on the capacity of the buffer in the relay device. For example, if the bandwidth is insufficient with respect to the input traffic volume, the delay time increases.

  Therefore, in order to determine an appropriate band so that the delay time generated in the relay device falls within the allowable delay time, it is necessary to monitor the traffic amount on the line input to the relay device. Further, by monitoring the traffic volume, it is possible to determine the soundness of the line and to determine the necessity of adding a line. In other words, it is possible to monitor whether or not the traffic is passing through the relay apparatus within a predetermined delay time, or to detect a steady increase in the traffic amount and to plan the addition of the line.

  Here, the traffic volume can be acquired by collecting MIB (Management Information Base) information stored in the relay apparatus using SNMP (Simple Network Management Protocol).

  The MIB information includes the total number of bytes of packets received by each interface of the relay device. When monitoring the traffic volume, generally, MIB information is collected at intervals of 5 minutes by SNMP, and the latest MIB is collected. From the difference between the total number of bytes included in the information and the total number of bytes included in the MIB information collected last time, the number of bytes of the packet received by the relay device in 5 minutes is calculated, and the average traffic amount (bps: 5 minutes) Bits Per Second) is determined.

  However, in recent years, with the increase in speed and capacity of IP networks, the use of real-time applications such as VoIP (Voice over IP) and video distribution that require real-time data transmission and reception with a short allowable delay time has increased. Yes. A real-time application has a characteristic that a large amount of traffic is generated in a burst manner, and in order to perform high-accuracy bandwidth management, information on a traffic amount with high time resolution is required.

  As described above, since the traffic volume generally monitored is an average traffic volume for 5 minutes, an instantaneous burst of a packet that is actually flowing cannot be grasped. If the bandwidth is determined based on the traffic amount information having a low temporal resolution such as the average traffic amount for 5 minutes, the bandwidth is set to a small value without taking into account the instantaneous burst of the packet. As a result, during a traffic burst that frequently occurs in a real-time application, packets input to the relay apparatus are buffered by the buffer in the switch, resulting in an increased delay. If the packet capacity exceeds the buffer capacity, some packets are discarded. As described above, when the bandwidth is determined based on the traffic amount information with low time resolution, there is a possibility that the real-time application having bursty traffic characteristics may be hindered.

  In order to acquire information of traffic volume with high time resolution, it is necessary to collect MIB information from the relay device at short time intervals by SNMP. In this case, MIB information is transmitted in addition to packet relay processing. Therefore, the load on the CPU of the relay device increases. In addition, there is a method for collecting traffic with high time resolution by installing measurement equipment directly in the line, but in an IP network consisting of many lines, installation of measurement equipment on all lines Is not realistic.

  Therefore, in order to realize a quantitative and smooth operation of an IP network, Patent Document 1 uses a rough time interval (for example, an interval of 5 minutes) acquired by SNMP by using self-similarity of bursty traffic characteristics. ) To estimate bandwidth fluctuations at fine time intervals (for example, every 10 seconds) to perform highly accurate bandwidth management.

  Specifically, MIB information is collected from the relay apparatus at intervals of 5 minutes, and an average traffic amount for 5 minutes (300 seconds) is calculated a plurality of times in a fixed time along a time series. Then, from the time-series data of the average traffic volume for 300 seconds, time-series data of coarser time intervals such as time-series data of the average traffic volume of 600 seconds and time-series data of the average traffic volume of 900 seconds are calculated. The variance value of each time series data is calculated.

  Then, an approximate function is set based on the self-similarity from the calculated variance value of each time series data, and a value indicating the traffic amount variation in a fine time interval is set as, for example, 10 using the set approximate function. Estimate the variance of the average traffic volume per second. Further, the maximum traffic amount when 5 minutes are divided at 10-second intervals is estimated from the estimated dispersion value, and the band is determined based on the estimated maximum traffic amount.

JP 2005-86566 A

  In the current IP network, the frequency of use of real-time applications is increasing further, and the time resolution required for traffic volume information is required to be further subdivided, for example, at intervals of 10 milliseconds. .

  However, in the conventional technique described above, when the variance value is measured from the traffic amount actually measured at a time interval shorter than 10 seconds, the measured variance value deviates greatly from the approximated straight line. Specifically, when the above-described conventional technique is used, the variance value tends to be estimated lower than the measured value.

  As described above, the above-described conventional technique cannot accurately estimate the dispersion value at a time interval shorter than 10 seconds, such as an interval of 10 milliseconds. For this reason, information on traffic volume with high time resolution (specifically, However, since the estimation accuracy of the maximum traffic volume is low and an appropriate bandwidth cannot be determined, the bandwidth management with high accuracy required for realizing the quantitative and smooth operation of the IP network cannot be performed. was there.

  In addition, as the performance of CPUs in recent years increases, a relay apparatus equipped with a high-performance CPU can collect MIB information, for example, at intervals of 1 second by SNMP, but 10 mm. It is difficult to collect MIB information at intervals of seconds because the CPU load increases rapidly.

  Therefore, the present invention has been made to solve the above-described problems of the prior art, and by accurately estimating information on traffic volume with high time resolution, an appropriate band is determined and high accuracy is achieved. An object of the present invention is to provide a bandwidth management program, a bandwidth management device, and a bandwidth management method that enable bandwidth management.

  In order to solve the above-described problems and achieve the object, this program causes a computer to execute a bandwidth management method for managing a bandwidth of a relay device that relays packets between lines constituting an IP network. The information collection procedure for collecting the packet information input from the line to the relay apparatus at a certain time interval, and the information of the packet collected by the information collection procedure at every certain time interval. A traffic information generation procedure for generating a traffic information sequence that is traffic amount information of the traffic information, and generating coarse-grained traffic information that is a traffic information sequence when temporal resolution is coarse-grained from the generated traffic information sequence; The traffic information sequence generated by the traffic information generation procedure and the coarse-grained traffic A shape change index calculation procedure for calculating a shape change index, which is an index indicating the magnitude of the shape change of each of the traffic information, and each of the traffic information series and the coarse-grained traffic information calculated by the shape change index calculation procedure. Using the shape change index, an approximate function determining procedure for determining an approximate function, and using the approximate function determined by the approximate function determining procedure, a target index that is a shape change index up to a target time resolution is determined. A target index determination procedure, a distribution estimation procedure for estimating a traffic amount distribution at the target time resolution using the target index determined by the target index determination procedure, and an estimation by the distribution estimation procedure Based on the distribution of traffic volume at the target time resolution, the response time is within a predetermined target delay time. It is required for the to execute a bandwidth calculation step of calculating the range, to the computer.

