JP6615808B2 - Method, apparatus and program for predicting packet delay in server - Google Patents

Description

  The present invention relates to a technique for predicting packet delay in a server.

  Conventionally, there is a technique for reproducing a processing model of a software router and acquiring the packet delay using a traffic simulator (see Non-Patent Document 1, for example). According to this technology, a model simulating the packet processing process of Linux (registered trademark) OS is created and implemented, and linked to a network simulator. As a result, the packet processing delay can be predicted for an arbitrary traffic pattern.

  There is also a technique for observing delay fluctuations in time series, creating a model based on the observation results, and predicting the state of future delay fluctuations (see, for example, Patent Document 1). According to this technique, a time series model based on two different methods is generated from a measurement result of a delay fluctuation time series. Then, the accuracy of the model is improved by correcting the generated time series model based on the divergence between the models.

Japanese Patent Application Laid-Open No. 2014-135585

A. Beifub, D. Raumer, P. Emmerich and TM Runge, “A study of networking software induced latency,” in Proc. Of NetSys2015, March 2015, [online], [February 11, 2017 search], Internet <URL: https://www.net.in.tum.de/publications/papers/NetSys2015.pdf>

However, according to the technologies described in Non-Patent Document 1 and Patent Document 1 described above, it is assumed that the server configuration is set in advance as fixed. In other words, it is impossible to predict how the delay will change due to the server setting change.
If it is attempted to predict a change in delay due to a setting change based on Non-Patent Document 1 and Patent Document 1, a model must be generated and corrected for each setting change. That is, a lot of measurement work and calibration need to be performed.

  Therefore, an object of the present invention is to provide a method, an apparatus, and a program capable of predicting a packet transfer delay according to a change in server settings without performing many preliminary measurements.

According to the present invention, in a delay prediction method for an apparatus that inputs a packet to a server and predicts a packet transfer delay of the server based on a measurement result of the packet output from the server.
The device
As a preliminary stage,
A first step of setting the number of reception network interfaces = 1 for the server, and measuring the first throughput λ _out (1), the delay distribution D, and the number of hardware interrupts σ of the reception queue per unit time;
A second step of setting the number of received network interfaces = Q (> 1) for the server and measuring the second throughput λ _out (Q);
Using the first throughput λ _out (1) and the second throughput λ _out (Q), the received network interface number q (> 1) from the delay distribution D and the hardware interrupt number σ of the reception queue per unit time. And a third step of calculating a probability density function f (x) of the waiting time according to
Using the parameter of the probability density function f (x), a packet transfer delay corresponding to the number q of received network interfaces of the server is predicted.

According to another embodiment of the delay prediction method of the apparatus of the present invention,
The reception network interface number q is the reception queue number q.
The probability density function f (x) is based on a parameter calculated by approximating the Erlang distribution to the delay distribution D.
The packet transfer delay is also preferably calculated using parameters.

τ＝ｋ／β＋γ
ｋ：分布の形状を表すパラメータ（正の整数）
β：分布の広がりを表すパラメータ（正の実数）
γ：遅延の原点からのズレ（位置）を表すパラメータ（正の実数）
ことも好ましい。 According to another embodiment of the delay prediction method of the apparatus of the present invention,
The probability density function f (x) and the average packet transfer delay τ are expressed as follows using the parameters k, β, and γ.

τ = k / β + γ
k: parameter representing the shape of the distribution (positive integer)
β: Parameter indicating the spread of the distribution (positive real number)
γ: Parameter indicating the deviation (position) from the origin of the delay (positive real number)
It is also preferable.

ことも好ましい。 According to another embodiment of the delay prediction method of the apparatus of the present invention,
Using the hardware interrupt number σ of the reception queue per unit time when the reception queue number q = 1 acquired in the first step,
The throughput λ _out (q) and the parameters k, β, γ at the number of queues q are expressed as follows:

It is also preferable.

According to the present invention, in a delay prediction apparatus that inputs a packet to a server and predicts a packet transfer delay of the server based on a measurement result of the packet output from the server.
A first preliminary measurement unit configured to set the number of reception network interfaces = 1 for the server and measure the first throughput λ _out (1), the delay distribution D, and the number of hardware interrupts σ of the reception queue per unit time; ,
A second preliminary measuring means for setting the number of received network interfaces = Q (> 1) for the server and measuring the second throughput λ _out (Q);
Using the first throughput λ _out (1) and the second throughput λ _out (Q), the received network interface number q (> 1) from the delay distribution D and the hardware interrupt number σ of the reception queue per unit time. A probability distribution calculating means for calculating a probability density function f (x) of the waiting time according to
And a delay prediction unit that predicts a packet transfer delay according to the number q of received network interfaces of the server using a parameter of the probability density function f (x).

