CN104536894A - Global optimization method based on maintenance charge and for two-tier software aging phenomenon - Google Patents

Abstract

The invention discloses a global optimization method based on the maintenance charge and for a two-tier software aging phenomenon. The method includes the following steps that the consumed memory Xi of an application tier within the time interval and the consumed memory Yi of an operation system tier within the time interval are monitored by a monitor; a two-tier software aging analysis model is built based on the updating process; the optimum value of an alarm threshold value of the operation system tier, the optimum value of the fatigue threshold value of the operation system tier and the optimum value of the alarm threshold value of the application tier are obtained according to the two-tier software aging analysis model; and the available maximum value of a two-tier software system is obtained. By means of the method, the overall availability can be improved effectively for a regeneration strategy method of the two-tier software.

Description

For the global optimization method based on maintenance cost of two layers of software catabiosis

Technical field

The invention belongs to field of software performance test, particularly relating to can minimum maintenance expense, for the global optimization method based on maintenance cost of two layers of software catabiosis.

Background technology

When software aging phenomenon is software long-play, cause the phenomenon that software performance declines gradually due to the consumption of computer resource.The consequence that this phenomenon may cause is serious, it not only affects the operation of common server software, and may to the key area requiring high reliability, software as used in business, finance, science and technology and the field such as military impacts, in the software environment that security requirement is high, the software aging phenomenon personnel that even may cause injure even fame loss.For this phenomenon, scholar proposes the method that one is called " software regeneration (Software Rejuvenation) ", namely by restarting server software or whole computer system termly, reinitialize the internal state of server, release may cause aging occupied system resource, the state of software and performance are restored, thus avoid or reduce the even loss that causes of the software systems machine of delaying of the aging serious hydraulic performance decline caused.In the middle of the application of software regeneration method, the determination of regeneration intervals is a very important problem, if regeneration intervals is selected long, then may not avoid the harm that software aging phenomenon causes, if regeneration intervals is selected too short, then this expense brought as software systems of initiative regeneration behavior is excessive with regard to possibility, causes the reduction of software efficiency of actual.Usually, the value that the software regeneration time interval can select to be suitably shorter than the software expects life-span, therefore, to the prediction of software lifetime with estimate it is a focus in the correlative study of software aging field always.In order to the probability distribution in Estimation Software life-span, can carry out abstract fully to actual software system, utilize the mathematical models such as Markov model, Semi-Markov Process, stochastic reward net, stochastic Petri net to carry out modeling to system, thus take out the feature of software lifetime; Also real software systems can be studied, utilize the detection means contrived experiment of various performance parameter, from real experiment, the various delta datas of acquisition system performance parameter, then utilize statistical method or intelligent algorithm etc., describe and the life-span of forecasting software.But, carry out the large obstacle of test existence one to real software system, server software is all designed to run uninterruptedly under normal circumstances provides service, even if there is catabiosis, the life-span of software is also very long, is also just difficult to the sample obtaining the software failure time by experiment.For this phenomenon, scholar proposes one and is called " accelerated deterioration test (ADT) " and " accelerating lifetime testing (ALT) " technology, namely utilize accelerating lifetime testing theoretical, obtained the lifetime data of software in acceleration situation by shorter accelerating lifetime testing consuming time, calculate the true lifetime of software in non-acceleration situation.

Along with the complicacy of system software and running environment thereof improves constantly, system software aging is not only caused by application layer or operating system layer merely, the aging collapse that whole service all can be caused to serve of any one deck, and traditional method of testing is all only limited to one deck.The present invention builds two layers of software aging analysis model, computing system aging threshold level, utilize the accelerating lifetime testing of widespread use in traditional industry field theoretical, dispose and implement to test for the accelerating lifetime testing of two layers of software catabiosis, the time interval of adjustment monitor monitors internal memory change, calculate true lifetime and other parameters of non-acceleration software under each monitor monitors time interval, obtain the probability distribution of system software availability under normal circumstances.

Many experts and scholars are studied software aging, catabiosis for example in people [2008] the research web server such as Yun-Fei Jia, they have built an experiment porch with an Apache Server and multiple client, run and organize experiment more, be collected in the relevant information of system resource use amount on server in often group experiment, they observe software aging process is nonlinear and chaotic; The people such as Cotroneo [2010] have studied linux kernel code, analyze workload parameters, by highlighted display and the related subsystem of aging tendency, for the potential source of software aging provides proof.But they seldom study for the aging of two layers of software, but the availability of whole system not only only relates to the availability of application layer (operating system layer), it and above-mentionedly both have close relationship, the inefficacy of any one deck software all can cause system to be disabled.

Summary of the invention

The object of this invention is to provide a kind of can minimum maintenance expense, for the global optimization method based on maintenance cost of two layers of software catabiosis.

The present invention is achieved by the following technical solutions:

For the global optimization method based on maintenance cost of two layers of software catabiosis, it is characterized in that, comprise following step:

Step one: record application layer can utilize internal memory A when initial health _totalinternal memory O can be utilized when initial health with operating system layer _total, monitor monitors application layer the time interval (τ (i-1), τ i] the internal memory X of internal consumption _iwith operating system layer the time interval (τ (i-1), τ i] the internal memory Y of internal consumption _i, wherein τ is monitoring time interval, and i is monitoring total degree;

Step 2: build two layers of software aging analysis model based on renewal process:

$A(k\·\mathrm{\τ})=A_{\mathrm{total}}-\underset{i=1}{\overset{k}{\mathrm{\Σ}}}{X}_i$

$O(k\·\mathrm{\τ})=O_{\mathrm{total}}-\underset{i=1}{\overset{k}{\mathrm{\Σ}}}{Y}_i$

