CN101098255A - Option pricing model scheduling algorithm based implementation in interactive gridding system - Google Patents

Abstract

A distribution method of interactive grid based on option price mode belongs to computer distribution system technical field, which is characterized in that selectively applying BS potion price mode and dis-rational market into an interactive grid system, using a resource price mode to evaluate the operation state of a software server in each managed domain, to evaluate and screen memory spatial resource, and using the potion of memory state of a character software sever to dynamically evaluate the memory resource price and relative invest earning rate in each time section, using market rational parameters as reference to screen different missions. The simulation analysis has proved that the method has better distribution average property, and safety and economic property of resource distribution, according to time analysis, load analysis or the like.

Description

In the interactive gridding system based on the realization of Black-Scholes Option Pricing Model Black-Scholes dispatching algorithm

Technical field

Belong to distributed computing technology and system field based on the Black-Scholes Option Pricing Model Black-Scholes dispatching algorithm in the interactive gridding system, especially relating to task scheduling field and the field that has a large amount of manual operations.

Background technology

Along with the continuous development of network technology and distributed computing technology, the integration of software and hardware resources and the importance of distribution show especially day by day.Along with going deep into of grid research, and the friendly of user interface of software strengthens day by day, the widespread usage of visualization function, single order line grid can not satisfy the instructions for use of active user to software and hardware resources, is badly in need of interactive gridding technology of future generation is studied and used.

Interactive gridding technology of future generation, mainly be meant in the Application Grid technology and solve in the process of resource allocation and scheduling, use visual graphical interfaces and provide friendly user interface for the user, and fully take into account operator's degree of participation and participate in frequency, grid system and visual resource allocation and integration are combined.From application, it is friendly inadequately thoroughly to change in the past in the grid system user interface, to the not enough drawback of software through pictures support.From the definition of interactive gridding technology, it mainly contains following two big distinctive characteristics: the one, and patterned User Interface, the 2nd, there is the intervention of a large amount of manual operations in the task run process.Patterned User Interface has increased several reference indexs such as bandwidth, data migration and computing capability in the process of scheduling; Human intervention in the task run, be the maximum characteristics of the existing grid system of interactive gridding difference, in interactive gridding system used, the user adopted interactively using method at any time to running, running status and the task executions correct of current system.Because there are above two distinctive characteristics in interactive gridding, its requirement to dispatching algorithm and realization is also higher than the traditional type grid, traditional gridding scheduling algorithm can't satisfy the dispatching requirement of interactive system, is badly in need of research and realizes that a kind of new dispatching algorithm solves the scheduling problem of resource and task in the interactive gridding.

Solve the scheduling problem in the interactive gridding, key both ways: the one, how to weigh the value of resource and the value of task, be equivalent to a pricing problem; The 2nd, how resource and task are mated corresponding selection problem.Introducing ECONOMICAL APPROACH TO, utilize ripe pricing model that the value of resource is fixed a price, is to solve a solution weighing resource value; Utilize market model, the marketing process of artificial participation is arranged, make the process of selection more be close to the artificial task scheduling that participates in the interactive gridding by simulation.Before concrete applied economics method, the demand of Black-Scholes Option Pricing Model and irrational market theory-compliant interactive gridding must be described.

The applicability of Black-Scholes Option Pricing Model.Option is a kind of financial derivatives peace treaty, and it is given and makes an appointment with a kind of right of holder by the price of agreement, to buy in or to sell certain particular commodity at a certain special time or in the specific period in future.Option is applicable in following certain hour, and the appraisal of the security that fluctuate around a certain price can be rejected fluctuation to a certain extent by the notion of using option, represents the issuable influence of potential fluctuation with a constant price.Black-Scholes Option Pricing Model is classical Black-Scholes Option Pricing Model Black-Scholes, and core concept is exactly the appraisal to financial option, and marrow is to reduce because the uncertain cost of being paid.The characteristics of task are exactly the graphic interactive operation that the people participates in the interactive gridding, the uncertainty of the operation resource consumption of software through pictures itself, the influence of the especially artificial factor that participates in, make its demand that great fluctuation be arranged, and this fluctuation is a mean value with a software recommendation resource distribution to resource.If only dispatch assessment according to certain time point wherein, perhaps do not consider fluctuation, only recommending resource distribution with it is that standard dispatches all can be owing to existing of fluctuation causes system load unbalanced, i.e. the appearance of crest and trough, and then influence the scheduling and the operational efficiency of system.The fluctuation of the task resource of comprehensive interactive gridding, and the notion of option and characteristics, being to have fluctuation on the one hand, is the influence that floating fluctuation is brought on the other hand, we can say the especially task scheduling of the very suitable interactive gridding of Black-Scholes Option Pricing Model of option.

