CN103023703A - Network timely reliability accelerated test method based on M/M/s queuing model - Google Patents

Abstract

The invention discloses a network timely reliability accelerated test method based on an M/M/s queuing model. The method includes the following steps that (1) components of a queuing model are obtained according to a delayed fault mechanism of a communication network queuing model, and service intensity requirements are determined; (2) a network timely reliability model is obtained; (3) a reliability accelerated model is obtained on the basis of a similarity theory; and (4) a network timely reliability accelerated test is performed. According to the network timely reliability accelerated test method based on the M/M/s queuing model, problems that current network reliability tests are overlong in test time, extremely high in costs or insufficient in quantity of short time test samples and low in confidence coefficient can be effectively solved, and thereby the test efficiency is improved.

Description

Based on the timely reliability accelerated test method of the network of M/M/s queuing model

Technical field

The invention belongs to network service and reliability engineering field, be specifically related to the timely reliability accelerated test method of a kind of network based on the M/M/s queuing model.

Background technology

Along with development and the application of network technology, to network quantitatively and the understanding of science of qualitative features, become an extremely important challenge subjects, even be called as " new science of network ".Along with popularizing that network uses, offered load increases, and has become the major issue that the network quantitative characteristic is understood by the congested timely reliability that causes.

Before a new network built up, before a kind of new service was come into operation, test was the important channel of examination network reliability.Yet, the network task cycle is generally longer, in order effectively to expose fault, the network reliability test duration is the several times of its duty cycle (list of references [1]: Zhang Jiantao often, open sword. forces network combined reliability test and inspection [J]. electronic product reliability and environmental test, 25 (2), 2007:19-22), this directly causes the lead time long.In order in reliability test, to expose fast design defect, determine the network reliability level, be necessary to take accelerated test, increase the cycle-index in the unit interval, the appearance of acceleration disturbance pattern.Acceleration model is the prerequisite of design accelerated test.For the timely reliability of network, its fault mode is that time delay is long, and the queuing mechanism of network provides support for exploring delay fault mechanism and definite acceleration model.Similarity theory is the theory of the various physical process principles of similitude in research nature and the engineering, is the theoretical foundation of determining acceleration model.

The research of existing accelerated test and acceleration model is hardware art mostly, does not carry out the exploration of reliability acceleration model and test method for communication network.The method that there is no solves the problem that the network reliability test duration is long, expense is too high or the short-term test sample size is not enough, confidence level is on the low side.

Summary of the invention

The objective of the invention is in order to solve reliability test overlong time or short-term test assessment confidence level problem on the low side, the timely reliability accelerated test method of a kind of network based on the M/M/s queuing model is proposed, by derivation and the checking of carrying out the reliability acceleration model, formulate the timely reliability accelerated test of network scheme.

The timely reliability accelerated test method of a kind of network based on the M/M/s queuing model comprises the steps:

Step 1: according to the delay fault mechanism of communication network queuing model, obtain the composition of queuing model, determine the service intensity requirement;

Step 2: obtain the timely reliability model of network;

Step 3: obtain the reliability acceleration model based on similarity theory;

Step 4: carry out the timely reliability accelerated test of network;

Advantage of the present invention and good effect are:

(1) the inventive method has proposed based on the timely reliability acceleration model of the network of queueing theory, the network reliability acceleration model of derivation and checking M/M/s queuing system under the guidance of similarity theory, this is the another application of similarity theory on accelerated test, also be its another application on network flow simultaneously, this is the core of accelerated test, is the model basis of planning accelerated test.

(2) the inventive method is the network reliability accelerated test method basis that theorizes: the acceleration model that draws according to derivation, can further determine the communication network test method, this is the popularization of product accelerated life test on network object, the problem of can effectively solve current network reliability test overlong time, expense is too high or the short-term test sample size not enough, confidence level is on the low side, and then improve test efficiency.

Description of drawings

Fig. 1 is method flow diagram of the present invention;

Fig. 2 is that OPNET sets up M/M/s queuing model exemplary plot among the present invention;

Fig. 3 is certain communication network topology exemplary plot in the embodiment of the invention.