Wherein, internal memory available in application layer when A (k τ) is the secondary monitoring of monitor kth, internal memory available in operating system layer when O (k τ) is the secondary monitoring of monitor kth;

Step 3: according to two layers of software aging analysis model, obtains the alarm threshold O of operating system layer _redoptimum value, operating system layer fatigue threshold O _blueoptimum value, and the alarm threshold A of application layer _redoptimum value;

The alarm threshold O of operating system layer _redoptimum value be:

$O_{\mathrm{red}}^{*}=\{O_{\mathrm{red}}:P[Y_{K+1}>O_{\mathrm{red}}|O(K\·\mathrm{\τ})=O_{\mathrm{red}}]=\frac{\frac{c_{\mathrm{Op}}\·\mathrm{\τ}}{(\frac{O_{\mathrm{total}}-O_{\mathrm{red}}}{E\left(Y\right)}\·\mathrm{\τ}+E\left(\mathrm{\Δ}\right))((\frac{O_{\mathrm{total}}-O_{\mathrm{red}}}{E\left(Y\right)}+1)\·\mathrm{\τ}+E\left(\mathrm{\Δ}\right))}}{\frac{c_{\mathrm{Or}}}{((\frac{O_{\mathrm{total}}-O_{\mathrm{red}}}{E\left(Y\right)}+1)\·\mathrm{\τ}+E\left({\mathrm{\Δ}}^{\′}\right))}-\frac{c_{\mathrm{Op}}}{((\frac{O_{\mathrm{total}}-O_{\mathrm{red}}}{E\left(Y\right)}+1)\·\mathrm{\τ}+E\left(\mathrm{\Δ}\right))}}\}$

Wherein, for the alarm threshold O of operating system layer _redoptimum value, before time (K+1) τ operating system collapse probability α be:

$\mathrm{\α}=P[Y_{K+1}>O_{\mathrm{red}}|O(K\·\mathrm{\τ})=O_{\mathrm{red}}]=\frac{\frac{c_{\mathrm{Op}}\·\mathrm{\τ}}{(K\·\mathrm{\τ}+\mathrm{\Δ})((K+1)\·\mathrm{\τ}+\mathrm{\Δ})}}{\frac{c_{\mathrm{Or}}}{(K+1)\·\mathrm{\τ}+{\mathrm{\Δ}}^{\′}}-\frac{c_{\mathrm{Op}}}{(K+1)\·\mathrm{\τ}+\mathrm{\Δ}}},$

The fatigue threshold O of operating system layer _blueoptimum value be:

$O_{\mathrm{blue}}^{*}=\left\{\begin{array}{c}{O}_{\mathrm{blue}}:\frac{c_{\mathrm{Ap}}}{\frac{O_{\mathrm{blue}}-O_{\mathrm{red}}^{*}}{E\left(Y\right)}+\frac{E\left(\mathrm{\δ}\right)}{\mathrm{\τ}}}+\frac{c_{\mathrm{Op}}}{\frac{O_{\mathrm{total}}-O_{\mathrm{red}}^{*}}{E\left(Y\right)}+\frac{E\left(\mathrm{\Δ}\right)}{\mathrm{\τ}}}=\\ \frac{(E\left(N\right)-1)\·c_{\mathrm{Ap}}}{\frac{E\left(N\right)\·(A_{\mathrm{total}}-A_{\mathrm{red}}^{*})}{E\left(X\right)}+\frac{E\left(N\right)\·E\left(\mathrm{\δ}\right)}{\mathrm{\τ}}}+\frac{c_{\mathrm{Op}}}{\frac{O_{\mathrm{total}}-O_{\mathrm{blue}}}{E\left(Y\right)}+\frac{E\left(\mathrm{\Δ}\right)}{\mathrm{\τ}}}\end{array}\right\}$

Wherein, for the fatigue threshold O of operating system layer _blueoptimum value,

The alarm threshold A of application layer _redoptimum value be:

$A_{\mathrm{red}}^{*}=\{A_{\mathrm{red}}:P[X_{K+1}>A_{\mathrm{red}}|A(K\·\mathrm{\τ})=A_{\mathrm{red}}]=\frac{\frac{c_{\mathrm{Ap}}\·\mathrm{\τ}}{(\frac{A_{\mathrm{total}}-A_{\mathrm{red}}}{E\left(X\right)}\·\mathrm{\τ}+E\left(\mathrm{\δ}\right))((\frac{A_{\mathrm{total}}-A_{\mathrm{red}}}{E\left(X\right)}+1)\·\mathrm{\τ}+E\left(\mathrm{\δ}\right))}}{\frac{c_{\mathrm{Ar}}}{((\frac{A_{\mathrm{total}}-A_{\mathrm{red}}}{E\left(X\right)}+1)\·\mathrm{\τ}+E\left({\mathrm{\δ}}^{\′}\right))}-\frac{c_{\mathrm{Ap}}}{((\frac{A_{\mathrm{total}}-A_{\mathrm{red}}}{E\left(X\right)}+1)\·\mathrm{\τ}+E\left(\mathrm{\δ}\right))}}\}$

Wherein, for the alarm threshold A of application layer _redoptimum value, before time (K+1) τ application layer collapse probability be:

$\mathrm{\β}=P[Y_{K+1}>A_{\mathrm{red}}|A(K\·\mathrm{\τ})=A_{\mathrm{red}}]=\frac{\frac{c_{\mathrm{Ap}}\·\mathrm{\τ}}{(K\·\mathrm{\τ}+\mathrm{\δ})((K+1)\·\mathrm{\τ}+\mathrm{\δ})}}{\frac{c_{\mathrm{Ar}}}{(K+1)\·\mathrm{\τ}+{\mathrm{\δ}}^{\′}}-\frac{c_{\mathrm{Ap}}}{(K+1)\·\mathrm{\τ}+\mathrm{\δ}}},$

Wherein, E (X) is X _iexpectation value, E (Y) is Y _iexpectation value, c _opand c _orthat operating system regenerates and passive expense of restarting each time respectively, Δ and Δ ' be respectively operating system regeneration and passive time of restarting, E (Δ) and E (Δ ') be respectively Δ and Δ ' expectation value, c _apand c _arbe that application layer regenerates and passive expense of restarting each time respectively, δ and δ ' is respectively application layer regeneration and passive time of restarting, and E (δ) and E (δ ') is the expectation value of δ and δ ' respectively.