  Further, this device is a bandwidth management device that manages the bandwidth of a relay device that relays packets between lines that constitute an IP network, and that receives information on the packet input from the line to the relay device. A traffic information sequence that is traffic volume information for each fixed time interval from the information collected by the information collecting means that collects at regular time intervals and the information of the packets collected by the information collecting means, and the generated traffic information Traffic information generating means for generating coarse-grained traffic information, which is a traffic information series when the time resolution is coarse-grained from the series, the traffic information series generated by the traffic information generating means and the coarse-grained traffic A shape change finger that calculates a shape change index that is an index indicating the magnitude of the shape change of each information A calculating means; an approximate function determining means for determining an approximate function using the traffic information series and the coarse-grained traffic information calculated by the shape change index calculating means; and the approximate function determining means. Using the approximate function determined by the above, the target index determining means for determining a target index that is a shape change index up to the target time resolution, and using the target index determined by the target index determining means, Based on the distribution estimation means for estimating the traffic amount distribution at the target time resolution and the traffic amount distribution at the target time resolution estimated by the distribution estimation means, the response is made within a predetermined target delay time. And a bandwidth calculating means for calculating the determined bandwidth.

  Further, this method is a bandwidth management method for managing the bandwidth of a relay device that relays packets between lines constituting an IP network, wherein the packet information input from the line to the relay device is received. An information collection step for collecting at regular time intervals, and a traffic information sequence that is information on the amount of traffic at each regular time interval is generated from the information on the packets collected by the information collection step, and the generated traffic information A traffic information generation step for generating coarse-grained traffic information, which is a traffic information sequence when the time resolution is coarse-grained from the sequence, and the traffic information sequence generated by the traffic information generation step and the coarse-grained traffic Calculate the shape change index, which is an index indicating the magnitude of the shape change of each information. A shape change index calculating step, an approximate function determining step for determining an approximate function using the traffic information series calculated by the shape change index calculating step and the shape change index of each of the coarse-grained traffic information, Using the approximate function determined in the approximate function determining step, a target index determining step for determining a target index that is a shape change index up to a target time resolution, and the target index determined in the target index determining step Using a distribution estimation step for estimating a traffic amount distribution at the target time resolution, and a predetermined target delay based on the traffic amount distribution at the target time resolution estimated by the distribution estimation step A bandwidth calculating step for calculating a bandwidth according to time. And requirements that it.

  According to the disclosed program, apparatus, and method, it is possible to accurately determine bandwidth information with high time resolution, thereby determining an appropriate bandwidth and performing highly accurate bandwidth management.

  Exemplary embodiments of a bandwidth management program, a bandwidth management device, and a bandwidth management method according to the present invention will be explained below in detail with reference to the accompanying drawings. In the following, a bandwidth management device configured to include a bandwidth management program according to the present invention will be described as an embodiment.

[Configuration of Bandwidth Management Device in This Example]
First, the configuration of the bandwidth management apparatus according to the present embodiment will be described with reference to FIGS. FIG. 1 is a diagram for explaining the outline of the bandwidth management apparatus in the present embodiment, and FIG. 2 is a diagram for explaining the configuration of the bandwidth management apparatus in the present embodiment.

  As shown in FIG. 1, the bandwidth management apparatus 10 in the present embodiment is connected to a switch 20 that relays packets between lines 30 constituting an IP network.

  Here, the switch 20 accumulates the packet input from the line 30 as the input line in the intra-switch buffer 21 provided in the switch 20, and the line as the output line based on the bandwidth set in the switch 20. 1, the bandwidth management apparatus 10 according to the present exemplary embodiment uses an application that is used by a user of an IP network for the time until the packet input to the switch 20 is output to the line 30 as illustrated in FIG. 1. The outline is to manage the bandwidth of the switch 20 so that it falls within the target delay time set based on the allowable delay time required from the above.

  The bandwidth management apparatus 10 according to the present embodiment is mainly characterized in that it is possible to perform bandwidth management with high accuracy. The main features will be described below with reference to FIG.

  As shown in FIG. 2, the bandwidth management device 10 in this embodiment includes an input unit 11, an output unit 12, a communication unit 13, an input / output control I / F unit 14, a storage unit 15, and a processing unit 16. And is connected to the switch 20 via a network or the like.

  The input unit 11 inputs various types of information and includes a keyboard, a mouse, and the like. Particularly closely related to the present invention is a time interval of MIB information received by the communication unit 13 and a time to be described later. Information for setting the time resolution of the time series traffic volume information generated by the sequence traffic volume information generation unit 16a, the types of approximation functions used in the approximation function determination unit 16c described later, the objective parameter determination unit 16d described later, Bandwidth management includes time resolution (for example, 10 milliseconds) used for processing of the traffic amount distribution estimation unit 16e, a target delay time (for example, 100 milliseconds) corresponding to a band calculated by the band calculation unit 16f described later. It is received and input from a network administrator who is an operator of the apparatus 10.

  The output unit 12 outputs various types of information and is configured to include a monitor and a speaker. Particularly, as closely related to the present invention, the traffic amount at the target time resolution estimated by the traffic amount distribution estimation unit 16e described later is provided. The distribution and the band according to the target delay time calculated by the band calculation unit 16f described later are displayed on the monitor screen to notify the network administrator.

  The communication unit 13 communicates with other devices. In particular, as closely related to the present invention, the communication unit 13 is stored in the switch 20 by the SNMP (Simple Network Management Protocol) with the switch 20. MIB (Management Information Base) information is received at regular time intervals. Here, the MIB information includes the total number of bytes of packets input from the line 30 by each interface of the switch 20. The communication unit 13 corresponds to an “information collection procedure” described in the claims.

  Here, the time interval at which the communication unit 13 receives the MIB information from the switch 20 is set by the network administrator so as not to cause any trouble in the packet relay processing according to the processing capability of the CPU of the switch 20. Hereinafter, a case where “1 second” is set by the network administrator as the minimum time resolution for obtaining MIB information, and the communication unit 13 receives MIB information from the switch 20 at intervals of 1 second will be described.

  The input / output control I / F unit 14 controls data transfer between the input unit 11, the output unit 12, the communication unit 13, the storage unit 15, and the processing unit 16.

  The storage unit 15 stores data used for various types of processing by the processing unit 16 and various types of processing results by the processing unit 16, and particularly as closely related to the present invention, as shown in FIG. 15a, time-series traffic amount information storage unit 15b, calculation parameter storage unit 15c, decision approximation function storage unit 15d, objective parameter storage unit 15e, estimated traffic amount distribution storage unit 15f, calculation band storage unit 15g, Is provided.

  The reception data storage unit 15a receives and stores the MIB information received by the communication unit 13 at regular time intervals (1 second intervals) via the input / output control I / F unit 14.