Embodiment

The present invention is described in further detail below in conjunction with drawings and Examples.

The present invention proposes the timely reliability accelerated test method of a kind of network based on the M/M/s queuing model, comprises the steps:

Step 1: according to the delay fault mechanism of communication network queuing model, obtain the composition of queuing model, determine the service intensity requirement.

Specifically comprise the steps:

Step 1.1, obtain the composition of queuing model: the composition of queuing model by input process, arrive rule, queue discipline, service organization's structure, service time, service regulation and form.

The M/M/s queuing model, the expression input process is the negative exponent distribution that data are spaced apart λ the time of advent, arriving rule is the single arrival of data, data source totally is that infinite source is overall, queue discipline is First Come First Served, and service organization's structure is the service in parallel of s information desk, and capacity is infinite, service time, service regulation was for once serving the queuing model of individual data in order to obey the negative exponent distribution that average service time is μ.(list of references [2] Tang Yinghui, Tang individual. queueing theory-basis and analytical technology [M]. Beijing: Science Press, 2006:33) after network packet arrives, idle such as switch presence service platform, then begin to provide data exchange service, otherwise wait in line, until all packets in front are finished exchanges data.If residence time is long, when reaching failure criterion, delay fault occurs then.

Step 1.2 determines that the service intensity of queuing model requires: work as ρ _s=λ/s μ＜1 o'clock, ρ _sExpression queuing model service intensity, queuing model can reach statistical equilibrium, consists of probability distribution residence time, is the precondition of the inventive method; Otherwise data arrive accumulation can be more and more, and queuing model can't reach stable state, and queuing delay can be in time and increases progressively trend, and this situation is inquired into delay fault and had little significance.

Step 2: obtain the timely reliability model of network;

Specifically comprise the steps:

Step 2.1 is determined the timely reliability expression of network, and reliability is the metric of reliability on probability, and in time reliability expression is in network:

R=P{D≤D _max} （1）

In the formula, D represents network data transmission time delay, D _MaxThe maximum delay that the expression user allows, namely failure criterion, R represents the timely reliability of network, P represents that the actual time delay of network is no more than the probability of the maximum delay of user's permission.

Step 2.2 is determined distribution function residence time, and distribution function residence time of the queuing model of M/M/s is:

The queuing system of M/M/s residence time distribution function according to list of references [2] Tang Yinghui, Tang individual. queueing theory-basis and analytical technology [M]. Beijing: Science Press, 2006:33 can access.

$W\left(t\right)=P\left(W\≤t\begin{array}{}\end{array}\right)=\left\{\begin{array}{c}1-e^{-\mathrm{\μt}}[1+\frac{p_s}{1-{\mathrm{\ρ}}_s}\mathrm{\μt}],\mathrm{\ρ}=s-1,\\ 1-e^{-\mathrm{\μt}}-\frac{p_s}{(s-\mathrm{\ρ}-1)(1-{\mathrm{\ρ}}_s)}[e^{-\mathrm{\μt}}-e^{-\mathrm{\μ}(s-\mathrm{\ρ})t}],\mathrm{\ρ}\≠s-1.\end{array}\right.---\left(2\right)$

In the formula: W is the residence time of packet in model, for the stand-by period and service time sum.T is the time independent variable.The residence time W of W (t) expression packet in model is no more than the probability of t.

When queuing model was determined, the service number of units was s, and s is constant, p _sFor Number of Customers in the model is the probability of s, expression formula can be designated as p _s=f (ρ).

In fact, formula (2) is exactly the expression formula of the timely reliability of communication network.In the formula (2), t is exactly given time delay threshold value D _MaxConvolution (1) and formula (2), the timely reliability model of network can be expressed as:

$R=P(D{\≤D}_{\max }\begin{array}{}\end{array})=\left\{\begin{array}{c}1-e^{-\mathrm{\μ}{D}_{\max }}[1+\frac{p_s}{1-{\mathrm{\ρ}}_s}{\mathrm{\μD}}_{\max }],\mathrm{\ρ}=s-1,\\ 1-e^{-{\mathrm{\μD}}_{\max }}-\frac{p_s}{(s-\mathrm{\ρ}-1)(1-{\mathrm{\ρ}}_s)}[e^{{-\mathrm{\μD}}_{\max }}-e^{-\mathrm{\μ}(s-\mathrm{\ρ})D_{\max }}],\mathrm{\ρ}\≠s-1.\end{array}\right.---\left(3\right)$

In the formula: R is the timely reliability of network.