C ₀＝S ₀N(d ₁)-Xe ^-rTN(d ₂)

${\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="A20071009959500161.png"\; state="\{\{state\}\}">d</figure-callout>}}_1=\frac{\ln ({\mathrm{<figure-callout\; id="0"\; label="s"\; filenames="A20071009959500161.png"\; state="\{\{state\}\}">s</figure-callout>}}_0/X)+(r+{\mathrm{\&sigma;}}^2/2)T}{\mathrm{\&sigma;}\sqrt{T}}$

${\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="A20071009959500161.png"\; state="\{\{state\}\}">d</figure-callout>}}_2=d_1-\mathrm{\&sigma;}\sqrt{T}$

C ₀---current call option price

S ₀---current stock price

N (d)-standardized normal distribution is less than the probability of d

The X----strike price

Wherein: the end of e----natural logrithm

The r----risk free rate

T----option expiration time

Ln---natural logrithm function

The annualized return standard deviation of σ--stock continuous compound rate

Formula 1 cloth Rec-Clarke Scholes option valuation computing formula

This dispatcher software, use for reference the successful Application of this model in option valuation, by economic notion and computational methods are incorporated into the computer system scheduling, utilize the existing systems parameter, by the mapping relations on computer meaning and the economics meaning, draw the possible operational factor of system on the future a certain time point.And then be used for subject matter and normative reference as next step selection.

The applicability of irrational city field theory.Marketing is a kind of best mode that resource is configured, and it participates in the individual individual transaction decision-making of the marketing thing being made according to certain price by market, and the effect that the application group selects reaches OPTIMAL ALLOCATION OF RESOURCES.The proposition of city's field theory is the summary from experience in the daily life, is that a cover is the refinement of participative decision making process and abstract at numerous people, and has good performance through checking in resource allocation that has artificial decision-making to participate in and scheduling.The characteristics and the specific aim in market mainly comprise: market has the participant that can make independent decision-making, and having on the market can be for the product of transaction, the confirmable measurement of the price of marketing thing.The development of city's field theory is through plurality of processes, from initial free market, through the transformation of rational market to irrational market.Irrational city field theory is a kind of in-depth and the development to city's field theory that proposes nineteen nineties.Irrational city field theory is thought, has numerous irrational selection factors in the participant in market, and in some special stage, very the person is revealed as the irrational decision-making and the behavior of whole market.Irrational factors is meant, just the participant in the market participates in the process of marketing, because some influences of factor outside the venue, the participant can make the decision-making that a kind of and its interests do not conform to and take the behavior of interests contradiction with it, and especially (as: stock, futures, option, foreign exchange etc.) seem particularly evident on financial transaction market.Task in the interactive gridding is owing to have a large amount of artificial decision factors inside, and each artificial decision-making all has independence, makes it possess the independent decision-making people that the application market theory dispatches and participates in condition; In this market, task of dispatching and the resource of participating in the distribution can be used as the product of marketing; By using Black-Scholes Option Pricing Model, task in the task scheduling and resource there be one rational " appraisal ", can determine the condition weighed thereby possessed the price of on market, concluding the business, and because the appearance system of " price " can determine the rational decision making mode and the irrational decision-making mode of marketing according to the theory of price height in the price system.Above-mentioned three, prove that task scheduling can adopt the mode of marketing to carry out in the interactive gridding.Irrational city field theory is the expansion to city's field theory, makes its simulation process more approach real marketing process, so can carry out the scheduling and the selection of task in the interactive gridding in this process of using the theoretical modeling marketing of irrational market.

Irrational marketing model.Irrational market is meant has a certain proportion of participant to carry out market operation not according to the market logic of the rational faculty in the marketing process, and quite the participant of vast scale operates formed trade market according to the thinking that meets the market logic.Irrational marketing model is exactly the Trading Model in the irrational like this market of simulation.Three key parameters of this model are: the rational degree in the rational choice mode in market, the irrational selection mode in market and market.

● the rational choice mode in market is meant, is in market under the state of burying property, and the participant in market according to which kind of logical order selects marketing product and price thereof.The rational choice mode in market is according to the selective sequential from low to high of subject matter price in this dispatcher software.This mode meets in the transaction of open market, buyer's behavior and thinking standard.

The irrational selection mode in market is meant which kind of order irrational selection people adopt marketing product and price thereof are selected in the market.The irrational selection mode in market is to adopt the mode of picked at random to realize in this dispatcher software.This mode meets marketing impulse purchase person's Impulse Buy behavior, and the randomness on selecting.