  The time-series traffic volume information storage unit 15b stores time-series traffic volume information generated by a time-series traffic volume information generation unit 16a described later, and the calculation parameter storage unit 15c stores parameters calculated by a parameter calculation unit 16b described later. The determined approximate function storage unit 15d stores the approximate function determined by the approximate function determination unit 16c described later, and the objective parameter storage unit 15e has the target time resolution determined by the target parameter determination unit 16d described later. The estimated traffic amount distribution storage unit 15f stores a traffic amount distribution at a target time resolution estimated by a traffic amount distribution estimation unit 16e described later, and the calculated band storage unit 15g stores a band calculation unit described later. The bandwidth calculated by 16f is stored.

  The processing unit 16 executes various processes based on the received data (MIB information) transferred from the input / output control I / F unit 13 and stored in the received data storage unit 15a, and is particularly closely related to the present invention. As shown in FIG. 2, the time series traffic amount information generating unit 16a, the parameter calculating unit 16b, the approximate function determining unit 16c, the target parameter determining unit 16d, the traffic amount distribution estimating unit 16e, and the band calculating unit 16f and a band setting unit 16g. Here, the time-series traffic volume information generation unit 16a corresponds to the “traffic information generation procedure” described in the claims, and the parameter calculation unit 16b also corresponds to the “shape change index calculation procedure”. The determination unit 16c also corresponds to the “approximation function determination procedure”, the objective parameter determination unit 16d corresponds to the “object index determination procedure”, and the traffic amount distribution estimation unit 16e also corresponds to the “distribution estimation procedure”. The bandwidth calculation unit 16f also corresponds to the “bandwidth calculation procedure”, and the bandwidth setting unit 16g also corresponds to the “bandwidth setting procedure”.

  Processing executed by each functional block included in the processing unit 16 will be described with reference to FIG. FIG. 3 is a diagram for explaining an outline of processing executed by the bandwidth management apparatus according to this embodiment.

  As shown in FIG. 3, the traffic information input to the switch 20 is included in the MIB information stored in the switch 20, and as described above, the reception data storage unit 15a receives it at intervals of 1 second. Stored MIB information.

  The MIB information includes the total number of bytes of packets received by each interface of the switch 20, and is based on a difference value between the total number of bytes included in the latest MIB information and the total number of bytes included in the MIB information received last time. The number of bytes of packets received by the switch 20 per second can be calculated, and the average traffic amount (bps: Bits Per Second) per second can be obtained.

  Accordingly, MIB information is received from the switch 20 at intervals of 1 second in a predetermined period (for example, t minutes), “average traffic amount per second” is sequentially calculated, and a plurality of calculated (for example, “t” (60 × 1)) “average traffic volume per second” is generated as a histogram, thereby generating a traffic volume distribution with a time resolution of 1 second based on actually measured data (see (1) in FIG. 3). ).

  Here, the traffic amount distribution estimation unit 16e uses the processing results of the time-series traffic amount information generation unit 16a, the parameter calculation unit 16b, the approximate function determination unit 16c, and the target parameter determination unit 16d to provide a traffic amount distribution with high time resolution. For example, the traffic amount distribution with a time resolution of 10 milliseconds is estimated (see (3) in FIG. 3).

  For this reason, first, the time-series traffic volume information generation unit 16a shown in FIG. 2 calculates the average of 1-second intervals from the total number of bytes included in the 1-second interval MIB information stored in the reception data storage unit 15a. A plurality of “average traffic volume per second” is calculated along the time series, and time-series traffic volume information that is “average traffic volume per second” along the time series is generated.

  Then, the time-series traffic volume information generation unit 16a generates coarse-grained time-series traffic volume information, which is time-series traffic volume information when the time resolution is coarse-grained, from the generated time-series traffic volume information. The time series traffic volume information corresponds to the “traffic information series” recited in the claims, and the coarse-grained time series traffic volume information also corresponds to the “coarse-grained traffic information”.

  Here, before describing the processing of the time-series traffic volume information generation unit 16a in detail, the time scale used in this embodiment will be described with reference to FIG. FIG. 4 is a diagram for explaining a time scale used in the present embodiment.

As shown in FIG. 4, “m ₁ ” is a time scale indicating the minimum time resolution at which MIB information can be collected. Further, as shown in FIG. 4, “m ₀ ” is an MWM (Multifractal Wavelet Model) (“RHRiedi, MSCrouse, VJRibeiro” calculated based on collected MIB information, that is, measured time-series traffic volume information. , RGBaraniuk, “A Multifractal Wavelet Model with Application to TCP Network Traffic.”, IEEE Transactions on Information Theory, Special issue on multiscale statistical signal analysis and its applications, 45: 992-1018, April, 1999.) On the other hand, it is a time scale that is set in order to define a range that fits the approximate function. The MWM parameters and the approximate function will be described in detail in the description of the parameter calculation unit 16b and the approximate function determination unit 16c. For example, in this embodiment, “m ₁ ” is set to a time scale corresponding to a time resolution of “1 second”, and “m ₀ ” is set to a time scale corresponding to a time resolution of “4 seconds”. Is done.

Further, “m ₂ ” is a time scale indicating the time resolution of the estimated traffic distribution as shown in FIG. For example, in this embodiment, “m ₂ ” is set to a time scale corresponding to a time resolution of “10 milliseconds”.

In the time scale “m”, the time “t” is equally divided into 2 to the power of “m”, such as “2 divisions, 4 divisions, 8 divisions,... In this case, the numerical value is determined by “t = Δt × 2 ^m ”.

That is, the time-series traffic information generation unit 16a generates the time-series traffic information timescale "m _1", further, from the time-series traffic information timescale "m _1", the time scale "m _1" To coarse-grained time-series traffic amount information in a range determined by the time scale “m ₀ ”.

For example, as shown in FIG. 5, the time-series traffic volume information generation unit 16a calculates time-series traffic volume information (time-series traffic volume information of the time scale “m ₁ ”) from the time-series traffic volume information that is “1-second traffic volume”. Coarse-grained time-series traffic amount information that is “amount of traffic for two seconds” coarse-grained by half the resolution is generated. Further, as shown in FIG. 5, the time-series traffic volume information generation unit 16a generates time-series traffic volume information that is “traffic volume for 2 seconds”, and then coarsens the time resolution to one half. The coarse-grained time-series traffic amount information (time-series traffic amount information on the time scale “m ₀ ”) that is the “4-second traffic amount” is sequentially generated. Here, FIG. 5 is a diagram for explaining the time-series traffic amount information generation unit.

The processing of the time series traffic volume information generation unit 16a described above will be described using mathematical expressions. First, it is assumed that the “k” -th value of the time-series traffic amount information on the time scale “m ₁ ” composed of “N” values is expressed by the following equation (1). The “k” -th value is the traffic amount (bit) measured during the time interval [kΔt, (k + 1) Δt]. For example, in this embodiment, “Δt” is “1 second”.