Step 3: obtain the reliability acceleration model based on similarity theory;

Specifically comprise the steps:

If formula (3) is the reliability model of primitive network, then the reliability model of similar network is:

$R^{\′}=\left\{\begin{array}{c}1-e^{{-\mathrm{\μ}}^{\′}{D}_{\max }^{\′}}[1+\frac{{p^{\′}}_s}{1-{{\mathrm{\ρ}}^{\′}}_s}{\mathrm{\μ}}^{\′}{D}_{\max }^{\′}],{\mathrm{\ρ}}^{\′}=s-1,\\ 1-e^{-{\mathrm{\μ}}^{\′}{D}_{\max }^{\′}}-\frac{{p^{\′}}_s}{(s-{\mathrm{\ρ}}^{\′}-1)(1-{{\mathrm{\ρ}}^{\′}}_s)}[e^{-{\mathrm{\μ}}^{\′}{D}_{\max }^{\′}}-e^{-{\mathrm{\μ}}^{\′}(s-{\mathrm{\ρ}}^{\′})D_{\max }^{\′}}],{\mathrm{\ρ}}^{\′}\≠s-1.\end{array}\right.---\left(4\right)$

In the formula: R' is the timely reliability of similar network, D' _MaxThe maximum delay that the expression user allows,

λ ' is the similar network data interval time of advent, and μ ' is the average service time of similar network, and the service number of units is s.

Make the service number of units s in the similar network not change, consider

p _s=f (ρ), actual in the formula (3) have 4 physical quantitys, and namely R, λ, μ and D make affinity constant be respectively c _R, c _λ, c _μAnd c _D, represent in the similar network variation multiple of relevant parameter in the parameter and primal system, that is:

$\left\{\begin{array}{c}{R}^{\′}=c_R\·R\\ {\mathrm{\μ}}^{\′}=c_{\mathrm{\μ}}\·\mathrm{\μ}\\ {\mathrm{\λ}}^{\′}=c_{\mathrm{\λ}}\·\mathrm{\λ}\\ D_{\max }^{\′}=c_D\·D_{\mathrm{ma}}\end{array}\right.---\left(5\right)$

For simplicity, require reliability R' in the similar network and the reliability R in the primitive network to remain unchanged, that is: c _R=1; And it is equal according to the affinity constant of interarrival time and average service time to take the mean, i.e. c _μ=c _λAccording to similar first theorem, simultaneous formula (3), formula (4) and (5) then can get: c _μC _D=1

Thus, obtain 3 similarity criterions of M/M/s queuing model, this criterion is the reliability acceleration model:

$\left\{\begin{array}{c}{c}_R=1\\ c_{\mathrm{\μ}}=c_{\mathrm{\λ}}\\ c_{\mathrm{\μ}}\·c_D=1\end{array}\right.---\left(6\right)$

Along with the increase of network data arrival intensity, the packet number that arrives in the same time increases, and the reliability information amount increases.Require in order to reach the required data volume of reliability test truncation (the demonstration test scheme [S] of list of references [3] GB5080.5-85. equipment dependability success of the test rate. the Ministry of Electronics Industry of the People's Republic of China (PRC), the .1985:5-9 of Ministry of Astronautics Industry), network data arrives intensity and increases c _λDoubly, the test duration can reduce c _λDoubly, the data volume of twice test is constant.The pass of namely testing duration and network data arrival intensity is:

c _λ＝t/t′ （7）

In the formula: t is primitive network test duration, and t ' is similar network test duration.