Step 4: according to the alarm threshold O of operating system layer _redoptimum value, operating system layer fatigue threshold O _blueoptimum value, and the alarm threshold A of application layer _redoptimum value, obtain two layers of software system availability maximal value.

The present invention is directed to the global optimization method based on maintenance cost of two layers of software catabiosis, also comprise:

Obtain the method for two layers of software system availability maximal value, comprise following step,

1) state of application layer and operating system layer is divided, work as A _red< A (t)≤A _totaltime, application layer is in a safe condition; As 0 < A (t)≤A _redtime, application layer is on the alert; When A (t)=0, application layer is in spent condition; Work as O _blue< O (t)≤O _totaltime, operating system layer is in a safe condition; Work as O _red< O (t)≤O _bluetime, operating system layer is in fatigue state; As 0 < O (t)≤O _redtime, operating system layer is on the alert; When O (t)=0, operating system layer is in spent condition;

2) try to achieve when application layer is on the alert or spent condition, and operating system layer is in the Probability p of fatigue state _o1, and the availability A of now two layers of software system ₁for:

$P_{O1}=\frac{{O^{*}}_{\mathrm{blue}}-{O^{*}}_{\mathrm{red}}}{\frac{E\left(Y\right)}{\mathrm{\&tau;}}\&CenterDot;\frac{A_{\mathrm{total}}-{A^{*}}_{\mathrm{red}}}{\frac{E\left(X\right)}{\mathrm{\&tau;}}}}=\frac{({O^{*}}_{\mathrm{blue}}-{O^{*}}_{\mathrm{red}})\&CenterDot;E\left(X\right)}{(A_{\mathrm{total}}-{A^{*}}_{\mathrm{red}})\&CenterDot;E\left(Y\right)}$

$A_1=\frac{\frac{(O_{\mathrm{total}}-{O^{*}}_{\mathrm{blue}})\&CenterDot;\mathrm{\&tau;}}{E\left(Y\right)}-[\frac{\frac{(O_{\mathrm{total}}-{O^{*}}_{\mathrm{blue}})\&CenterDot;\mathrm{\&tau;}}{E\left(Y\right)}}{\frac{(A_{\mathrm{total}}-{A^{*}}_{\mathrm{red}})\&CenterDot;\mathrm{\&tau;}}{E\left(X\right)}+t_{\mathrm{AM}}}-1]\&CenterDot;t_{\mathrm{AM}}}{\frac{(O_{\mathrm{total}}-{O^{*}}_{\mathrm{blue}})\&CenterDot;\mathrm{\&tau;}}{E\left(Y\right)}+E\left(\mathrm{\&Delta;}\right)}$

When the Probability p that operating system layer is on the alert _o2, and the availability A of now two layers of software system ₂for:

p _O2＝(1-p _O1)(1-α)

$A_2=\frac{\frac{(O_{\mathrm{total}}-{O^{*}}_{\mathrm{red}})\&CenterDot;\mathrm{\&tau;}}{E\left(Y\right)}-[\frac{\frac{(O_{\mathrm{total}}-{O^{*}}_{\mathrm{red}})\&CenterDot;\mathrm{\&tau;}}{E\left(Y\right)}}{\frac{(A_{\mathrm{total}}-{A^{*}}_{\mathrm{red}})\&CenterDot;\mathrm{\&tau;}}{E\left(X\right)}+t_{\mathrm{AM}}}-1]\&CenterDot;t_{\mathrm{AM}}}{\frac{(O_{\mathrm{total}}-{O^{*}}_{\mathrm{red}})\&CenterDot;\mathrm{\&tau;}}{E\left(Y\right)}+E\left(\mathrm{\&Delta;}\right)},$

When operating system layer arrives the Probability p of spent condition _o3, and the availability A of now two layers of software system ₃for:

p _O3＝(1-p _O1)α

$A_3=\frac{\frac{O_{\mathrm{total}}\&CenterDot;\mathrm{\&tau;}}{E\left(Y\right)}-[\frac{\frac{O_{\mathrm{total}}\&CenterDot;\mathrm{\&tau;}}{E\left(Y\right)}}{\frac{(A_{\mathrm{total}}-{A^{*}}_{\mathrm{red}})\&CenterDot;\mathrm{\&tau;}}{E\left(X\right)}+t_{\mathrm{AM}}}-1]\&CenterDot;t_{\mathrm{AM}}}{\frac{O_{\mathrm{total}}\&CenterDot;\mathrm{\&tau;}}{E\left(Y\right)}+E\left({\mathrm{\&Delta;}}^{\&prime;}\right)},$

Wherein, t _aM=: β δ '+(1-β) δ is the averaging time of a maintenance application layer,

3) the availability maximal value asking for two layers of software system is:

Availability＝p _O1·A ₁+p _O2·A ₂+p _O3·A ₃。

Beneficial effect:

The present invention from the memory refreshing Procedure Acquisition of two layers of software to some internal memory delta datas after just can construct the aging analysis model of two layers of software, definition in conjunction with the aging analysis model built and optimal threshold level can calculate the threshold level of the aging and regeneration of the best of two layers of software on the basis of minimum maintenance expense, within very short time, so just effectively can calculate the optimal availability size of whole system.Range of application of the present invention can expand the system regions of any one two layers of software to.