According to the present invention, in a program for inputting a packet to a server and causing a computer mounted on a device that predicts a packet transfer delay of the server to function based on a measurement result of the packet output from the server,
A first preliminary measurement unit configured to set the number of reception network interfaces = 1 for the server and measure the first throughput λ _out (1), the delay distribution D, and the number of hardware interrupts σ of the reception queue per unit time; ,
A second preliminary measuring means for setting the number of received network interfaces = Q (> 1) for the server and measuring the second throughput λ _out (Q);
Using the first throughput λ _out (1) and the second throughput λ _out (Q), the received network interface number q (> 1) from the delay distribution D and the hardware interrupt number σ of the reception queue per unit time. A probability distribution calculating means for calculating a probability density function f (x) of the waiting time according to
Using the parameter of the probability density function f (x), the computer is caused to function as a delay prediction unit that predicts a packet transfer delay according to the number q of received network interfaces of the server.

  According to the delay prediction method, apparatus, and program of the present invention, there are provided a method, apparatus, and program capable of predicting a packet transfer delay according to a change in server settings without performing many preliminary measurements. For the purpose.

It is a system block diagram containing the delay prediction apparatus of this invention. It is a functional block diagram of a measuring object server. It is a functional block diagram of the delay prediction apparatus in this invention. It is a framework showing the calculation process of the average packet delay prediction model based on Erlang k distribution. It is a graph showing the parameter according to the number of reception queues for every parameter of a probability density function. It is a graph showing the throughput and average packet transfer delay with respect to the number of reception queues.

  Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings.

  FIG. 1 is a system configuration diagram including a delay prediction apparatus according to the present invention.

  The delay prediction apparatus 1 of the present invention inputs a test packet to the measurement target server 2 and predicts the packet transfer delay of the measurement target server based on the measurement result of the packet output from the measurement target server.

  According to FIG. 1 (a), the delay prediction apparatus 1 is directly connected to the input interface and the output interface of the measurement target server 2. The delay prediction apparatus 1 itself outputs a test packet directly to the measurement target server 2 and receives the measurement packet from the measurement target server 2. In order to measure packet transfer delay, it is not affected by the network at all.

  According to FIG. 1B, the test traffic transmission device 101 is connected to the input interface of the measurement target server 2, and the measurement traffic reception device 102 is connected to the output interface of the measurement target server 2. The delay prediction apparatus 1 operated by an operator controls the test traffic transmission apparatus 101 and the measurement traffic reception apparatus 102 via a network. The test traffic transmitter 101 and the measurement traffic receiver 102 are dedicated devices for testing, and are controlled from the delay prediction device 1 via an API (Application Programming Interface).

  The delay prediction apparatus 1 can change the setting of the reception network interface number q of the measurement target server 2 via the network. The reception network interface number q specifically means the reception queue number q of the reception ring buffer.

When the test traffic transmitting apparatus 101 receives a measurement start instruction from the delay prediction apparatus 1, the test traffic transmitting apparatus 101 transmits test traffic to the input interface of the measurement target server 2 (for example, 10 Gbps).
When the measurement traffic receiving apparatus 102 receives a measurement start instruction from the delay prediction apparatus 1, the measurement traffic receiving apparatus 102 starts measuring a packet output from the output interface of the measurement target server 2. Specifically, the measurement traffic receiving apparatus 102 measures the following information and transmits the measurement result to the delay prediction apparatus 1.
λ: Throughput (number of received packets per unit time)
D: Packet delay distribution

  Further, the delay prediction apparatus 1 acquires the hardware interrupt number σ of the reception queue (ring buffer) per unit time from the measurement target server 2 after measuring the packet transfer delay in the measurement target server 2.

  FIG. 2 is a functional configuration diagram of the measurement target server.

  The measurement target server 2 forms a plurality of buffers resulting from packet delay at the input stage and output stage of packet processing. FIG. 2 shows an architecture that is a framework for packet transfer processing in Linux.