Step 4: use the OPNET emulation platform reliability acceleration model is verified;

Specifically comprise the steps:

Step 4.1 is set up the M/M/s queuing model with OPNET;

Step 4.2, design is chosen λ, μ and D based on the reliability model of the primitive network of M/M/s queuing model, and test duration t, carries out OPNET emulation;

Step 4.3, design is chosen λ, μ and the corresponding similarity factor c of D based on the reliability model of the similar network of M/M/s queuing model according to (6) formula _λ, c _μAnd c _D, determine similar network reliability model parameter, and test duration t ', satisfy t'=t/c _λ, carry out OPNET emulation;

Step 4.4 is calculated the timely reliability of primitive network and similar network, and is compared.In the emulation, the statistical method of the timely reliability of network is:

R=N _n/N _t （8）

In the formula, N _tThe total number of packet of expression Internet Transmission, N _nThe expression network transfer delay is no more than the maximum delay D that the user allows _MaxThe packet number, namely transmit timely packet number.

Constantly calculate reliability at primitive network with the corresponding t of similar network, calculate its mean square error.If increase in the emulation of multiple in the failure criterion of many groups and stress, primitive network and similar Reliability of network mean square error think that then this acceleration model is correct and reasonably all within the acceptable range.

Step 5: carry out the timely reliability accelerated test of network;

Specifically comprise the steps:

Step 5.1 is determined network data collection quantity, and the hypothetical network model is the M/M/s queuing model, and delay fault is obeyed binomial distribution, value check upper limit R, discrimination ratio D, producer risk α and consumer's risk β.So, can check in the Delay quantity that requirement needs to collect packet at least in the reliability compliance test.

Step 5.2 is obtained the accelerated test parameter, if primitive network mission profile parameter and time delay threshold value are λ, μ and D _Max, the test duration is t.Choose λ, μ and D according to (6) formula rule _MaxCorresponding similarity factor c _λ, c _μAnd c _D, can obtain λ ', μ ' and D ' _MaxCarrying out duration according to the accelerated test parameter is t'=t/C _λThe reliability accelerated test, obtain the timely reliability of this accelerating network.It is identical with the timely reliability of primitive network that this value can be thought, namely can obtain the timely reliability of primitive network.

Embodiment:

Emulation part in the embodiment of the invention is specifically set forth the simulating, verifying of the middle acceleration model of the inventive method take OPNET queuing model shown in Figure 2 as example, and test portion is set forth concrete reliability accelerated test scheme take actual communication networks shown in Figure 3 as example.

3 nodes are arranged among Fig. 2, are respectively data sending terminal (src), queueing mechanism (queue) and data receiver (sink).At transmitting terminal the distribution of packet arrival interval and long data packet can be set, queue discipline and distribution service time can be set at the queueing mechanism place.

The timely reliability accelerated test method of network based on the M/M/s queuing model of the present invention, step as shown in Figure 1, wherein step 1, two, three identical with embodiment the inside is not repeated herein, step 4 and five concrete grammars are as follows:

Step 4: use the OPNET emulation platform reliability acceleration model is verified that concrete grammar is:

Step 4.1 is set up the M/M/s queuing model with OPNET, and as shown in Figure 2: this data arrival interval and long data packet distribution that is in the src data sending terminal selects the exponential negative exponent to distribute, and the transaction module of queue queueing mechanism is selected acb_fifo_ms.

Step 4.2, design is based on the reliability model of the primitive network of M/M/s queuing model, choose certain λ, μ, t and D, carry out OPNET emulation: in this checking case, the network service rate is 9,600bit/s, data arrive intensity and obey the negative exponent distribution that average is 2.67packet/s, and data package size is obeyed the negative exponent distribution that average is 9,000bit, the service number of units is 5, i.e. ρ _s=0.5.The hypothetical network delay fault is obeyed binomial distribution, get check upper limit R=0.999, discrimination ratio D=1.50, producer risk α and consumer's risk β are 10%, so, require to need at least to collect the Delay of 32922 packets in the reliability compliance test, therefore needed at least emulation 3.425 hours, just can arrive the packet of this quantity.Use OPNET emulation 4 hours, altogether collect 35789 packets.