Accompanying drawing explanation

Fig. 1 is execution schematic flow sheet of the present invention.

Fig. 2 is the renewal process model of two layers of software regeneration.

Fig. 3 is the application state based on A (t), O (t) and alarm threshold.

Embodiment

Below in conjunction with accompanying drawing, the present invention is described in further details.

The invention reside in the analytical model and accelerated test theory that utilize system software update process, the lifetime data of test two layers of software in acceleration situation, derive the two-layer aging probability of availability distribution under normal level being subject to software aging phenomena impair, thus draw the availability size of system on the basis of minimum maintenance expense.This object can realize according to following steps, as shown in Figure 1:

The first step: build two layers of software aging analysis model based on renewal process.Software upgrading process refers to and reinitializes software inhouse state, discharges occupied memory source.

Second step: the threshold level of define system state.

3rd step: analytic system availability.System availability refers to the ratio of time shared by the whole system time that system software normally runs.

The present invention carries out system availability research to the web server software (application layer) of an e-commerce website and the operating system under it.Below in conjunction with other accompanying drawings, the process maximizing system availability is described further.

1, build experiment porch, obtain output parameter

1.1, experiment porch is built: in application layer, introduce a module with memory overflow bug, this module when server normal process HTTP request by random call, by controlling the probability calling this module, make it that memory overflow speed occur to differ, in operating system layer, load a character device module, do not discharged to operating system application memory block by write method in this character device module, cause the memory overflow of operating system.When the module introduced extra in application layer is called, character device module is also called.

1.2, record application layer and can utilize memory size A when initial health _totalmemory size O can be utilized when initial health with operating system layer _total

1.3, running experiment, use simultaneously monitor monitors application layer the time interval (τ (i-1), τ i] the memory size X of internal consumption _iwith monitor operating system layer the time interval (τ (i-1), τ i] the memory size Y of internal consumption _i, be then saved in respectively in file tomcatMem.log and sysMeminfo.log, wherein τ is the monitor monitors time interval, and i is the total degree of monitor monitors.The working time of whole experiment is one hour.

1.4, X is calculated _iand Y _iexpectation value E (X), E (Y).

2, the A will obtained in the 1st step _total, O _total, X _iand Y _ibe updated to

$A(k\&CenterDot;\mathrm{\&tau;})=A_{\mathrm{total}}-\underset{i=1}{\overset{k}{\mathrm{\&Sigma;}}}{X}_i$ With $O(k\&CenterDot;\mathrm{\&tau;})=O_{\mathrm{total}}-\underset{i=1}{\overset{k}{\mathrm{\&Sigma;}}}{Y}_i$

In, obtain building two layers of software aging analysis model based on renewal process, see Fig. 2.Wherein, k is the number of times of monitor monitors, time when k τ is monitor kth time monitoring, memory size available in application layer when A (k τ) is time monitoring of monitor kth, memory size available in operating system layer when O (k τ) is time monitoring of monitor kth.

3, the optimal threshold level of computing system state.Definition A _redfor the alarm threshold of application layer, O _bluefor the fatigue threshold of operating system layer, O _redfor the alarm threshold of operating system layer.By the E (X) that obtains in the 1st step and E (Y) and the aging empirical value c obtained of previous scholars research _op, c _or, Δ, Δ ', c _ap, c _ar, the following equation of δ and δ ' calculates O respectively _red, A _redand O _blueoptimum value, wherein c _opand c _orthat operating system regenerates and passive expense of restarting each time respectively, Δ and Δ ' be respectively operating system regeneration and passive time of restarting, E (Δ) and E (Δ ') be respectively Δ and Δ ' expectation value, c _apand c _arbe that application layer regenerates and passive expense of restarting each time respectively, δ and δ ' is respectively application layer regeneration and passive time of restarting, and E (δ) and E (δ ') is the expectation value of δ and δ ' respectively.

3.1, O _redthe determination of optimum value

$O_{\mathrm{red}}^{*}=\{O_{\mathrm{red}}:P[Y_{K+1}>O_{\mathrm{red}}|O(K\&CenterDot;\mathrm{\&tau;})=O_{\mathrm{red}}]=\frac{\frac{c_{\mathrm{Op}}\&CenterDot;\mathrm{\&tau;}}{(\frac{O_{\mathrm{total}}-O_{\mathrm{red}}}{E\left(Y\right)}\&CenterDot;\mathrm{\&tau;}+E\left(\mathrm{\&Delta;}\right))((\frac{O_{\mathrm{total}}-O_{\mathrm{red}}}{E\left(Y\right)}+1)\&CenterDot;\mathrm{\&tau;}+E\left(\mathrm{\&Delta;}\right))}}{\frac{c_{\mathrm{Or}}}{((\frac{O_{\mathrm{total}}-O_{\mathrm{red}}}{E\left(Y\right)}+1)\&CenterDot;\mathrm{\&tau;}+E\left({\mathrm{\&Delta;}}^{\&prime;}\right))}-\frac{c_{\mathrm{Op}}}{((\frac{O_{\mathrm{total}}-O_{\mathrm{red}}}{E\left(Y\right)}+1)\&CenterDot;\mathrm{\&tau;}+E\left(\mathrm{\&Delta;}\right))}}\}$