(S21) The input packet is temporarily stored in a ring buffer as an interface of q (≧ 1) NICs (Network Interface Controllers). The ring buffer outputs packets to q reception queues by round robin.
(S22) Each time a reception hardware interrupt occurs, the packets stored in q reception queues are output to the reception buffer Poll_list on the Linux OS by a fixed number (maximum w).
(S23) Next, every time a reception software interrupt occurs, a certain number (maximum B) is read from the reception buffer, and these packets are input to the packet processing unit.
(S24) The packet processing unit executes various processes as a server such as transfer processing (destination identification, packet update, etc.).
(S25) The packet output from the packet processing unit is output to the transmission buffer Qdisc.
(S26) Each time a transmission software interrupt occurs, a packet is read from the transmission buffer and output to a ring buffer Tx-ring as a transmission-side NIC interface.
(S27) Each time a transmission hardware interrupt occurs, the packet is read from the ring buffer, and the packet is output from the measurement target server 2.

  The packet output from the measurement target server 2 is output with a variable delay. Therefore, the delay distribution D can be derived by measuring the packet group output in time series from the measurement target server 2.

<Observed event of packet transfer>
First, the maximum throughput decreases monotonically as the number of reception queues increases, but the average packet delay is a convex function with respect to the number of reception queues.
Second, the packet transfer delay distribution D is very similar to the Erlang distribution.

<Inventors' attention points>
First, the inventors of the present application focused on the fact that the packet transfer delay distribution D follows an Erlang distribution.
Second, the inventors of the present application indicate that the parameters k, β, and γ that characterize the Erlang distribution correspond to the throughput λ, the NIC reception queue number q, and the reception hardware interrupt number σ per unit time. Focused on having a strong correlation.
The inventors considered that a packet transfer delay corresponding to the number of reception queues q can be predicted by constructing a packet delay prediction model based on the Erlang distribution.

  FIG. 3 is a functional configuration diagram of the delay prediction apparatus according to the present invention.

  According to FIG. 3, the delay prediction apparatus 1 includes a first preliminary measurement unit 11, a second preliminary measurement unit 12, a probability distribution calculation unit 13, and a delay prediction unit 14. These functional components can be realized by executing a program that causes a computer installed in the delay prediction apparatus to function. Further, the processing flow of these functional components can also be understood as a device delay prediction method.

[First preliminary measurement unit 11]
The first preliminary measurement unit 11 sets the number of reception queues (number of reception network interfaces) q = 1 for the measurement server 2, the first throughput λ _out (1), the delay distribution D, and the unit time. The number of hardware interrupts σ in the reception queue is measured.

The first preliminary measurement unit 11 executes the following steps.
(S110) The first preliminary measurement unit 11 registers test traffic information in advance in the test traffic transmitter 101.
(S111) Next, the first preliminary measurement unit 11 sets the number of reception queues q = 1 for the measurement target server 2. It also resets (initializes) the OS counter for the number of received hardware interrupts.
(S112) Next, the first preliminary measurement unit 11 instructs the measurement traffic receiving apparatus 102 to initialize a received packet number counter and delay distribution recording.
(S113) Then, the first preliminary measurement unit 11 instructs the test traffic transmitting apparatus 101 to start transmitting test traffic for a predetermined measurement time T, and instructs the measurement traffic receiving apparatus 102 to start measurement.
(S114) After the elapse of the predetermined measurement time T, the first preliminary measurement unit 11 instructs the measurement traffic receiving apparatus 102 to end the measurement.
Then, the first preliminary measurement unit 11 acquires the reception hardware interrupt number σ per unit time in the reception queue number q = 1 based on the OS counter of the measurement target server 2.
Also, the first preliminary measurement unit 11 acquires the first throughput λ _out (1) and the delay distribution D from the measurement traffic receiving apparatus 102.
λ _out (1): Number of received packets per unit time when the number of receive queues q = 1

[Second preliminary measurement unit 12]
The second preliminary measurement unit 12 sets the number of reception queues (number of reception network interfaces) q = Q (> 1) for the measurement target server 2 and measures the second throughput λ _out (Q).