Step 4.3, design is chosen c based on the reliability model of the similar network of M/M/s queuing model according to (6) formula rule _λ, c _μ, c _tAnd c _D, determine similar network reliability model parameter, and test duration t ', carry out OPNET emulation: get c _μ=c _λ=4, C _D=c _t=0.25, t'=1 hour, t ₀State is identical constantly.So, the network service rate is 19200bit/s, and the negative exponent distribution that average is 5.34packet/s is obeyed at the average data interval time of advent, and data package size is obeyed the negative exponent distribution that average is 9000bit.According to acceleration model, 36000 packets are collected in emulation 1 hour altogether.

Step 4.4 is calculated the timely reliability of primitive network and similar network, and is compared.In the emulation, the statistical method of the timely reliability of network is:

R=N _n/N _t （8）

In the formula, N _tThe total number of packet of expression Internet Transmission, N _nThe expression network transfer delay is no more than the maximum delay D that the user allows _MaxThe packet number, namely transmit timely packet number.

In former network and similar network respectively take 8 minutes and 2 minutes as the interval, point estimate according to the end-to-end timely reliability of formula (8) computing network, and under different delay fault criterions, calculate the mean square error of primitive network and the timely reliability of similar network, as shown in table 1.In the present embodiment, when primitive network time delay threshold value when 2 ~ 5s changes, mean square error illustrates that all less than 0.02 under the value of different delay fault criterions, the applicability of the method is all stronger.Along with the increase of time delay threshold value, its mean square error is more and more less, and primitive network is higher with the similitude of similar network on reliability.Table 1 has also been discussed the absolute error of two timely reliabilitys of network, and it is worth all less than 3 * 10 ^-3, and the delay fault threshold value is stricter, i.e. the higher network of reliability to calculating, and absolute error is less, and the accuracy of this acceleration model is higher.

Table 1 failure criterion is on the impact of acceleration model

Table 2 has further been discussed network to be increased under the multiple at different stress, the mean square error of primitive network and similar Reliability of Network.Here, when stress increased multiple 2 ~ 12 times of variations, the mean square error of two timely reliabilitys of network and absolute error changed little.This explanation, the multiple that network stress increases does not affect primitive network and the similitude of similar network on reliability.

Table 2 stress increases multiple to the impact of acceleration model

In above-mentioned analysis, because each Δ t time period (Δ t=8min in the primitive network, Δ t=2min in the similar network) 1200 data of only having an appointment, so the timely reliability of two networks remains in certain error, absolute error is all 10 ^-4Near.If increase the data volume of unit interval, then error will significantly reduce.Table 3 be the information desk number on the impact of similar network, can find out that the variation of information desk number does not affect the applicability of the method yet.

Table 3 information desk number is on the impact of acceleration model

Step 5: carry out the timely reliability accelerated test of network, the theoretical model of corresponding diagram 2, test portion are set forth concrete reliability accelerated test scheme take actual communication networks shown in Figure 3 as example:

Communication network is by two end systems among Fig. 3, and a switch forms.End system can be the system with specific function, such as AFDX avionics subsystem, also can be the common notebook in the local area network (LAN).Here end system mainly is to carry out transceiving data, sends data flow by end system A and is finally received by end system B by switch.

Step 5.1 is determined network data collection quantity, and the tentation data bag is the M/M/s queuing model by the time delay of switch, and delay fault is obeyed binomial distribution.According to user's requirement, as get check upper limit R=0.999, discrimination ratio D=1.50, producer risk α and consumer's risk β are 10%.So, by relevant criterion (the demonstration test scheme [S] of list of references [3] GB5080.5-85. equipment dependability success of the test rate. the Ministry of Electronics Industry of the People's Republic of China (PRC), the .1985:5-9 of Ministry of Astronautics Industry) can check in the Delay quantity that requirement needs to collect packet at least in the reliability compliance test, be 32922 packets herein.

Step 5.2 is obtained the accelerated test parameter, if primitive network mission profile parameter and time delay threshold value are λ=1packet/s, μ=2packet/s and D _Max=50ms, the test duration is can collect at least 32922 packets more than the t=9.145h.Choose λ, μ and D according to (6) formula rule _MaxCorresponding similarity factor c _λ, c _μAnd c _D, can obtain λ ', μ ' and D ' _MaxAs get c _μ=c _λ=4, c _D=0.25, D _Max=12.5ms.Carrying out duration according to the accelerated test parameter is t'=t/c _λThe reliability accelerated test of=9.145/4=2.23h by hardware tools or each packet of software measurement time delay by switch, just can obtain stipulating to be no less than the delay data of 32922 packets.Utilize the delay data of these acquisitions, can calculate the timely reliability R of this accelerating network in conjunction with (8) formula, be assumed to be 0.99, it is identical with the timely reliability of primitive network that this reliability value can be thought, can think that namely the timely reliability of primitive network is 0.99.