As a result, the “k” -th value of “coarse-grained time series traffic volume information on time scale“ m ”” consisting of “N to the power of“ mm ₁ ”” is expressed by the following equation (2). Is done. Here, the “k” -th value of the coarse-grained time-series traffic amount information is the traffic amount (bit) measured during the time interval [kτ _m , (k + 1) τ _m ]. “Τ _m ” is an integral multiple of “Δt”.

In other words, the time-series traffic amount information generation unit 16a has a time scale “m−1” obtained by coarse-graining the “time scale“ m ”, which is composed of“ N to the power of “mm ₁ ” ”, by half. The “k” -th value of the “coarse-grained time series traffic amount information” is calculated by the following equation (3). As a result, the time-series traffic volume information generation unit 16a sequentially begins with “m = m ₁ ”, “m = m ₁ −1”, “m = m ₁ −2”,. ₀ ”coarse-grained time-series traffic volume information is generated.

  Further, the time series traffic volume information generation unit 16a generates the “k” -th value of the coarse-grained time series traffic volume information of the time scale “m−1”, and the time scale “m” that is the target of summation. The “difference component between the“ 2k ”-th value and the“ 2k + 1 ”-th value” of the traffic amount information of “is also generated sequentially at the same time using equation (4).

  Then, the time-series traffic volume information generation unit 16a stores the generated time-series traffic volume information and coarse-grained time-series traffic volume information in the time-series traffic volume information storage unit 15b.

  Returning to FIG. 2, the parameter calculation unit 16b calculates a parameter indicating the magnitude of the shape change of each of the time-series traffic amount information and the coarse-grained time-series traffic amount information generated by the time-series traffic amount information generation unit 16a. To do. The “parameter” corresponds to the “shape change index” recited in the claims.

  Here, it has been clarified that TCP (transmission control protocol) traffic, which is the main traffic flowing in the IP network, has multifractal characteristics (for example, “RHRiedi, MSCrouse, VJRibeiro, RGBaraniuk,“ A Multifractal Wavelet Model with Application to TCP Network Traffic. ”, IEEE Transactions on Information Theory, Special issue on multiscale statistical signal analysis and its applications, 45: 992-1018, April, 1999.

  In addition, it has been clarified that the multifractality of traffic can accurately represent the correlation of traffic volume between different temporal resolutions (for example, “RHRiedi and J.Levy-Vehel.“ TCP traffic is multifractal: a numerical study. ”Technical Report No. 3129, INRIA Rocquencourt, France, Feb., 1997”).

  In the present embodiment, in order to set a band according to the target allowable time, a traffic amount distribution with a high time resolution is estimated by using the multifractal nature of the traffic described above.

Here, since the MWM that is a multifractal model has a parameter “p ^(m) ” for each time scale “t = Δt × 2 ^m ”, the parameter calculation unit 16 b includes a time-series traffic amount information storage unit. The parameter of the MWM indicating the magnitude of change in the traffic pattern of each of the time-series traffic amount information and the coarse-grained time-series traffic amount information stored in 15b, “p ^(m) (m = m ₀ , m ₀ +1,. , m ₁ ) ”is calculated using equation (5). The larger the parameter value, the smaller the change in the traffic pattern, and the smaller the parameter value, the greater the change in the traffic pattern.

Then, the parameter calculation unit 16b stores the calculated parameter “p ^(m) (m = m ₀ , m ₀ +1,..., M ₁ )” in the calculation parameter storage unit 15c.

The approximate function determination unit 16c stores each of the time-series traffic amount information of “time resolution based on actually measured data (time scale“ m = m ₀ , m ₀ +1,..., M ¹ ”) stored in the calculation parameter storage unit 15c. An approximate function is determined from the MWM parameter “p ^(m) (m = m ₀ , m ₀ +1,..., M ₁ )”. That is, the approximate function determining unit 16c determines an approximate function for calculating a parameter of time-series traffic amount information with a reduced time resolution from parameters calculated based on actually measured data.

Specifically, the approximate function determination unit 16c determines the parameter in the time scale “m ₂ ” corresponding to the above-described time resolution of “10 milliseconds”, so that the approximate function “p ^(m) = f (m ) (m = m ₁ +1, m ₁ +2,..., m ₂ ) ”.

More specifically, the approximate function determination unit 16c sets the exponential function “f _exp (m) = exp (a ₁ + a ₂ m)” as the approximate function “f (m)”, and sets the parameter based on the actually measured data. , Parameters “a ₁ ” and “a ₂ ” of approximate functions satisfying “p ^(m) (m = m ₀ , m ₀ +1,..., M ₁ )” are determined by the method of least squares.

  Then, the approximate function determining unit 16c stores the determined approximate function in the determined approximate function storage unit 15d.

  In the present embodiment, the case where the approximate function determining unit 16c uses an exponential function as the approximate function has been described. However, the present invention is not limited to this, and the parameter calculating unit 16b is based on actual measurement data. Any function that can approximate the calculated parameter can be set as an approximate function. For example, the approximate function determination unit 16c may use a power series function as an approximate function.

For example, the approximate function determination unit 16c uses the power series function “f (m) = a ₁ + a ₂ m + a ₃ m ² + a ₄ m ³ + a ₅ m ⁴ ” as the approximate function “f (m)”. Set the parameters based on the actual measurement data, the approximate function parameters “a ₁ ” to “a ₄ ” that satisfy “p ^(m) (m = m ₀ , m ₀ +1,…, m ₁ )”. It may be determined by multiplication.

In this embodiment, the time scale “m ₀ ” for prescribing the fitting range of the approximation function is set in advance so that only the parameters having a certain fluctuation tendency are used. Approximation using the parameter “p ^(m) (m = m ₀ , m ₀ +1,..., M ₁ )” calculated based on the actual measurement data in the range up to “m ₀ ” Although the case where the function is determined has been described, the present invention is not limited to this, and the parameter “p ^(m) (m = m ⁾ can be set by arbitrarily setting“ m ₀ ”smaller than“ m ₁ ”. _{0, m 0 +1, ...,} m 1) "is calculated and the" ^{p (m) (m = m} 0, m 0 +1, ..., m 1) "among the certain constant variation tendency parameter The approximate function determination unit 16c may determine the approximate function using only

  The objective parameter determination unit 16d determines parameters up to the target time resolution using the approximation function stored in the decision approximation function storage unit 15d.

Specifically, the objective parameter determination unit 16d adds “m = m ₁ +1”, “m = m ₁ +2” to “f _exp (m) = exp (a ₁ + a ₂ m)”, ... “M = m ₂ : time scale corresponding to a time resolution of 10 milliseconds” is substituted in order, and parameters up to a time resolution of “10 milliseconds” are determined.

  Then, the objective parameter determination unit 16d stores the parameters up to the determined time resolution of “10 milliseconds” in the objective parameter storage unit 15e.