Wherein $\mathrm{\&alpha;}=P[Y_{K+1}>O_{\mathrm{red}}|O(K\&CenterDot;\mathrm{\&tau;})=O_{\mathrm{red}}]=\frac{\frac{c_{\mathrm{Op}}\&CenterDot;\mathrm{\&tau;}}{(K\&CenterDot;\mathrm{\&tau;}+\mathrm{\&Delta;})((K+1)\&CenterDot;\mathrm{\&tau;}+\mathrm{\&Delta;})}}{\frac{c_{\mathrm{Or}}}{(K+1)\&CenterDot;\mathrm{\&tau;}+{\mathrm{\&Delta;}}^{\&prime;}}-\frac{c_{\mathrm{Op}}}{(K+1)\&CenterDot;\mathrm{\&tau;}+\mathrm{\&Delta;}}}$ It is the probability of operating system collapse before time (K+1) τ.

3.2, A _redthe determination of optimum value

$A_{\mathrm{red}}^{*}=\{A_{\mathrm{red}}:P[X_{K+1}>A_{\mathrm{red}}|A(K\&CenterDot;\mathrm{\&tau;})=A_{\mathrm{red}}]=\frac{\frac{c_{\mathrm{Ap}}\&CenterDot;\mathrm{\&tau;}}{(\frac{A_{\mathrm{total}}-A_{\mathrm{red}}}{E\left(X\right)}\&CenterDot;\mathrm{\&tau;}+E\left(\mathrm{\&delta;}\right))((\frac{A_{\mathrm{total}}-A_{\mathrm{red}}}{E\left(X\right)}+1)\&CenterDot;\mathrm{\&tau;}+E\left(\mathrm{\&delta;}\right))}}{\frac{c_{\mathrm{Ar}}}{((\frac{A_{\mathrm{total}}-A_{\mathrm{red}}}{E\left(X\right)}+1)\&CenterDot;\mathrm{\&tau;}+E\left({\mathrm{\&delta;}}^{\&prime;}\right))}-\frac{c_{\mathrm{Ap}}}{((\frac{A_{\mathrm{total}}-A_{\mathrm{red}}}{E\left(X\right)}+1)\&CenterDot;\mathrm{\&tau;}+E\left(\mathrm{\&delta;}\right))}}\}$

Wherein, $\mathrm{\&beta;}=P[Y_{K+1}>A_{\mathrm{red}}|A(K\&CenterDot;\mathrm{\&tau;})=A_{\mathrm{red}}]=\frac{\frac{c_{\mathrm{Ap}}\&CenterDot;\mathrm{\&tau;}}{(K\&CenterDot;\mathrm{\&tau;}+\mathrm{\&delta;})((K+1)\&CenterDot;\mathrm{\&tau;}+\mathrm{\&delta;})}}{\frac{c_{\mathrm{Ar}}}{(K+1)\&CenterDot;\mathrm{\&tau;}+{\mathrm{\&delta;}}^{\&prime;}}-\frac{c_{\mathrm{Ap}}}{(K+1)\&CenterDot;\mathrm{\&tau;}+\mathrm{\&delta;}}}$ It is the probability of application layer collapse before time (K+1) τ.

3.3, O _bluethe determination of optimum value

$O_{\mathrm{blue}}^{*}=\left\{\begin{array}{c}{O}_{\mathrm{blue}}:\frac{c_{\mathrm{Ap}}}{\frac{O_{\mathrm{blue}}-O_{\mathrm{red}}^{*}}{E\left(Y\right)}+\frac{E\left(\mathrm{\&delta;}\right)}{\mathrm{\&tau;}}}+\frac{c_{\mathrm{Op}}}{\frac{O_{\mathrm{total}}-O_{\mathrm{red}}^{*}}{E\left(Y\right)}+\frac{E\left(\mathrm{\&Delta;}\right)}{\mathrm{\&tau;}}}=\\ \frac{(E\left(N\right)-1)\&CenterDot;c_{\mathrm{Ap}}}{\frac{E\left(N\right)\&CenterDot;(A_{\mathrm{total}}-A_{\mathrm{red}}^{*})}{E\left(X\right)}+\frac{E\left(N\right)\&CenterDot;E\left(\mathrm{\&delta;}\right)}{\mathrm{\&tau;}}}+\frac{c_{\mathrm{Op}}}{\frac{O_{\mathrm{total}}-O_{\mathrm{blue}}}{E\left(Y\right)}+\frac{E\left(\mathrm{\&Delta;}\right)}{\mathrm{\&tau;}}}\end{array}\right\}$

Wherein, E (N) meets following expression formula:

$E\left(N\right)=\frac{\frac{O_{\mathrm{total}}-O_{\mathrm{red}}^{*}}{E\left(Y\right)}}{\frac{A_{\mathrm{total}}-A_{\mathrm{red}}^{*}}{E\left(Y\right)}+\frac{E\left(\mathrm{\&delta;}\right)}{\mathrm{\&tau;}}}$

4, system availability size is determined

4.1, α, β, O is obtained _red, A _redand O _blueoptimum value after, definition work as A _red< A (t)≤A _totaltime application layer in a safe condition; As 0 < A (t)≤A _redtime application layer be on the alert; When A (t)=0, application layer is in spent condition, works as O _blue< O (t)≤O _totaltime operating system layer in a safe condition; Work as O _red< O (t)≤O _bluetime operating system layer be in fatigue state; As 0 < O (t)≤O _redtime operating system layer be on the alert; When O (t)=0, operating system layer is in spent condition.As shown in Figure 3.