The second preliminary measurement unit 12 executes the following steps.
(S121) The second preliminary measurement unit 12 sets the number of reception queues q = Q (> 1) for the measurement target server 2.
(S122) Next, the second preliminary measurement unit 12 instructs the measurement traffic receiving apparatus 102 to initialize the received packet number counter and the delay distribution recording.
(S123) Then, the second preliminary measurement unit 12 instructs the test traffic transmission apparatus 101 to start transmission of test traffic for a predetermined measurement time T, and instructs the measurement traffic reception apparatus 102 to start measurement.
(S124) After the predetermined measurement time T has elapsed, the second preliminary measurement unit 12 instructs the measurement traffic receiving apparatus 102 to end the measurement.
Then, the second preliminary measurement unit 12 acquires the second throughput λ _out (Q) from the measurement traffic receiving apparatus 102.
λ _out (Q): number of received packets per unit time when the number of reception queues q = Q

[Probability distribution calculation unit 13]
The probability distribution calculating unit 13 uses the first throughput λ _out (1) and the second throughput λ _out (Q) to determine the waiting time corresponding to the number q (> 1) of received network interfaces from the delay distribution D. A probability density function f (x) is calculated.

ｋ：分布の形状を表すパラメータ（正の整数）
β：分布の広がりを表すパラメータ（正の実数）
γ：遅延の原点からのズレ（位置）を表すパラメータ（正の実数） The probability density function f (x) is based on parameters k, β, and γ calculated by approximating the Erlang distribution to the delay distribution D.
The probability density function f (x) and parameters are expressed as follows:

k: parameter representing the shape of the distribution (positive integer)
β: Parameter indicating the spread of the distribution (positive real number)
γ: Parameter indicating the deviation (position) from the origin of the delay (positive real number)

  According to the present invention, an Erlang-k-based curve fitting method is used to estimate the delay distribution of packet transfer. This method is not for predicting the average packet delay, but for clarifying the relationship between the parameters k, β, and γ.

The probability density function of the Erlang k distribution is defined by f (x) with mean k / β + γ and variance k / β ² . The problem of approximating the Erlang k distribution with respect to the packet delay distribution is to derive parameters k, β, and γ that minimize the least square error between the measurement result and the approximate curve. Using the parameters k, β, and γ of the probability density function f (x) obtained by approximation, a packet transfer delay according to the number of reception queues q is predicted.

FIG. 4 is a framework showing the calculation process of the average packet delay prediction model based on the Erlang k distribution.
FIG. 5 is a graph showing parameters according to the number of reception queues for each parameter of the probability density function.

σ：受信キュー数ｑ＝１における、単位時間当たりの受信キューのハードウェア割込み数 The throughput λ _out (q) and the parameters k, β, γ at the number of queues q are expressed as follows:

σ: Number of hardware interruptions of the reception queue per unit time when the number of reception queues q = 1

<Calculation of throughput λ _out (q)>
First, a prediction model of throughput λ _out (q) corresponding to the number of reception queues q is calculated. Here, two throughputs λ _out (1) and λ _out (Q) that are preliminarily measured with different queue numbers q = 1, Q (> 1) are used.
First throughput λ _out (1):
The number of reception queues in the measurement target server measured by the first preliminary measurement unit 11
Throughput measured with q = 1 set Second throughput λ _out (Q):
The number of reception queues measured by the second preliminary measurement unit 12 in the measurement target server
Throughput measured after setting q = Q (> 1) Using λ _out (1) and λ _out (Q) measured in _advance , λ _out (q) (1 <q ≦ M (M: reception queue) (Maximum number), q ≠ Q) is calculated as a prediction model of the throughput λ _out (q).

FIG. 5 shows changes in k, β, γ, and τ calculated by fitting the delay distribution D measured for each reception queue number q to the Erlang k distribution equation.
FIG. 5A is a graph showing changes in the parameter k for each reception queue number q.
FIG. 5B is a graph showing changes in the parameter β for each reception queue number q.
FIG. 5C is a graph showing changes in the parameters γ and τ for each reception queue number q.

All three parameters k, β, and γ of the Erlang k distribution are expressed as a function using the reception queue number q. Further, according to FIG. 5C, there is also a correlation between γ and τ (q).
The average packet delay prediction model refers to the maximum throughput prediction model. The Erlang k distribution parameters k, λ, and γ are defined as k (q), λ (q), and γ (q) as a function of the number of reception queues q.