The processing so far corresponds to (2) in FIG. That is, the time-series traffic volume information generation unit 16a generates time-series traffic volume information (time resolution “1 second”) of the measured data itself, and time-series traffic volume information (coarse-grained time series) with low time resolution. (Traffic amount information) is generated, and “p ^(m) ” obtained by parameterizing the traffic pattern change of each piece of traffic information in the approximate function matching range is calculated by the parameter calculating unit 16b, and the approximate function determining unit 16c Then, an exponential function that approximates the calculated “p ^(m) ” is determined, and the target parameter determination unit 16d determines parameters up to the target time resolution “10 milliseconds”.

Returning to FIG. 2, the traffic amount distribution estimation unit 16e uses the parameters up to the time resolution of “10 milliseconds” stored in the target parameter storage unit 15e to perform traffic at the target time resolution of “10 milliseconds”. Estimate the distribution of quantities. In other words, the traffic amount distribution estimation unit 16e estimates the traffic amount distribution of “time scale“ m ₂ ”” with high time resolution.

  Specifically, first, the traffic volume distribution estimation unit 16e uses the time series traffic volume information generated by the time series traffic volume information generation unit 16a based on the actual measurement data as a starting point, as shown in FIG. High time-series traffic volume information is generated sequentially and sequentially. FIG. 6 is a diagram for explaining time-series traffic volume information generation processing with high time resolution by the traffic volume distribution estimation unit.

  For example, as shown in FIG. 6, the traffic amount distribution estimation unit 16e uses the “k” -th value in the time-series traffic amount information on the time scale “m” as “a random variable for randomly dividing the traffic amount”. Is divided into two, and the “2k” -th value and “2k + 1” -th value in the time-series traffic volume information of the time scale “m + 1” having a time resolution twice that of the time scale “m” Generate the value of.

  When this process is expressed using mathematical formulas, formula (6) is obtained.

However, the difference component “W _k with the superscript“ (m) ”” used when the “k” -th value in the time-series traffic volume information of the time scale “m” is divided is shown in FIG. Using the “random variable for randomly dividing the traffic amount” shown in FIG.

  Here, the “random variable for randomly dividing the traffic amount” is generally a random variable defined on (−1, 1), and in this embodiment, “to randomly divide the traffic amount” ”Is assumed to be a random variable sequence that follows an independently identical beta distribution“ β (p (m), p (m)) ”. “P (m)” uses a parameter determined by the target parameter determination unit 16d.

The average of “β (p (m), p (m))” is “0”, and the variance is given by “(2p (m) +1) ⁻¹ ”. Therefore, the larger the value of “p (m)”, the smaller the variance value of the random variable, and the amount of change in the traffic amount distribution can be kept small even if the time resolution is increased. Conversely, the smaller the value of “p (m)”, the larger the variance value of the random variable, and the higher the time resolution, the greater the amount of change in the traffic amount distribution.

In this manner, the traffic amount distribution estimation unit 16e sequentially generates time-series traffic amount information with high time resolution such as “m = m ₁ +1” and “m = m ₁ +2” sequentially, and finally Specifically, the time-series traffic amount information of the time scale “m = m ₂ ” corresponding to the time resolution of “10 milliseconds” represented by the equation (8) is generated.

  Then, the traffic amount distribution estimation unit 16e forms a histogram of the generated time-series traffic amount information with a time resolution of “10 milliseconds”, as shown in FIG. 3 (3), so that the time resolution is 10 milliseconds. The traffic amount distribution is estimated, and the result is stored in the estimated traffic amount distribution storage unit 15f.

  The processing so far corresponds to (3) in FIG. That is, as shown in (1) of FIG. 3, in the traffic amount distribution with a time resolution of 1 second based on the measured data, “the minimum traffic amount is about 450 Mbps” and “the maximum traffic amount is about 700 Mbps”. However, as shown in (3) of FIG. 3, by the processing by the traffic amount distribution estimation unit 16e, the “minimum traffic amount is about 400 Mbps” in the traffic amount distribution with a time resolution of 10 milliseconds, and the “maximum traffic amount is about A traffic amount distribution with a high time resolution is estimated, such as “800 Mbps”.

  Returning to FIG. 2, the bandwidth calculation unit 16f outputs the traffic input to the switch 20 to the line 30 based on the traffic amount distribution at the target time resolution stored in the estimated traffic amount distribution storage unit 15f. A bandwidth is calculated so that the time until it falls within the target delay time.

  Specifically, the bandwidth calculation unit 16f calculates a bandwidth in which the 95% point of the traffic amount distribution with a time resolution of 10 milliseconds is the target delay time “100 milliseconds”.

More specifically, the bandwidth calculating unit 16f firstly sets the time series traffic amount information “U” of the time scale “m = m ₂ ” corresponding to the time resolution of “10 milliseconds” generated by the traffic amount distribution estimating unit 16e. Two types of delay times when “ _k ” is input to the single intra-switch buffer 21 in the switch 20 are determined by a recursive equation represented by the following equation. That is, two types of delay times in the simple switch model are determined by a recursive equation represented by Equation (9).

“Τ = Δt / 2 ^(m1−m2) ” is a time resolution corresponding to “m = m ₂ ”, and “C” represents the bandwidth of the output link of the buffer 21 in the switch.

Here, “D _k ” to which the superscript “(upper)” is assigned is processed after the traffic “U _k ” that arrived within the time “τ” is once accumulated in the buffer 21 within the switch. Represents the delay time, and gives the upper bound of the delay time due to true buffering.

On the other hand, “D _k ” to which the superscript “(lower)” is given is the delay time when traffic “U _k ” that arrives within the time “τ” is processed by cut-through without being accumulated. And gives the lower bound of the delay time due to true buffering.

Then, the band calculating unit 16f calculates the 95% point of the distribution of “D _k ” to which the superscript “(upper)” is assigned and “D _k ” to which the superscript “(lower)” is assigned. The bandwidth of 100 milliseconds is calculated as “C ^(upper) ” and “C ^(lower) ” respectively. In the case of a storage and exchange type switch, “C ^(upper) ” is calculated, and the cut-through type switch In some cases, “C ^(lower) ” is calculated as a band for accommodating the target delay time of “100 milliseconds”.

  Then, the bandwidth calculation unit 16f stores the calculated bandwidth in the calculated bandwidth storage unit 15g.

  In the above description, the band calculating unit 16f has described the case where the 95% point of the traffic amount passing through the switch 20 calculates the band where the target delay time is “100 milliseconds”. However, the bandwidth calculation unit 16f may calculate a bandwidth in which the 95% point of the number of packets passing through the switch 20 is “100 milliseconds” that is the target delay time.

  That is, the bandwidth calculation unit 16f obtains the packet number distribution from the traffic amount distribution at the target time resolution stored in the estimated traffic amount distribution storage unit 15f, and is input to the switch 20 based on the obtained packet number distribution. There may be a case in which a bandwidth is calculated so that the time until the traffic is output to the line 30 falls within the target delay time.