The rational degree in market is meant have the people of much ratios to take rational selection mode among all participants in market, and nearly the people of ratio adopts irrational selection mode.This parameter is that division market is a line of demarcation in whole rational market or whole irrational market.The rational degree in market is to choose according to 0.2 ratio in this dispatcher software, and in other words, it is rational dealer that 80% dealer is arranged among the marketing person, and what they adopted is that target price order is from high to low chosen the Object of Transaction thing; 20% dealer is irrational dealer, and they adopt is that at random mode is chosen the Object of Transaction thing.

At the characteristics of interactive gridding resource allocation and task scheduling, with reference to existing traditional scheduler method and the economics theory model that is widely used, propose and realized in the interactive gridding dispatching algorithm based on Black-Scholes Option Pricing Model Black-Scholes

Black-Scholes Option Pricing Model (is called for short: the BS model), be the Black-Scholes Option Pricing Model Black-Scholes that was proposed in 1973 by Bu Laike and Clarke Scholes, and obtained Nobel prize in economics in 1997.The BS model is to be based upon on the statistical basis, takes into full account the fluctuation ratio of security price and the uncertainty that changes in a period of time, and a kind of measurement that draws is at the economics model of the required present price of paying of a certain fixed time acquisition prospective earnings in future.Be characterized in solving and how represented a certain security value over time, and these security have the characteristic of carrying out uncertain fluctuation within the specific limits in a period of time in future with current value.The computing formula of BS model is shown in formula 1 cloth Rec-Clarke Scholes option valuation computing formula.

Summary of the invention

The object of the present invention is to provide a kind of method that solves task scheduling in the interactive gridding, so that a kind of support of basis is provided for the large-scale application of interactive gridding.The present invention is directed to the characteristics of interactive gridding, introduce the pricing model and the market model of option in the economics, provide solution there being a large amount of artificial participating in of tasks to dispatch.

Based on the dispatching method of Black-Scholes Option Pricing Model Black-Scholes, its characteristics are that this method is to realize according to the following steps successively in the interactive gridding system that is made of data center, a plurality of autonomous territory, grid inlet and virtual bus in the interactive gridding system:

Step (1) system initialization

In each autonomous territory, set up following register format in each software server, data item wherein is respectively

VGIP-SIP: being the ID by IP group in the territory of the IP of the virtual gateway in each autonomous territory and each software server and a single software server forming, is an address format of this software server of visit;

SystemInfo: be software server information, content comprises the grid memory headroom resource that indicates acquisition time of this software server current C PU load, memory usage, offered load occupancy and above three parameters;

SoftwareInfo: dbase and the version number of containing the software that this software server can provide;

The contact of in each autonomous territory, setting up each software server and virtual gateway, and the contact of a local data cache and this virtual gateway;

In the Web portal of interactive gridding system, set up the contact between grid service server and the database server;

In data center, set up the contact between dispatcher software server and the borde gateway, and the contact between this borde gateway and the concentrated storage server of each user data, also to set up the contact between borde gateway and the DB Backup server;

In interactive gridding system inside, set up dispatcher software server in the data center and the contact between the local data local caches in each autonomous territory, and the contact between the webserver in this dispatcher software server and the described Web portal;

In the dispatcher software server of data center, set up scheduler module, wherein contain:

Based on the system resource price price computing formula of Black-Scholes Option Pricing Model computing formula,

C ₀＝S ₀N(d ₁)-Xe ^-rTN(d ₂)

${\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="A20071009959500161.png"\; state="\{\{state\}\}">d</figure-callout>}}_1=\frac{\ln ({\mathrm{<figure-callout\; id="0"\; label="s"\; filenames="A20071009959500161.png"\; state="\{\{state\}\}">s</figure-callout>}}_0/X)+(r+{\mathrm{\&sigma;}}^2/2)T}{\mathrm{\&sigma;}\sqrt{T}}$

${\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="A20071009959500161.png"\; state="\{\{state\}\}">d</figure-callout>}}_2=d_1-\mathrm{\&sigma;}\sqrt{T}$

C ₀: resource price

S ₀: current obtainable number of resources

X: task is recommended resource use amount, given value

T: task execution time section, initialization have task to specify

Wherein: r: the ratio of certain vacant stock number of main frame and average abundance

σ: the standard deviation of vacant stock number

N (d ₁): standardized normal distribution is less than d ₁Probability

N (d ₂): standardized normal distribution is less than d ₂Probability

Between the option period that the user sets in the T=TimeSpan, the formula of computational resource price