Claims (1)

1. the timely reliability accelerated test method of the network based on the M/M/s queuing model comprises the steps:

Step 1: according to the delay fault mechanism of communication network queuing model, obtain the composition of queuing model, determine the service intensity requirement;

Specifically comprise the steps:

Step 1.1, obtain the composition of queuing model: the composition of queuing model by input process, arrive rule, queue discipline, service organization's structure, service time, service regulation and form;

The M/M/s queuing model, the expression input process is the negative exponent distribution that data are spaced apart λ the time of advent, arriving rule is the single arrival of data, data source totally is that infinite source is overall, queue discipline is First Come First Served, and service organization's structure is the service in parallel of s information desk, and capacity is infinite, service time, service regulation was for once serving the queuing model of individual data in order to obey the negative exponent distribution that average service time is μ; After network packet arrives, idle such as switch presence service platform, then begin to provide data exchange service, otherwise wait in line, until all packets in front are finished exchanges data; If residence time is long, when reaching failure criterion, delay fault occurs then;

Step 1.2 determines that the service intensity of queuing model satisfies ρ _s=λ/s μ＜1, ρ _sExpression queuing model service intensity;

Step 2: obtain the timely reliability model of network;

Specifically comprise the steps:

Step 2.1 is determined the timely reliability expression of network, and in time reliability expression is in network:

R=P{D≤D _max} （1）

In the formula, D represents network data transmission time delay, D _MaxThe maximum delay that the expression user allows, namely failure criterion, R represents the timely reliability of network, P represents that the actual time delay of network is no more than the probability of the maximum delay of user's permission;

Step 2.2 is determined distribution function residence time, and distribution function residence time of the queuing model of M/M/s is:

$W\left(t\right)=P\left(W\≤t\begin{array}{}\end{array}\right)=\left\{\begin{array}{c}1-e^{-\mathrm{\μt}}[1+\frac{p_s}{1-{\mathrm{\ρ}}_s}\mathrm{\μt}],\mathrm{\ρ}=s-1,\\ 1-e^{-\mathrm{\μt}}-\frac{p_s}{(s-\mathrm{\ρ}-1)(1-{\mathrm{\ρ}}_s)}[e^{-\mathrm{\μt}}-e^{-\mathrm{\μ}(s-\mathrm{\ρ})t}],\mathrm{\ρ}\≠s-1.\end{array}\right.---\left(2\right)$

In the formula: W is the residence time of packet in model, for the stand-by period and service time sum; T is the time independent variable; The residence time W of W (t) expression packet in model is no more than the probability of t;

When queuing model was determined, the service number of units was s, and s is constant, p _sFor Number of Customers in the model is the probability of s, expression formula can be designated as p _s=f (ρ);

In fact, formula (2) is exactly the expression formula of the timely reliability of communication network; In the formula (2), t is exactly given time delay threshold value D _MaxConvolution (1) and formula (2), the timely reliability model of network can be expressed as:

$R=P(D{\≤D}_{\max }\begin{array}{}\end{array})=\left\{\begin{array}{c}1-e^{-\mathrm{\μ}{D}_{\max }}[1+\frac{p_s}{1-{\mathrm{\ρ}}_s}{\mathrm{\μD}}_{\max }],\mathrm{\ρ}=s-1,\\ 1-e^{-{\mathrm{\μD}}_{\max }}-\frac{p_s}{(s-\mathrm{\ρ}-1)(1-{\mathrm{\ρ}}_s)}[e^{{-\mathrm{\μD}}_{\max }}-e^{-\mathrm{\μ}(s-\mathrm{\ρ})D_{\max }}],\mathrm{\ρ}\≠s-1.\end{array}\right.---\left(3\right)$