  Here, the MIB information collected from the switch 20 and stored in the received data storage unit 15a includes information on the total number of packets as well as the total number of bytes received by each interface in the switch 20.

  Therefore, for example, the bandwidth calculating unit 16f, during the measurement period, the total number of bytes and the total number of packets included in the “first collected MIB information” and the total number of bytes and the total number included in the “last collected MIB information”. Calculate the “total packet length” by calculating the total number of bytes and total number of packets in the measurement period from the difference between each and the number of packets, and dividing the total number of packets in the measurement period by the total number of packets in the measurement period. Is calculated in advance.

Then, the bandwidth calculation unit 16f calculates the time-series traffic amount information “U _k ” of the time scale “m = m ₂ ” corresponding to the time resolution of “10 milliseconds” generated by the traffic amount distribution estimation unit 16e. The number of packets is calculated by dividing by “average packet length”. That is, the bandwidth calculating unit 16f calculates the number of packets for each time-series traffic amount information “U _k ” of “m = m ₂ ” to obtain the packet number distribution with respect to the delay time, and the 95% point is the target delay time. The bandwidth that is “100 milliseconds” is calculated.

Specifically, the bandwidth calculation unit 16f calculates the “average packet length” and then sets the time scale “m = m ₂ ” corresponding to the time resolution of “10 milliseconds” generated by the traffic amount distribution estimation unit 16e. Similarly to the above case, the two types of delay times when the time series traffic volume information “U _k ” is input to the single intra-switch buffer 21 in the switch 20 are expressed by Expression (9). Determined by recursive expression.

At this time, the traffic amount “U _k ” for “D _k ” with the superscript “(upper)” and “D _k ” with the superscript “(lower)” The number of packets is calculated by dividing by “average packet length”.

Then, the bandwidth calculation unit 16f includes 95 of the packet number distribution of “D _k ” to which the superscript “(upper)” is assigned and “D _k ” to which the superscript “(lower)” is assigned. Bands where the% point is 100 milliseconds are calculated as “C ^(upper) ” and “C ^(lower) ”, respectively. In the case of a storage and exchange type switch, “C ^(upper) ” is also used, and cut-through In the case of the type switch, “C ^(lower) ” is calculated as a band for accommodating the target delay time “100 milliseconds”.

  This makes it possible to calculate an appropriate bandwidth not only for a bandwidth setting request that achieves the target delay time based on the traffic volume, but also for a bandwidth setting request that achieves the target delay time based on the number of packets. it can.

  The bandwidth setting unit 16g sets a bandwidth for the switch 20 to be within “100 milliseconds” that is the target delay time stored in the calculated bandwidth storage unit 15g.

Specifically, the band setting unit 16g reads “C ^(upper) ” or “C ^(lower) ” calculated by the band calculation unit 16f from the calculated band storage unit 15g and sets the same in the switch 20.

The processing so far corresponds to (4) in FIG. That is, as shown in (3) of FIG. 3, from the estimated traffic distribution with a time resolution of 10 milliseconds, the target delay time “100 milliseconds” in the simple switch model as shown in (4) of FIG. "C ^(upper) " and "C ^(lower) ", which are bands when the target delay time "100 milliseconds" is satisfied with a probability of 95%, is calculated. Then, the calculated bandwidth is set in the switch 20.

[Processing procedure by the bandwidth management apparatus in this embodiment]
Next, processing of the bandwidth management apparatus 10 in the present embodiment will be described with reference to FIG. FIG. 7 is a flowchart for explaining the processing of the bandwidth management apparatus according to this embodiment.

  As shown in FIG. 7, the bandwidth management device 10 according to the present exemplary embodiment, when the MIB data stored in the received data storage unit 15a from the switch 20 via the communication unit 13 has measured data for a predetermined period (step). (Yes in S701), the time-series traffic volume information generating unit 16a generates time-series traffic volume information at time intervals based on the measured data, and coarse-grained with coarse-grained time resolution from the generated time-series traffic volume information. Time-series traffic volume information is generated (step S702).

  Then, the parameter calculation unit 16b calculates the MWM parameters of the time-series traffic amount information and the coarse-grained time-series traffic amount information generated by the time-series traffic amount information generation unit 16a (step S703).

  Subsequently, the approximate function determination unit 16c determines an approximate function from the MWM parameters of the time series traffic amount information and the coarse-grained time series traffic amount information calculated by the parameter calculation unit 16b (Step S704). The parameter determination unit 16d determines parameters up to the target time resolution using the approximate function determined by the approximate function determination unit 16c (step S705).

  Subsequently, the traffic amount distribution estimation unit 16e estimates the traffic amount distribution at the target time resolution using the parameters up to the target time resolution determined by the target parameter determination unit 16d (step S706). Based on the traffic amount distribution at the target time resolution estimated by the traffic amount distribution estimating unit 16e, the calculation unit 16f determines the time until the traffic input to the switch 20 is output to the line 30. A bandwidth to be accommodated within the delay time is calculated (step S707).

  Then, the bandwidth setting unit 16g sets the bandwidth calculated by the bandwidth calculation unit 16f in the switch 20 (step S708), and ends the process.

[Effect of this embodiment]
As described above, according to the present embodiment, the time-series traffic volume information generation unit 16a generates time-series traffic volume information at time intervals based on measured data, and the time resolution from the generated time-series traffic volume information. The coarse-grained time-series traffic amount information generated by coarse-graining is generated, and the parameter calculation unit 16b generates the time-series traffic amount information and the coarse-grained time-series traffic amount information generated by the time-series traffic amount information generation unit 16a, respectively. The approximate function determination unit 16c calculates the MWM parameter indicating the magnitude of the shape change of the time series traffic amount information and the coarse-grained time series traffic amount information calculated by the parameter calculation unit 16b. The approximate function is determined, and the objective parameter determining unit 16d is determined by the approximate function determining unit 16c. Using an approximate function that determines parameters up to the time resolution of interest.

  The traffic amount distribution estimation unit 16e estimates the traffic amount distribution at the target time resolution using the parameters up to the target time resolution determined by the target parameter determination unit 16d, and the bandwidth calculation unit 16f Based on the traffic amount distribution at the target time resolution estimated by the traffic amount distribution estimating unit 16e, a band corresponding to the target delay time is calculated, and the band setting unit 16g calculates the band calculated by the band calculating unit 16f. Is set in the switch 20, so that it is possible to determine an appropriate band by accurately estimating the traffic amount information with high time resolution, and to perform the band management with high precision as described above. Is possible.