T′＝{T′|T _i′＜TimeSpan，TimeSpan＞T}

T is described task execution time section, i=1,2 ... I is set by the user;

$\stackrel{~}{{\mathrm{<figure-callout\; id="0"\; label="C"\; filenames="A20071009959500161.png"\; state="\{\{state\}\}">C</figure-callout>}}_0}=\underset{i=0}{\overset{I}{\mathrm{\&Sigma;}}}{C}_{0i}*W_i$

$W_i=\left\{W_i\right|W_i=\frac{\mathrm{TimeSpan}-T_i^{\&prime;}+1}{\underset{T_i^{\&prime;}\&Element;T^{\&prime;}}{\mathrm{\&Sigma;}}\mathrm{TimeSpan}-T_i^{\&prime;}+1},{T^{\&prime;}}_i\&Element;T^{\&prime;}\}$

Wherein: C _0i: T _iThe memory headroom resource price of ' time period;

The memory headroom resource price of T ' time period;

W _i: T _iThe weight of the resource price of ' time period

When the user carries out irrational Market Selection: the computing formula of investment yield ROI:

With the rational coefficient r ' in the market behind the irrational market dispatch:

$r^{\&prime;}=r^{\&prime;}*\tilde{r}$ (r ' 0 ~ 1 fluctuation)

Be the adjustment coefficient, $\tilde{r}=\frac{n_1}{{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="A20071009959500161.png"\; state="\{\{state\}\}">n</figure-callout>}}_2}$

n ₁: autonomous territory internal burden surpasses 80% software server number

n ₂: autonomous territory internal burden is less than 20% software server number

Virtual gateway in each autonomous territory of step (2) the log-on data of each software server in this autonomous territory set by step (1) described register format mail to webserver registration in the grid inlet, and deposit database server in the Web portal in, simultaneously the log-on data of software server is separately deposited in local data cache device in the individual autonomous territory;

Step (3) is behind the dispatcher software server in the arrival Web portal of each task, this dispatcher software server is just transferred in the system memory headroom resource information of software server in each autonomous territory from the local data cache device in each autonomous territory, whether analyze these information is in the time period of setting, information time unit is minute, if then enter step (5), otherwise, enter step (4);

Step (4) regains Installed System Memory space resources information from the database server of the Web portal of system, change step (5) over to;

The dispatcher software server of step (5) in step (3) calculates current available resource according to the current memory headroom resource of system that obtains and counts S in step (3) or step (4) ₀, the ratio of the average vacant stock number of certain vacant stock number of software server and current system and the standard deviation sigma of vacant stock number, calculate current resource price C according to these parameters and the known memory headroom resource use amount X that recommends by the given task execution time section T of task, task ₀

Step (6) is T '=TimeSpan between the option period that the user sets, and T _i' ∈ T ', i=1,2 ... I calculates the weighting resource price

Dispatcher software server shown in the step (7) to current memory headroom resource according to memory headroom resource price formula weighting memory headroom resource price, select the memory headroom resource that is fit to mission requirements, join and wait for scheduling in the qualified resource queue, if the quantity of qualified memory headroom equals 0, then change step (3) over to;

Step (8) dispatcher software server calculates each weighting time period T ₁' memory headroom resource price C _0iWith

And corresponding investment yield ROI, use for scheduling;

The time interval of the setting described in each step of step (9) (3) is calculated the rational coefficient in market $r^{\&prime;}=r^{\&prime;}*\tilde{r},$ In repeating step (8), do the use of irrational selection for the user.

Based on the dispatching method of Black-Scholes Option Pricing Model Black-Scholes, it is characterized in that in the described interactive gridding system, at described T _iAmong ' ∈ the T ', i=1,2,3, T ₁'=1, T ₂'=2, T ₃'=4.

System environments

● the unit node

Hardware environment: 1GHz CPU, 512M internal memory, 1G hard disk, the 10M network bandwidth

Software environment: Linux Red Hat F3 system, Java SDK 1.5-04 environment, Tomcat 5.5 containers

● network environment

Grid Ingress node: 1

System database node: 2

Autonomy field system: 3

Software server node in the territory: 4/autonomous territory

Compare with other dispatching methods

● the contrast dispatching method

1. weighted round robin dispatching algorithm: the weighted round robin dispatching algorithm is on the basis of robin scheduling algorithm, adds the state information parameter of current system, generates the weighted round robin dispatching algorithm that certain weights and priority are arranged.