<Calculation of parameter k (q)>
k (q) is considered to correspond to the number of exponential distributions with an average 1 / β (q) included in the Erlang k distribution according to the number of reception queues q.
Further, regarding the reception buffer poll_list and the transmission buffer Qdisc of the measurement target server, it can be considered that packets waiting during the same reception software interrupt and transmission software interrupt have the same characteristics of the waiting time.

k (1) is derived by approximating the delay distribution D and the probability density function f (x) by the least square method or the like. k (q) is calculated using k (1) obtained from curve approximation.
k (q) = floor (k (1) / q)
floor (): Floor function

<Calculation of parameter β (q)>
The packet delay is predicted to correspond to a random variable X (an average k / β Erlang k distribution) that is a sum of _k random variables X _{1 to} X _k having an average 1 / β common exponential distribution.
Packets waiting in the reception buffer poll_list have the same average waiting time when the processing time is constant, and the packet arrival interval is sufficiently shorter than the processing time. For this reason, k is presumed to be highly dependent on the received software interrupt.
1 / β corresponds to the average of variables X _{i having} a common exponential distribution. The factor that causes the variable average to scale in / out is the time that the packet waits in the receive ring buffer. Therefore, it is estimated that β is related to σ.

Since 1 / β (q) corresponds to the average value of k exponential distributions, 1 / β (q) changes according to the time that a packet waits in the reception queue (Rx ring buffer).
1 / β (1) = 1 / λ _out (1) × λ _out (1) / σ
= 1 / σ
1 / λ _out (1): This is the time that the packet stays in the measurement target server.
Average time a packet is waiting in the receive ring buffer
σ: reception hardware per unit time when the number of reception queues q = 1
Wear interrupts
λ _out (1) / σ: From the reception ring buffer when the number of reception queues q = 1
Number of packets moved to receive buffer poll_list

Next, when q = Q (> 1), the packet is uniformly distributed in q reception queues. Therefore, σ is utilized by mapping the traffic flowing into each ring buffer. That is, the traffic load σ assigned to each ring buffer is associated as follows.
η (q) = λ _out (1) / σ
Thus, the average waiting time in the packet reception queue is calculated as follows.
1 / β (q) = q / λ _out (q) × qη (q)
= Q ² η (q) / λ _out (q)
β (q) = λ _out (q) / (q ² η (q))
= Λ _out (q) / (q ² λ _out (1) / σ)
= Σλ _out (q) / (q ² λ _out (1))
As described above, β (q) is calculated using λ _out (1) and σ when the number of reception queues q = 1 and the predicted throughput λ _out (q).

<Calculation of parameter γ (q)>
γ (q) means the minimum time that a packet stays in the reception queue. Here, it is calculated as follows using the mapping function η (q).
1 / λ _out (q) × qη (q)
Then, it is scaled by the average value 1 / (k (q) β (q)) of the distribution, and is calculated as follows.
γ (q) = (1 / λ _out (q)) × qη (q) × (β (q) / k (q))
= (Qη (q) β (q)) / (λ _out (q) k (q))
= (Q (λ _out (1) / σ) β (q)) / (λ _out (q) k (q))
= (Qλ _out (1) β (q)) / (σλ _out (q) k (q))
Thus, λ _out (q), k (q), and β (q) are used for prediction of γ (q).

[Delay Prediction Unit 14]
The delay prediction unit 14 predicts an average packet transfer delay τ according to the number of reception queues (the number of reception network interfaces) q of the measurement target server 2 using the parameters k, β, and γ of the probability density function f (x). .
As described above, each parameter k, β, γ of the probability density function f (x) is expressed as a function of the reception queue number q.
The average packet transfer delay τ is calculated as follows using the parameters k, β, and γ.
τ = k / β + γ
That is, the average packet transfer delay τ can be calculated using a parameter corresponding to the setting of the reception queue number q.

  FIG. 6 is a graph showing the throughput and average packet transfer delay with respect to the number of reception queues.

FIG. 6A is a graph showing the throughput λ _out (q) with respect to the number of reception queues q. Here, it can be understood that the throughput λ _out (1) is maximized when the number of reception queues q = 1.
On the other hand, FIG. 6B is a graph showing the average packet transfer delay τ with respect to the reception queue number q. Here, it can be understood that the average packet transfer delay τ is minimized when the number of reception queues q = 3.

  As described above in detail, according to the delay prediction method, apparatus, and program of the present invention, it is possible to predict a packet transfer delay according to a change in server settings without performing many preliminary measurements. it can.