4.2, computing application layer or operating system layer are in the availability size of each shape probability of state and system.

4.2.1, when application layer warning or spent condition is in, and Probability p when operating system is in fatigue state _o1and the availability size A of system ₁be respectively

$P_{O1}=\frac{{O^{*}}_{\mathrm{blue}}-{O^{*}}_{\mathrm{red}}}{\frac{E\left(Y\right)}{\mathrm{\&tau;}}\&CenterDot;\frac{A_{\mathrm{total}}-{A^{*}}_{\mathrm{red}}}{\frac{E\left(X\right)}{\mathrm{\&tau;}}}}=\frac{({O^{*}}_{\mathrm{blue}}-{O^{*}}_{\mathrm{red}})\&CenterDot;E\left(X\right)}{(A_{\mathrm{total}}-{A^{*}}_{\mathrm{red}})\&CenterDot;E\left(Y\right)}$

$A_1=\frac{\frac{(O_{\mathrm{total}}-{O^{*}}_{\mathrm{blue}})\&CenterDot;\mathrm{\&tau;}}{E\left(Y\right)}-[\frac{\frac{(O_{\mathrm{total}}-{O^{*}}_{\mathrm{blue}})\&CenterDot;\mathrm{\&tau;}}{E\left(Y\right)}}{\frac{(A_{\mathrm{total}}-{A^{*}}_{\mathrm{red}})\&CenterDot;\mathrm{\&tau;}}{E\left(X\right)}+t_{\mathrm{AM}}}-1]\&CenterDot;t_{\mathrm{AM}}}{\frac{(O_{\mathrm{total}}-{O^{*}}_{\mathrm{blue}})\&CenterDot;\mathrm{\&tau;}}{E\left(Y\right)}+E\left(\mathrm{\&Delta;}\right)}$

4.2.2 the Probability p, when operating system is on the alert _o2and the availability size A of system ₂be respectively

p _O2＝(1-p _O1)(1-α)

$A_2=\frac{\frac{(O_{\mathrm{total}}-{O^{*}}_{\mathrm{red}})\&CenterDot;\mathrm{\&tau;}}{E\left(Y\right)}-[\frac{\frac{(O_{\mathrm{total}}-{O^{*}}_{\mathrm{red}})\&CenterDot;\mathrm{\&tau;}}{E\left(Y\right)}}{\frac{(A_{\mathrm{total}}-{A^{*}}_{\mathrm{red}})\&CenterDot;\mathrm{\&tau;}}{E\left(X\right)}+t_{\mathrm{AM}}}-1]\&CenterDot;t_{\mathrm{AM}}}{\frac{(O_{\mathrm{total}}-{O^{*}}_{\mathrm{red}})\&CenterDot;\mathrm{\&tau;}}{E\left(Y\right)}+E\left(\mathrm{\&Delta;}\right)}$

4.3.3 the Probability p, when operating system arrives spent condition _o3and the availability size A of system ₃be respectively

p _O3＝(1-p _O1)α

$A_3=\frac{\frac{O_{\mathrm{total}}\&CenterDot;\mathrm{\&tau;}}{E\left(Y\right)}-[\frac{\frac{O_{\mathrm{total}}\&CenterDot;\mathrm{\&tau;}}{E\left(Y\right)}}{\frac{(A_{\mathrm{total}}-{A^{*}}_{\mathrm{red}})\&CenterDot;\mathrm{\&tau;}}{E\left(X\right)}+t_{\mathrm{AM}}}-1]\&CenterDot;t_{\mathrm{AM}}}{\frac{O_{\mathrm{total}}\&CenterDot;\mathrm{\&tau;}}{E\left(Y\right)}+E\left({\mathrm{\&Delta;}}^{\&prime;}\right)}$

Wherein, t _aM=: β δ '+(1-β) δ is the averaging time of a maintenance application layer.

4.4, p is obtained _o1, A ₁, p _o2, A ₂, p _o3, A ₃after, be updated in following formula, obtained the availability maximal value of system.

Availability＝p _O1·A ₁+p _O2·A ₂+p _O3·A ₃。

Claims (2)

1. for the global optimization method based on maintenance cost of two layers of software catabiosis, it is characterized in that, comprise following step:

Step one: record application layer can utilize internal memory A when initial health _totalinternal memory O can be utilized when initial health with operating system layer _total, monitor monitors application layer the time interval (τ (i-1), τ i] the internal memory X of internal consumption _iwith operating system layer the time interval (τ (i-1), τ i] the internal memory Y of internal consumption _i, wherein τ is monitoring time interval, and i is monitoring total degree;

Step 2: build two layers of software aging analysis model based on renewal process:

$A(k\&CenterDot;\mathrm{\&tau;})=A_{\mathrm{total}}-\underset{i=1}{\overset{k}{\mathrm{\&Sigma;}}}{X}_i$

$O(k\&CenterDot;\mathrm{\&tau;})=O_{\mathrm{total}}-\underset{i=1}{\overset{k}{\mathrm{\&Sigma;}}}{Y}_i$

Wherein, internal memory available in application layer when A (k τ) is the secondary monitoring of monitor kth, internal memory available in operating system layer when O (k τ) is the secondary monitoring of monitor kth;

Step 3: according to two layers of software aging analysis model, obtains the alarm threshold O of operating system layer _redoptimum value, operating system layer fatigue threshold O _blueoptimum value, and the alarm threshold A of application layer _redoptimum value;

The alarm threshold O of operating system layer _redoptimum value be:

$O_{\mathrm{red}}^{*}=\{O_{\mathrm{red}}:P[Y_{K+1}>O_{\mathrm{red}}|O(K\&CenterDot;\mathrm{\&tau;})=O_{\mathrm{red}}]=\frac{\frac{c_{\mathrm{Op}}\&CenterDot;\mathrm{\&tau;}}{(\frac{O_{\mathrm{total}}-O_{\mathrm{red}}}{E\left(Y\right)}\&CenterDot;\mathrm{\&tau;}+E\left(\mathrm{\&Delta;}\right))((\frac{O_{\mathrm{total}}-O_{\mathrm{red}}}{E\left(Y\right)}+1)\&CenterDot;\mathrm{\&tau;}+E\left(\mathrm{\&Delta;}\right))}}{\frac{c_{\mathrm{Or}}}{((\frac{O_{\mathrm{total}}-O_{\mathrm{red}}}{E\left(Y\right)}+1)\&CenterDot;\mathrm{\&tau;}+E\left({\mathrm{\&Delta;}}^{\&prime;}\right))}-\frac{c_{\mathrm{Op}}}{((\frac{O_{\mathrm{total}}-O_{\mathrm{red}}}{E\left(Y\right)}+1)\&CenterDot;\mathrm{\&tau;}+E\left(\mathrm{\&Delta;}\right))}}\}$

Wherein, for the alarm threshold O of operating system layer _redoptimum value, before time (K+1) τ operating system collapse probability α be:

$\mathrm{\&alpha;}=P[Y_{K+1}>O_{\mathrm{red}}|O(K\&CenterDot;\mathrm{\&tau;})=O_{\mathrm{red}}]=\frac{\frac{c_{\mathrm{Op}}\&CenterDot;\mathrm{\&tau;}}{(K\&CenterDot;\mathrm{\&tau;}+\mathrm{\&Delta;})((K+1)\&CenterDot;\mathrm{\&tau;}+\mathrm{\&Delta;})}}{\frac{c_{\mathrm{Or}}}{(K+1)\&CenterDot;\mathrm{\&tau;}+{\mathrm{\&Delta;}}^{\&prime;}}-\frac{c_{\mathrm{Op}}}{(K+1)\&CenterDot;\mathrm{\&tau;}+\mathrm{\&Delta;}}},$

The fatigue threshold O of operating system layer _blueoptimum value be:

$O_{\mathrm{blue}}^{*}\text{=}\left\{\begin{array}{c}{O}_{\mathrm{blue}}:\frac{c_{\mathrm{Ap}}}{\frac{O_{\mathrm{blue}}-O_{\mathrm{red}}^{*}}{E\left(Y\right)}+\frac{E\left(\mathrm{\&delta;}\right)}{\mathrm{\&tau;}}}+\frac{c_{\mathrm{Op}}}{\frac{O_{\mathrm{total}}-O_{\mathrm{red}}^{*}}{E\left(Y\right)}+\frac{E\left(\mathrm{\&Delta;}\right)}{\mathrm{\&tau;}}}=\\ \frac{(E\left(N\right)-1)\&CenterDot;c_{\mathrm{Ap}}}{\frac{E\left(N\right)\&CenterDot;(A_{\mathrm{total}}-A_{\mathrm{red}}^{*})}{E\left(X\right)}+\frac{E\left(N\right)\&CenterDot;E\left(\mathrm{\&delta;}\right)}{\mathrm{\&tau;}}}+\frac{c_{\mathrm{Op}}}{\frac{O_{\mathrm{total}}-O_{\mathrm{blue}}}{E\left(Y\right)}+\frac{E\left(\mathrm{\&Delta;}\right)}{\mathrm{\&tau;}}}\end{array}\right\}$

Wherein, for the fatigue threshold O of operating system layer _blueoptimum value,

The alarm threshold A of application layer _redoptimum value be:

$A_{\mathrm{red}}^{*}=\{A_{\mathrm{red}}:P[X_{K+1}>A_{\mathrm{red}}|A(K\&CenterDot;\mathrm{\&tau;})=A_{\mathrm{red}}]=\frac{\frac{c_{\mathrm{Ap}}\&CenterDot;\mathrm{\&tau;}}{(\frac{A_{\mathrm{total}}-A_{\mathrm{red}}}{E\left(X\right)}\&CenterDot;\mathrm{\&tau;}+E\left(\mathrm{\&delta;}\right))((\frac{A_{\mathrm{total}}-A_{\mathrm{red}}}{E\left(X\right)}+1)\&CenterDot;\mathrm{\&tau;}+E\left(\mathrm{\&delta;}\right))}}{\frac{c_{\mathrm{Ar}}}{((\frac{A_{\mathrm{total}}-A_{\mathrm{red}}}{E\left(X\right)}+1)\&CenterDot;\mathrm{\&tau;}+E\left({\mathrm{\&delta;}}^{\&prime;}\right))}-\frac{c_{\mathrm{Ap}}}{((\frac{A_{\mathrm{total}}-A_{\mathrm{red}}}{E\left(X\right)}+1)\&CenterDot;\mathrm{\&tau;}+E\left(\mathrm{\&delta;}\right))}}\}$ Wherein, for the alarm threshold A of application layer _redoptimum value, before time (K+1) τ application layer collapse probability be:

$\mathrm{\&beta;}=P[X_{K+1}>A_{\mathrm{red}}|A(K\&CenterDot;\mathrm{\&tau;})=A_{\mathrm{red}}]=\frac{\frac{c_{\mathrm{Ap}}\&CenterDot;\mathrm{\&tau;}}{(K\&CenterDot;\mathrm{\&tau;}+\mathrm{\&delta;})((K+1)\&CenterDot;\mathrm{\&tau;}+\mathrm{\&delta;})}}{\frac{c_{\mathrm{Ar}}}{(K+1)\&CenterDot;\mathrm{\&tau;}+{\mathrm{\&delta;}}^{\&prime;}}-\frac{c_{\mathrm{Ap}}}{(K+1)\&CenterDot;\mathrm{\&tau;}+\mathrm{\&delta;}}},$

Wherein, E (X) is X _iexpectation value, E (Y) is Y _iexpectation value, c _opand c _orthat operating system regenerates and passive expense of restarting each time respectively, Δ and Δ ' be respectively operating system regeneration and passive time of restarting, E (Δ) and E (Δ ') be respectively Δ and Δ ' expectation value, c _apand c _arbe that application layer regenerates and passive expense of restarting each time respectively, δ and δ ' is respectively application layer regeneration and passive time of restarting, and E (δ) and E (δ ') is the expectation value of δ and δ ' respectively.