2. statistics Randomized scheduling algorithm: the statistics Randomized scheduling algorithm is on the basis of Randomized scheduling algorithm, adds up the state information of passing following period of time system, and calculates the proportion of each server in the random schedule based on statistical value.

● the contrast index

1. retardation rate average: the retardation rate average is meant under certain statistical parameter, average retardation rate.Retardation rate uses task queue total time of delay divided by the queuing theory deadline.Retardation rate average index is used for the quality of each dispatching algorithm of comparison on performance, and the dispatching algorithm of better performances is less on postponing, otherwise postpones more.

2. fluctuation variance: the fluctuation variance is a notion on the statistics.Main users is weighed a kind of stability of index, whether has a bigger fluctuation.Weigh dispatching algorithm in the operation dispatching process with the fluctuation variance, the stability that is had here.Corresponding fluctuation variance is more little, and fluctuation is more little, and performance is stable more.

● reduced parameter

1. time series: time series is chosen the time point on a period of time, according to running time from being short to long sequence arrangement, add up the performance index on each time point respectively.{ 1,2,3,4,5,6,7,8,9,10,11,12,13,26,39,52} represents short-term to a long-term process to select 13 time points here.

2. load sequence: the load sequence is meant, the number of tasks that arrives at most on some time points and the ratio of number of servers.

0.2 to be example, representative if there are 10 station servers that service is provided, has 10*0.2=2 task arrival at most on some time points.Because each task all has certain cycle of operation, so the load of system can not reach 1.Here, select 0.2,0.3,0.4,0.5,0.6,0.7} sequence as a comparison.

● analysis of experimental data

1. time series performance comparison figure (Fig. 3)

From this figure, in whole time series, the performance of Options market model is better than other two kinds of dispatching algorithms always except that indivedual points as can be seen.And generally, the Options market model will be better than other two kinds of algorithms far away in ultrashort phase and medium-term and long-term performance.This feature has reflected that resource allocation that algorithm is good and oneself adjust the ability that adapts to.

2. load sequence performance comparison diagram (Fig. 4)

From this figure, no matter under which kind of loading condition, the average behavior of Options market model all is better than other two kinds of algorithms as can be seen.And be that peak value appears in 0.6 place in load, illustrate that it is under 0.6 the situation that the Options market model algorithm is not suitable for operating in load.By contrast, weighting statistics stochastic model presents downward trend to being increased in of load always on the performance, illustrate that its sensitivity to load variations is the highest.

3. time series fluctuation comparison diagram (Fig. 5)

From this figure, (sampling period is preceding 12 cycles) as can be seen in a short time, three kinds of dispatching algorithms gap on fluctuation is not obvious, and total ripple is all little.But since the 13rd sampled point, the gap of three dispatching algorithms on fluctuation displays gradually.Be followed successively by: Options market model＜weighted round robin model＜weighting statistics stochastic model.From then on as can be seen, the Options market model has very good performance in the scheduling process of midium or long term, present stable scheduling performance.Do not enlarge the fluctuation of scheduling performance along with the variation of time.

4. load sequence fluctuation comparison diagram (Fig. 6)

From this figure, under different load conditions, the fluctuation ratio of Options market model changes little as can be seen, and whole scheduling performance tends towards stability.On the contrary, slightly to be inferior to the weighting statistics stochastic model fluctuation ratio of Options market model very big for performance in the load sequence, and whole scheduling performance is along with the variation of load produces huge fluctuation.

The situation of four width of cloth figure above comprehensive, we as can be seen, with regard to time series, the Options market model demonstrates good scheduling performance and stability in the midium or long term.In three kinds of algorithms, occupy first.With regard to the load sequence, the performance of Options market model all is better than by comparison other two kinds of dispatching algorithms on each load sampled point.Simultaneously, on fluctuation, the Options market model does not demonstrate and the same fluctuation of putting on weight of weighting statistics stochastic model, and integral body tends towards stability.Show good performance and stability generally.Draw thus, no matter from the seasonal effect in time series latitude, still from the latitude of load sequence, the Options market model all shows good performance and stability.

Description of drawings

Fig. 1: interactive gridding system framework map.

Fig. 2: the interactive gridding task scheduling is carried out FB(flow block).

Fig. 3: time series performance comparison figure:

The BSM dispatching method,

The DWR dispatching method,

The DSR dispatching method.

Fig. 4: load sequence performance comparison diagram:

The BSM dispatching method,

The DWR dispatching method,

The DSR dispatching method.

Fig. 5: time series fluctuation comparison diagram:

The BSM dispatching method,

The DWR dispatching method,

The DSR dispatching method.