  In addition, the approximate function determination unit 16c has a time resolution having a predetermined tendency to change among the MWM parameters of the time-series traffic amount information and the coarse-grained time-series traffic amount information calculated by the parameter calculation unit 16b. Since the approximate function is determined using the MWM parameter in the time-series traffic volume information of only the range, the accurate parameter is determined from the high-accuracy approximate function, so that the traffic volume information with high time resolution can be obtained more accurately. Can be estimated. As a result, a more appropriate band can be determined, and band management with higher accuracy can be performed.

[Comparative example]
Next, the usefulness of the proposed method disclosed in the present embodiment will be described with reference to FIG. Specifically, the case where the band is set by the proposed method disclosed in the present embodiment and the case where the band is set by the existing method disclosed in Japanese Patent Laid-Open No. 2005-86566 are actually high in time resolution. This will be described by comparing the case where the traffic volume distribution is measured and the band is set. Here, FIG. 8 is a diagram for explaining a comparative example.

  First, time-series traffic amount information and coarse-grained time-series traffic amount information are generated from actually measured data at 1-second intervals, and the respective parameters are calculated to determine a range in which the parameter fluctuation tendency is constant. . Further, the minimum time resolution applicable to the MWM was determined by measuring the traffic amount distribution having a time resolution higher than 1 second.

Thereby, the time scale “m ₁ ” is set to “13”, the time scale “m ₀ ” is set to “11”, and the time scale “m ₂ ” is set to “20”. In this comparative example, the time scale “13” corresponds to “1.28 seconds”, the time scale “11” corresponds to “5.12 seconds”, and the time scale “20” corresponds to “10 milliseconds”. ".

  Then, the target delay time was set to “100 milliseconds”, and MIB information at intervals of 1 second in the measurement time “174 minutes” was collected. At the same time, MIB information was collected at intervals of “10 milliseconds” in the measurement time “174 minutes”.

Then, based on the determined time scale “m ₁ = 13, m ₀ = 11, m ₂ = 20”, traffic amount information of “m = 13, 12, 11” is generated, and the parameter “p ⁽¹³⁾ , p ⁽¹²⁾ , p ⁽¹¹⁾ ”and satisfy“ p _exp (m) = exp (a ₁ + a ₂ m) satisfying these “p ⁽¹³⁾ , p ⁽¹²⁾ , p ⁽¹¹⁾ ” The approximate function was determined by determining “a ₁ , a ₂ ”.

Furthermore, “p ^{(14) to} p ^{( 20)} ” is determined from the determined approximate function, and from the traffic volume distribution corresponding to the time scale “13”, the traffic volume distribution and time scale corresponding to the time scale “14” Estimate the traffic volume distribution with high time resolution, such as the traffic volume distribution corresponding to “15”, and finally estimate the traffic volume distribution corresponding to the time scale “20”. Of 95%.

  As a result, as shown in “Proposed method” in FIG. 8A, the 95% point of the traffic amount distribution estimated by the method proposed in this example was calculated as “660.0 Mbps”. On the other hand, the 95% point of the traffic amount distribution estimated using the existing method (estimation of the maximum traffic amount by the variance value) disclosed in Japanese Patent Laid-Open No. 2005-86566 is shown in FIG. Calculated as “642.4 Mbps”, as shown in “Existing Method”.

  On the other hand, the 95% point of the traffic amount distribution obtained by actually collecting the MIB information at intervals of “10 milliseconds” is “686.4 Mbps” as shown in “Actual measurement data” in FIG. Met.

  As described above, it was found that the traffic amount distribution can be estimated more accurately when the “proposed method” is used than when the “existing method” is used.

  A case where the delay time is verified with respect to the estimated bandwidth by using a switch model (single switch model) having measured data as input will be described with reference to FIG. That is, as shown in FIG. 8B, the target delay time “100 milliseconds” can be realized by the set bandwidth “607.3 Mbps” based on the actually measured data (true value) at the intervals of “10 milliseconds”. .

On the other hand, as shown in “Proposed method” in FIG. 8B, in the case of (a) a storage-and-switch type switch, “set bandwidth: C ^(upper) ” is calculated as “609.0 Mbps”. As a result, the delay time is “71.8 milliseconds”, and in the case of (b) cut-through type switch, “set band: C ^(lower) ” is calculated as “607.2 Mbps”, and as a result, the delay time is calculated. Becomes “103.2 milliseconds”. The set bandwidth shown in “Proposed method” in FIG. 8B calculates the “average number of packets” from the total number of bytes and the total number of packets in the measurement time “174 minutes”, and the number of packets obtained by this calculation. This is a band calculated based on the distribution.

In this way, by setting “C ^(upper) ” calculated assuming the worst case storage-switching switch as the set bandwidth, a delay time lower than the target delay time “100 milliseconds” is achieved. Turned out to be. Even when “C ^(lower) ” calculated on the assumption of a cut-through switch is set as a set band, the delay time only slightly exceeds the target delay time.

On the other hand, as shown in FIG. 8B, in the “existing method”, in the case of (a) a storage-and-switch type switch, “set bandwidth: C ^(upper) ” is calculated as “565.0 Mbps”. As a result, the delay time is “35.4 seconds”, and (b) in the case of a cut-through type switch, “setting band: C ^(lower) ” is calculated as “564.9 Mbps”. The delay time is “35.6 seconds”, and the delay time greatly exceeds the target delay time.

  Further, as shown in FIG. 8B, when the “existing method” is used, the set bandwidth for satisfying the target delay time “100 milliseconds” is compared with the “measured data” by an error “42”. .3 Mbps ”is calculated only in the case of using the“ proposed method ”, but the set bandwidth for satisfying the target delay time“ 100 milliseconds ”is compared with the“ measured data ”by the error“ 1. It was found that it was possible to calculate with high accuracy within “7 Mbps”.

  Thus, in order to achieve the target delay time, it has been proved that it is useful to set the bandwidth calculated by the proposed method disclosed in the present embodiment.

  In the above-described embodiment, the case has been described in which the bandwidth calculated by the bandwidth calculation unit 16f is automatically set to the switch 20 by the bandwidth setting unit 16g, but the present invention is not limited to this. Alternatively, the network administrator may manually set the bandwidth calculated by the bandwidth calculation unit 16f for the switch 20.

  In the present embodiment, the case where the bandwidth management device 10 manages the bandwidth of one switch 20 has been described. However, the present invention is not limited to this, and the bandwidth management device 10 includes a plurality of switches 20. In this case, MIB information may be collected from each to manage the bandwidth of each of the plurality of switches 20.

  In addition, among the processes described in this embodiment, all or part of the processes described as being performed automatically can be performed manually, or the processes described as being performed manually can be performed. All or a part can be automatically performed by a known method. In addition, the processing procedure, control procedure, specific name, and information including various data and parameters shown in the above-described document and drawings can be arbitrarily changed unless otherwise specified.