Step 4: according to the alarm threshold O of operating system layer _redoptimum value, operating system layer fatigue threshold O _blueoptimum value, and the alarm threshold A of application layer _redoptimum value, obtain two layers of software system availability maximal value.

2. the global optimization method based on maintenance cost for two layers of software catabiosis according to claim 1, is characterized in that: the described method obtaining two layers of software system availability maximal value, comprises following step,

1) state of application layer and operating system layer is divided, work as A _red< A (t)≤A _totaltime, application layer is in a safe condition; As 0 < A (t)≤A _redtime, application layer is on the alert; When A (t)=0, application layer is in spent condition; Work as O _blue< O (t)≤O _totaltime, operating system layer is in a safe condition; Work as O _red< O (t)≤O _bluetime, operating system layer is in fatigue state; As 0 < O (t)≤O _redtime, operating system layer is on the alert; When O (t)=0, operating system layer is in spent condition;

2) try to achieve when application layer is on the alert or spent condition, and operating system layer is in the Probability p of fatigue state _o1, and the availability A of now two layers of software system ₁for:

$p_{O1}=\frac{{O^{*}}_{\mathrm{blue}}-{O^{*}}_{\mathrm{red}}}{\frac{E\left(Y\right)}{\mathrm{\&tau;}}\&CenterDot;\frac{A_{\mathrm{total}}-{A^{*}}_{\mathrm{red}}}{\frac{E\left(X\right)}{\mathrm{\&tau;}}}}=\frac{({O^{*}}_{\mathrm{blue}}-{O^{*}}_{\mathrm{red}})\&CenterDot;E\left(X\right)}{(A_{\mathrm{total}}-{A^{*}}_{\mathrm{red}})\&CenterDot;E\left(Y\right)}$

$A_1=\frac{\frac{(O_{\mathrm{total}}-{O^{*}}_{\mathrm{blue}})\&CenterDot;\mathrm{\&tau;}}{E\left(Y\right)}-[\frac{\frac{(O_{\mathrm{total}}-{O^{*}}_{\mathrm{blue}})\&CenterDot;\mathrm{\&tau;}}{E\left(Y\right)}}{\frac{(A_{\mathrm{total}}-{A^{*}}_{\mathrm{red}})\&CenterDot;\mathrm{\&tau;}}{E\left(X\right)}+t_{\mathrm{AM}}}-1]\&CenterDot;t_{\mathrm{AM}}}{\frac{(O_{\mathrm{total}}-{O^{*}}_{\mathrm{blue}})\&CenterDot;\mathrm{\&tau;}}{E\left(Y\right)}+E\left(\mathrm{\&Delta;}\right)}$

When the Probability p that operating system layer is on the alert _o2, and the availability A of now two layers of software system ₂for:

p _O2＝(1-p _O1)(1-α)

$A_2=\frac{\frac{(O_{\mathrm{total}}-{O^{*}}_{\mathrm{red}})\&CenterDot;\mathrm{\&tau;}}{E\left(Y\right)}-[\frac{\frac{(O_{\mathrm{total}}-{O^{*}}_{\mathrm{red}})\&CenterDot;\mathrm{\&tau;}}{E\left(Y\right)}}{\frac{(A_{\mathrm{total}}-{A^{*}}_{\mathrm{red}})\&CenterDot;\mathrm{\&tau;}}{E\left(X\right)}+t_{\mathrm{AM}}}-1]\&CenterDot;t_{\mathrm{AM}}}{\frac{(O_{\mathrm{total}}-{O^{*}}_{\mathrm{red}})\&CenterDot;\mathrm{\&tau;}}{E\left(Y\right)}+E\left(\mathrm{\&Delta;}\right)},$

When operating system layer arrives the Probability p of spent condition _o3, and the availability A of now two layers of software system ₃for:

p _O3＝(1-p _O1)α

$A_3=\frac{\frac{O_{\mathrm{total}}\&CenterDot;\mathrm{\&tau;}}{E\left(Y\right)}-[\frac{\frac{O_{\mathrm{total}}\&CenterDot;\mathrm{\&tau;}}{E\left(Y\right)}}{\frac{(A_{\mathrm{total}}-{A^{*}}_{\mathrm{red}})\&CenterDot;\mathrm{\&tau;}}{E\left(X\right)}+t_{\mathrm{AM}}}-1]\&CenterDot;t_{\mathrm{AM}}}{\frac{O_{\mathrm{total}}\&CenterDot;\mathrm{\&tau;}}{E\left(Y\right)}+E\left({\mathrm{\&Delta;}}^{\&prime;}\right)},$

Wherein, t _aM=: β δ '+(1-β) δ is the averaging time of a maintenance application layer,

3) the availability maximal value asking for two layers of software system is:

Availability＝p _O1·A ₁+p _O2·A ₂+p _O3·A ₃。