Fig. 6: load sequence fluctuation comparison diagram: The BSM dispatching method,

The DWR dispatching method, The DSR dispatching method.

Embodiment

The scheduling of this algorithm and realization all are based on interactive gridding system.Interactive gridding system can be divided into four parts (as shown in Figure 1) from framework, and four module functions comprise:

● grid inlet: the webserver and system database server that friendly user interface is provided

● software autonomy field system: comprise patterned interactive software server, local data cache and virtual gateway are provided, independently become some servers of an autonomy field system physically

● data center: comprise system database backup server, the concentrated storage server of user data

● virtual bus: above each intermodule interconnects by virtual bus and gateway, forms a grid system that can dynamically add and leave.Simultaneously, the management by bus realizes network security.

The scheduled for executing flow process

This algorithm is divided into two parts and carries out in operation.At first be in the system start-up stage, dispatching method is carried out initialization operation in system; Secondly, after system finishes startup, arrive task scheduling flow process of automated system operation at each task.This two-part detailed execution in step is as follows:

1. initialization: the process of system initialization comprises the initialization of autonomy field system and initialization two parts of system mode.

A) autonomy field system initialization:

Autonomy field system at first will start the operating software server node, and initialization virtual gateway and virtual bus, the contact of setting up each intermodule of system.Start the software server node, and register to the system database server according to following data format.

Register format:

VGIP-SIP

SystemInfo

SofwareInfo

● VGIP-SIP: with the mode of IP in combination virtual gateway IP and the software server territory, determine a single software server ID, this ID also can be called an address indication of this server of visit simultaneously.

● SystemInfo: send the essential information of software server, comprise the standard value of current C PU load, memory usage, network bandwidth occupancy and above three parameters

● SoftwareInfo: send the software of software name and version number can be provided on the current software server

B) system mode initialization:

Start the accreditation process that is deployed on the software server node, the running status of present node is reported to the system database server; Dispatcher software is collected current system status information by the system database server, and initialization Black-Scholes Option Pricing Model Black-Scholes parameter and irrational market parameter;

2. system task scheduling flow: the system call flow process is exactly according to certain step traffic control algorithm, selects a node that relatively is fit to provide service for task from numerous software server nodes.The task scheduling flow process is divided into three big steps, comprises:

A) parameter collection and arrangement stage

B) option premium calculation stages

C) the irrational market dummy run phase

Before using the theoretical solution in Black-Scholes Option Pricing Model and irrational market interactive gridding scheduling problem, at first the economics notion in the model to be mapped to corresponding parameters in the software systems.Table 1 Black-Scholes Option Pricing Model mapping table has been listed the mapping relations of the two

Parameter	The economics implication	Implication in the system
			C 0	Option premium	Resource price
S 0	Current security price	Current available resource number
			X	Strike price	Task is recommended the resource use amount
T	The option expiration time	Task execution time
			r	Risk free rate	The ratio of certain machine idle stock number and average abundance
σ	The standard deviation of security repayment	The standard deviation of vacant resource
			N(d)	Normal distribution	Normal distribution
e	Natural logrithm value (2.7183)	Natural logrithm value (2.7183)
			ln	The natural logrithm computing	The natural logrithm computing

Table 1 Black-Scholes Option Pricing Model mapping table

The applicability of Black-Scholes Model is improved.Black-Scholes Model is the assessment to some time point options worths in future, rather than to the prediction of a time period, the time that runs abort of task is uncertain owing to artificial participation by contrast, and single regular time is put the requirement that does not meet task scheduling.Therefore, before using Black-Scholes Option Pricing Model, at first need fixing time point option is calculated the option calculating that changes into the time period.What adopt is that weighted-average method is expanded.Weighted average is in a period of time, and certain several time point is sampled, and calculates the option premium on each sampled point; Calculate its weights respectively according to the ratio of shared time period of duration of time point correspondence again, utilize above-mentioned sampling account form to be weighted on average, obtain the weighting price and dispatch as final transaction value.