In the formula: R is the timely reliability of network;

Step 3: obtain the reliability acceleration model based on similarity theory;

Specifically comprise the steps:

If formula (3) is the reliability model of primitive network, then the reliability model of similar network is:

$R^{\′}=\left\{\begin{array}{c}1-e^{{-\mathrm{\μ}}^{\′}{D}_{\max }^{\′}}[1+\frac{{p^{\′}}_s}{1-{{\mathrm{\ρ}}^{\′}}_s}{\mathrm{\μ}}^{\′}{D}_{\max }^{\′}],{\mathrm{\ρ}}^{\′}=s-1,\\ 1-e^{-{\mathrm{\μ}}^{\′}{D}_{\max }^{\′}}-\frac{{p^{\′}}_s}{(s-{\mathrm{\ρ}}^{\′}-1)(1-{{\mathrm{\ρ}}^{\′}}_s)}[e^{-{\mathrm{\μ}}^{\′}{D}_{\max }^{\′}}-e^{-{\mathrm{\μ}}^{\′}(s-{\mathrm{\ρ}}^{\′})D_{\max }^{\′}}],{\mathrm{\ρ}}^{\′}\≠s-1.\end{array}\right.---\left(4\right)$

In the formula: R' is the timely reliability of similar network, D' _MaxThe maximum delay that the expression user allows,

λ ' is the similar network data interval time of advent, and μ ' is the average service time of similar network, and the service number of units is s;

Make the service number of units s in the similar network not change, consider

p _s=f (ρ), actual in the formula (3) have 4 physical quantitys, and namely R, λ, μ and D make affinity constant be respectively c _R, c _λ, c _μAnd c _D, represent in the similar network variation multiple of relevant parameter in the parameter and primal system, that is:

$\left\{\begin{array}{c}R\′=c_R\·R\\ \mathrm{\μ}\′=c_{\mathrm{\μ}}\·\mathrm{\μ}\\ \mathrm{\λ}\′=c_{\mathrm{\λ}}\·\mathrm{\λ}\\ D{\′}_{\max }=c_D\·D_{\mathrm{ma}}\end{array}---\left(5\right)\right.$

If the reliability R' in the similar network and the reliability R in the primitive network remain unchanged, that is: c _R=1; And it is equal according to the affinity constant of interarrival time and average service time to take the mean, i.e. c _μ=c _λAccording to similar first theorem, simultaneous formula (3), formula (4) and (5) then can get: c _μC _D=1;

Thus, obtain 3 similarity criterions of M/M/s queuing model, this criterion is the reliability acceleration model:

$\left\{\begin{array}{c}{c}_R=1\\ c_{\mathrm{\μ}}=c_{\mathrm{\λ}}\\ c_{\mathrm{\μ}}\·c_D=1\end{array}\right.---\left(6\right)$

Along with the increase of network data arrival intensity, the packet number that arrives in the same time increases, and the reliability information amount increases, and network data arrives intensity increase c _λDoubly, the test duration reduces c _λDoubly, the data volume of twice test is constant, and the pass of namely testing duration and network data arrival intensity is:

c _λ＝t/t′ （7）

In the formula: t is primitive network test duration, and t ' is similar network test duration;

Step 4: carry out the timely reliability accelerated test of network;

Specifically comprise the steps:

Step 4.1 is determined network data collection quantity, and the hypothetical network model is the M/M/s queuing model, and delay fault is obeyed binomial distribution, value check upper limit R, discrimination ratio D, producer risk α and consumer's risk β; Check in the Delay quantity that requirement needs to collect packet at least in the reliability compliance test;

Step 4.2 is obtained the accelerated test parameter, if primitive network mission profile parameter and time delay threshold value are λ, μ and D _Max, the test duration is t; Choose λ, μ and D according to (6) formula rule _MaxCorresponding similarity factor c _λ, c _μAnd c _D, obtain λ ', μ ' and D ' _MaxCarrying out duration according to the accelerated test parameter is t'=t/c _λThe reliability accelerated test, obtain the timely reliability of this accelerating network; It is identical with the timely reliability of primitive network that this value is thought, namely obtains the timely reliability of primitive network.

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