  Further, each component of each illustrated apparatus is functionally conceptual, and does not necessarily need to be physically configured as illustrated. In other words, the specific form of distribution / integration of each device is not limited to that shown in the figure, and all or a part thereof may be functionally or physically distributed or arbitrarily distributed in arbitrary units according to various loads or usage conditions. Can be integrated and configured. For example, the approximate function determining unit 16c and the objective parameter determining unit 16d shown in FIG. 2 may be integrated. Further, all or any part of each processing function performed in each device may be realized by a CPU and a program analyzed and executed by the CPU, or may be realized as hardware by wired logic.

  The bandwidth management method described in the present embodiment can be realized by executing a program prepared in advance on a computer such as a personal computer or a workstation. This program can be distributed via a network such as the Internet. The program can also be executed by being recorded on a computer-readable recording medium such as a hard disk, a flexible disk (FD), a CD-ROM, an MO, and a DVD and being read from the recording medium by the computer.

  As described above, the bandwidth management program, the bandwidth management device, and the bandwidth management method according to the present invention are useful when managing the bandwidth of a relay device that relays a packet between lines constituting an IP network, In particular, it is suitable for performing bandwidth management with high accuracy.

It is a figure for demonstrating the outline | summary of the bandwidth management apparatus in a present Example. It is a figure for demonstrating the structure of the band management apparatus in a present Example. It is a figure for demonstrating the outline of the process which the bandwidth management apparatus in a present Example performs. It is a figure for demonstrating the time scale used in a present Example. It is a figure for demonstrating a time series traffic amount information generation part. It is a figure for demonstrating the time series traffic amount information generation process with a high time resolution by the traffic amount distribution estimation part. It is a flowchart for demonstrating the process of the bandwidth management apparatus in a present Example. It is a figure for demonstrating a comparative example.

Explanation of symbols

DESCRIPTION OF SYMBOLS 10 Band management apparatus 11 Input part 12 Output part 13 Communication part 14 Input / output control I / F part 15 Storage part 15a Received data storage part 15b Time series traffic amount information storage part 15c Calculation parameter storage part 15d Determination approximate function storage part 15e Purpose Parameter storage unit 15f Estimated traffic amount distribution storage unit 15g Calculation band storage unit 16 Processing unit 16a Time series traffic amount information generation unit 16b Parameter calculation unit 16c Approximate function determination unit 16d Objective parameter determination unit 16e Traffic amount distribution estimation unit 16f Band calculation unit 16g Band setting part 20 Switch 21 Switch buffer 30 Line

Claims (8)

A bandwidth management program for causing a computer to execute a bandwidth management method for managing a bandwidth of a relay device that relays packets between lines constituting an IP network,
Information collection procedure for collecting information of the packet input from the line to the relay device at regular time intervals;
A traffic information sequence that is information on the amount of traffic at each predetermined time interval is generated from the information of the packet collected by the information collection procedure, and the time resolution is coarse-grained from the generated traffic information sequence A traffic information generation procedure for generating coarse-grained traffic information that is a traffic information sequence;
A shape change index calculation procedure for calculating a shape change index that is an index indicating the magnitude of the shape change of each of the traffic information sequence and the coarse-grained traffic information generated by the traffic information generation procedure;
An approximate function determination procedure for determining an approximate function using the traffic information series calculated by the shape change index calculation procedure and the shape change index of each of the coarse-grained traffic information;
A target index determination procedure for determining a target index that is a shape change index up to a target time resolution using the approximation function determined by the approximation function determination procedure;
A distribution estimation procedure for estimating a distribution of traffic volume at the target time resolution using the target index determined by the target index determination procedure;
A bandwidth calculation procedure for calculating a bandwidth according to a predetermined target delay time based on the traffic amount distribution at the target time resolution estimated by the distribution estimation procedure;
Management program for causing a computer to execute   The approximate function determination procedure uses only the shape change index that has a certain tendency to change among the shape change indices of the traffic information series and the coarse-grained traffic information calculated by the shape change index calculation procedure. The bandwidth management program according to claim 1, wherein the approximate function is determined.   The bandwidth calculation procedure calculates a bandwidth according to the predetermined target delay time based on a distribution of the number of packets calculated from the traffic amount distribution at the target time resolution estimated by the distribution estimation procedure. The bandwidth management program according to claim 1 or 2, wherein:   The bandwidth management program according to claim 1, further causing a computer to execute a bandwidth setting procedure for setting the bandwidth calculated by the bandwidth calculation procedure in the relay device.   The bandwidth management program according to claim 1, wherein the approximate function is an exponential function.   The bandwidth management program according to claim 1, wherein the approximate function is a power series function. A bandwidth management device that manages the bandwidth of a relay device that relays packets between lines constituting an IP network,
Information collecting means for collecting the information of the packet input from the line to the relay device at regular time intervals;
A traffic information sequence that is information on the amount of traffic for each predetermined time interval is generated from the information of the packet collected by the information collecting means, and the time resolution is coarse-grained from the generated traffic information sequence Traffic information generating means for generating coarse-grained traffic information that is a traffic information sequence;
A shape change index calculating means for calculating a shape change index that is an index indicating the magnitude of the shape change of each of the traffic information series and the coarse-grained traffic information generated by the traffic information generating means;
Approximation function determination means for determining an approximate function using the traffic information series calculated by the shape change index calculation means and the shape change indices of the coarse-grained traffic information,
Using the approximate function determined by the approximate function determining means, a target index determining means for determining a target index that is a shape change index up to a target time resolution;
Distribution estimation means for estimating a traffic amount distribution at the target time resolution using the objective index determined by the objective index determination means;
Band calculation means for calculating a band according to a predetermined target delay time based on the traffic amount distribution at the target time resolution estimated by the distribution estimation means;
A bandwidth management device comprising: A bandwidth management method for managing a bandwidth of a relay device that relays packets between lines constituting an IP network,
An information collecting step of collecting information of the packet input from the line to the relay device at regular time intervals;
A traffic information sequence that is information of the traffic volume at each fixed time interval is generated from the information of the packet collected by the information collecting step, and the time resolution is coarse-grained from the generated traffic information sequence A traffic information generation step for generating coarse-grained traffic information that is a traffic information sequence;
A shape change index calculation step for calculating a shape change index that is an index indicating the magnitude of the shape change of each of the traffic information series and the coarse-grained traffic information generated by the traffic information generation step;
An approximate function determining step for determining an approximate function using the shape change index of each of the traffic information series and the coarse-grained traffic information calculated by the shape change index calculating step;
A target index determination step of determining a target index that is a shape change index up to a target time resolution using the approximation function determined in the approximation function determination step;
A distribution estimation step of estimating a traffic amount distribution at the target time resolution using the target index determined by the target index determination step;
A bandwidth calculating step of calculating a bandwidth according to a predetermined target delay time based on the traffic amount distribution at the target time resolution estimated by the distribution estimating step;
A bandwidth management method comprising:

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