What to sum up, system adopted is a kind of improved weighting Black-Scholes Option Pricing Model.Calculate the weighting option premium and be divided into two key steps: calculate the option premium of each resource at certain time point; Calculate the weighting option premium.Corresponding computing formula is shown in formula 2 and formula 3:

C ₀＝S ₀N(d ₁)-Xe ^-rTN(d ₂)

${\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="A20071009959500161.png"\; state="\{\{state\}\}">d</figure-callout>}}_1=\frac{\ln ({\mathrm{<figure-callout\; id="0"\; label="s"\; filenames="A20071009959500161.png"\; state="\{\{state\}\}">s</figure-callout>}}_0/X)+(r+{\mathrm{\&sigma;}}^2/2)T}{\mathrm{\&sigma;}\sqrt{T}}$

${\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="A20071009959500161.png"\; state="\{\{state\}\}">d</figure-callout>}}_2=d_1-\mathrm{\&sigma;}\sqrt{T}$

Formula 2 cloth Rec-Clarke Scholes option valuation computing formula

T′＝{T′|T _i′＜TimeSpan，TimeSpan＞T}

$W_i=\left\{W_i\right|W_i=\frac{\mathrm{TimeSpan}-T_i^{\&prime;}+1}{\underset{T_i^{\&prime;}\&Element;T^{\&prime;}}{\mathrm{\&Sigma;}}\mathrm{TimeSpan}-T_i^{\&prime;}+1},{T^{\&prime;}}_i\&Element;T^{\&prime;}\}$

$\stackrel{~}{{\mathrm{<figure-callout\; id="0"\; label="C"\; filenames="A20071009959500161.png"\; state="\{\{state\}\}">C</figure-callout>}}_0}=\underset{i=0}{\overset{I}{\mathrm{\&Sigma;}}}{C}_{0i}*W_i$

i＝1，2，4

Formula 3 weighting option premium formula

The realization of irrational city field stimulation

In the irrational city field stimulation, emphasis will be determined two market parameters: the rational degree in market rational choice mode and market, and a fundamental in market itself, market access mode.The rational choice mode in market, according to price theory, rate of return on investment selective sequential trading object is from high in the end concluded the business, and rate of return on investment determines according to the merchant of current resource forecast consumption amount and resource option premium, as shown in Equation 4.The irrational selection mode in market, the dealer in market is in the people that all are participated in business, and the option dealing object is concluded the business at random.Market is in selection course, the rational degree value of dynamic adjustment, initial rational degree is 0.2,20% irrational dealer is promptly arranged according at random mode option dealing object in market, and all the other dealers of 80% are according to rate of return on investment rational choice mode option dealing object from high to low.The rational degree in market satisfies fluctuation 0 ~ 1 scope in, every 15 minutes, once adjusts, and the adjustment mode is according to as follows: calculate load in current and the system respectively above 80% machine quantity n ₁With less than 20% quantity n ₂, calculate the rational resize ratio in market according to formula 5

And on the basis of the rational coefficient in current market, adjusted according to resize ratio, as shown in Equation 6.To sum up, can determine the operational factor in irrational market to formula 6 by formula 4.The access mode in market, it is a kind of qualification authentication to the personnel that participate in business in the market, the staple market permit standard is the requirement to price in the realization of the task scheduling algorithm of interactive gridding, the price of any its resource of participant is a positive integer, that is to say, resource price can not occur and weigh, equally to participating in the task of scheduling to bearing or zero situation, its option premium equally can not be for negative, but can be zero.

Formula 4 investment yield computing formula

$\tilde{r}=\frac{n_1}{{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="A20071009959500161.png"\; state="\{\{state\}\}">n</figure-callout>}}_2}$

The rational degree in formula 5 markets is adjusted coefficient

$r^{\&prime;}=r^{\&prime;}*\tilde{r}$

The rational coefficient in formula 6 adjusted markets.

Claims (2)

1, in the interactive gridding system based on the dispatching method of Black-Scholes Option Pricing Model Black-Scholes, its characteristics are that this method is to realize according to the following steps successively: step (1) system initialization in the interactive gridding system that is made of data center, a plurality of autonomous territory, grid inlet and virtual bus

In each autonomous territory, set up following register format in each software server, data item wherein is respectively VGIP-SIP: being the ID by IP group in the territory of the IP of the virtual gateway in each autonomous territory and each software server and a single software server forming, is an address format of this software server of visit;

SystemInfo: be software server information, content comprises the grid memory headroom resource that indicates acquisition time of this software server current C PU load, memory usage, offered load occupancy and above three parameters;

SoftwareInfo: dbase and the version number of containing the software that this software server can provide;

The contact of in each autonomous territory, setting up each software server and virtual gateway, and the contact of a local data cache and this virtual gateway;

In the Web portal of interactive gridding system, set up the contact between grid service server and the database server;

In data center, set up the contact between dispatcher software server and the borde gateway, and the contact between this borde gateway and the concentrated storage server of each user data, also to set up the contact between borde gateway and the DB Backup server;

In interactive gridding system inside, set up dispatcher software server in the data center and the contact between the local data local caches in each autonomous territory, and the contact between the webserver in this dispatcher software server and the described Web portal;