  For example, the number of reception queues q that minimizes the packet transfer delay can be predicted. In particular, in a virtualized environment using a Linux server, it is assumed that services and applications are flexibly switched and operated. According to the present invention, a setting for an appropriate Linux server for each application can be derived.

  Various changes, modifications, and omissions of the above-described various embodiments of the present invention can be easily made by those skilled in the art. The above description is merely an example, and is not intended to be restrictive. The invention is limited only as defined in the following claims and the equivalents thereto.

DESCRIPTION OF SYMBOLS 1 Delay prediction apparatus 101 Test traffic transmission apparatus 102 Measurement traffic reception apparatus 11 1st preliminary measurement part 12 2nd preliminary measurement part 13 Probability distribution calculation part 14 Delay prediction part 2 Measurement object server

Claims (6)

In a delay prediction method for an apparatus that inputs a packet to a server and predicts a packet transfer delay of the server based on a measurement result of the packet output from the server.
The device is
As a preliminary stage,
A first step of setting the number of reception network interfaces = 1 for the server and measuring a first throughput λ _out (1), a delay distribution D, and a hardware interrupt number σ of a reception queue per unit time;
A second step of setting the number of received network interfaces = Q (> 1) for the server and measuring a second throughput λ _out (Q);
Using the first throughput λ _out (1) and the second throughput λ _out (Q), the number of received network interfaces q (>) from the delay distribution D and the number of hardware interrupts σ of the reception queue per unit time. 1) performing a third step of calculating a probability density function f (x) of the waiting time according to
A delay prediction method for an apparatus, wherein a packet transfer delay according to the number q of received network interfaces of the server is predicted using a parameter of the probability density function f (x). The reception network interface number q is the reception queue number q,
The probability density function f (x) is based on a parameter calculated by approximating the Erlang distribution to the delay distribution D;
The method of claim 1, wherein the packet transfer delay is calculated using the parameter. The probability density function f (x) and the average packet transfer delay τ are expressed as follows using the parameters k, β, and γ.

τ = k / β + γ
k: parameter representing the shape of the distribution (positive integer)
β: Parameter indicating the spread of the distribution (positive real number)
γ: Parameter indicating the deviation (position) from the origin of the delay (positive real number)
The delay prediction method for an apparatus according to claim 2, wherein: Using the hardware interrupt number σ of the reception queue per unit time when the reception queue number q = 1 acquired in the first step,
The throughput λ _out (q) and the parameters k, β, γ in the queue number q are expressed as follows:

The method for predicting delay of an apparatus according to claim 3. In a delay prediction apparatus that inputs a packet to a server and predicts a packet transfer delay of the server based on a measurement result of the packet output from the server.
First preliminary measurement means for setting the number of reception network interfaces = 1 for the server and measuring the first throughput λ _out (1), the delay distribution D, and the hardware interrupt number σ of the reception queue per unit time. When,
Second preliminary measurement means for setting the number of received network interfaces = Q (> 1) for the server and measuring a second throughput λ _out (Q);
Using the first throughput λ _out (1) and the second throughput λ _out (Q), the number of received network interfaces q (>) from the delay distribution D and the number of hardware interrupts σ of the reception queue per unit time. A probability distribution calculating means for calculating a probability density function f (x) of the waiting time according to 1);
A delay prediction apparatus, comprising: a delay prediction unit that predicts a packet transfer delay according to the number q of received network interfaces of the server using a parameter of the probability density function f (x). In a program for inputting a packet to a server and causing a computer mounted on a device that predicts a packet transfer delay of the server to function according to a measurement result of the packet output from the server,
First preliminary measurement means for setting the number of reception network interfaces = 1 for the server and measuring the first throughput λ _out (1), the delay distribution D, and the hardware interrupt number σ of the reception queue per unit time. When,
Second preliminary measurement means for setting the number of received network interfaces = Q (> 1) for the server and measuring a second throughput λ _out (Q);
Using the first throughput λ _out (1) and the second throughput λ _out (Q), the number of received network interfaces q (>) from the delay distribution D and the number of hardware interrupts σ of the reception queue per unit time. A probability distribution calculating means for calculating a probability density function f (x) of the waiting time according to 1);
A program that causes a computer to function as a delay prediction unit that predicts a packet transfer delay according to the number q of received network interfaces of the server using a parameter of the probability density function f (x).

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