In the dispatcher software server of data center, set up scheduler module, wherein contain:

Based on the system resource price price computing formula of Black-Scholes Option Pricing Model computing formula,

C ₀＝S ₀N(d ₁)-Xe ^-rTN(d ₂)

$d_1=\frac{1n(s_0/X)+(r+{\mathrm{\&sigma;}}^2/2)T}{\mathrm{\&sigma;}\sqrt{T}}$

$d_2=d_1-\mathrm{\&sigma;}\sqrt{T}$

C ₀: resource price

S ₀: current obtainable number of resources

X: task is recommended resource use amount, given value

T: task execution time section, initialization have task to specify

Wherein: r: the ratio of certain vacant stock number of main frame and average abundance

σ: the standard deviation of vacant stock number

N (d ₁): standardized normal distribution is less than d ₁Probability

N (d ₂): standardized normal distribution is less than d ₂Probability

Between the option period that the user sets in T '=TimeSpan, the formula of computational resource price

T′＝{T′|T _i′＜TimeSpan，TimeSpan＞T}

T is described task execution time section, i=1,2 ... I is set by the user;

$\widetilde{C_0}=\underset{i=0}{\overset{I}{\mathrm{\&Sigma;}}}{C}_{0i}*W_i$

$W_i=\left\{W_i\right|W_i=\frac{\mathrm{TimeSpan}-T_i^{\&prime;}+1}{\underset{T_i^{\&prime;}\&Element;T^{\&prime;}}{\mathrm{\&Sigma;}}\mathrm{TimeSpan}-T_i^{\&prime;}+1},{T^{\&prime;}}_i\&Element;T^{\&prime;}\}$

Wherein: C _0i: T _iThe memory headroom resource price of ' time period

: the memory headroom resource price W of T ' time period _i: T _iWhen the weight user of the resource price of ' time period carries out irrational Market Selection: the computing formula of investment yield ROI:

With the rational coefficient r ' in the market behind the irrational market dispatch:

$r^{\&prime;}=r^{\&prime;}*\tilde{r}$ (r is 0 ~ 1 fluctuation)

Be the adjustment coefficient, $\tilde{r}=\frac{n_1}{n_2}$

n ₁: autonomous territory internal burden surpasses 80% software server number;

n ₂: autonomous territory internal burden is less than 20% software server number;

Virtual gateway in each autonomous territory of step (2) the log-on data of each software server in this autonomous territory set by step (1) described register format mail to webserver registration in the grid inlet, and deposit database server in the Web portal in, simultaneously the log-on data of software server is separately deposited in local data cache device in the individual autonomous territory;

Step (3) is behind the dispatcher software server in the arrival Web portal of each task, this dispatcher software server is just transferred in the system memory headroom resource information of software server in each autonomous territory from the local data cache device in each autonomous territory, whether analyze these information is in the time period of setting, information time unit is minute, if then enter step (5), otherwise, enter step (4);

Step (4) regains Installed System Memory space resources information from the database server of the Web portal of system, change step (5) over to;

The dispatcher software server of step (5) in step (3) calculates current available resource according to the current memory headroom resource of system that obtains and counts S in step (3) or step (4) ₀, the ratio of the average vacant stock number of certain vacant stock number of software server and current system and the standard deviation sigma of vacant stock number, calculate current resource price C according to these parameters and the known memory headroom resource use amount X that recommends by the given task execution time section T of task, task ₀

Step (6) is T ' TimeSpan between the option period that the user sets, and T _i∈ T, i=1,2 ... I calculates the weighting resource price

Dispatcher software server shown in the step (7) to current memory headroom resource according to memory headroom resource price formula weighting memory headroom resource price, select the memory headroom resource that is fit to mission requirements, join and wait for scheduling in the qualified resource queue, if the quantity of qualified memory headroom equals 0, then change step (3) over to;

Step (8) dispatcher software server calculates each weighting time period T ₁' memory headroom resource price C _0iWith

And corresponding investment yield ROI, use for scheduling;

The time interval of the setting described in each step of step (9) (3) is calculated the rational coefficient in market $r^{\&prime;}=r^{\&prime;}*\tilde{r},$ In repeating step (8), do the use of irrational selection for the user.

2, in the interactive gridding system according to claim 1 based on the dispatching method of Black-Scholes Option Pricing Model Black-Scholes, it is characterized in that, at described T ' _iAmong the ∈ T ', i=1,2,3, T ₁'=1, T ₂'=2, T ₃'=4.

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