RU2542925C1 - Method of self-organisation of distributed multiprocessor system - Google Patents

Abstract

FIELD: information technologies.

SUBSTANCE: one processor element is identified within a system, and its objectives include tracking and control of system efficiency level, a set of parameters of all elements of the system is identified, which relate to assessment of efficiency, on the basis of which they build a mathematical model for assessment of the efficiency value of the distributed multiprocessor system in the form of target functionality of the system, in process of system functioning they receive data on the functionality value, if the functionality fails to reach the specified minimum permissible threshold value, the system characteristics are changed. To change characteristics of the system, they first start the mechanism of parametric self-organisation, in process of which they tune values of parameters of the system elements within specified limits on the basis of the method of cyclic coordinate-wise descent, then, if the minimum permissible threshold value of the target functionality is not achieved by means of parameters tuning, the mechanism of functional self-organisation of the system is started, in process of which they select optimal functions for elements of the system from multiple functions implemented by elements, and then, if the minimum permissible threshold value of the target functionality is not achieved by variation of functions of elements, the system structure is changed, first selecting optimal types of elements, then reconfiguring the system, by determination of optimal location of elements in the topology without variation of their quantitative composition, and finally adding elements of optimal types to optimal location.

EFFECT: increased efficiency of a distributed multiprocessor system.

4 dwg, 1 tbl

Description

The invention relates to distributed multiprocessor systems and can be used to evaluate and increase the productivity of such systems.

By distributed multiprocessor systems we will hereinafter mean a technical system consisting of many processor elements interacting with each other via communication channels and performing certain tasks. Examples of such systems can be a multi-core server for processing and storing information, a local network, virtual networks in which information is exchanged through the global network, etc.

Evaluation of the quality of functioning is one of the most important characteristics of a distributed multiprocessor system, which allows us to draw conclusions about its performance and ability to solve its tasks. In addition, you must have methods and tools to increase the productivity of such systems.

A known method for evaluating and increasing the performance of a distributed multiprocessor system (Figure 1) is that, analyzing the functioning of the system, select several parameters related to the integrated assessment of the functioning of the system, build a mathematical model of the system in the form of a neural network with at least one hidden layer of neurons (2). Further, to obtain an estimate of the system performance, an input vector of parameter values is supplied to the input of the network (1), and at the output (3), the desired estimate is obtained in the form of a set of output parameters. In case of dissatisfaction with the assessment of the quality of the system’s functioning, the neural network adjusts the weighting coefficients (4), (5) in the layers using well-known backpropagation algorithms in order to reach the required output values. In the future, the selected optimal values of the weights are used in the real system as element parameters. The disadvantage of this method is the need for a huge preparatory work to create on the basis of a real system its model in the form of a neural network. In the case of dynamic media, where the number and connections between elements change, in some cases, the construction of a single neural model is simply impossible. In addition, this method does not analyze the functions of the system and its structure (Pub. No. US 2006/0262726 A1 United States, Int. C1. H04L 12/26. Self-changing distributed system / Lieuallen BR, Samuel GA, Norton N., Singhal SK, Manion TR - Field 04/28/2006. - Pub date 11/23/2006. - Appl. No. 11/413538. - 14 p.).

The prototype of the claimed invention is a method for evaluating and increasing the performance of a distributed multiprocessor system (Pub. No. US 7913006 B2 United States, Int. C1. G06F 13/00, G06F 9/00, G06F 15/177, G06F 1/24. Self-organizing parallel computing system / Hamaoka Y., Ishibashi K., Hayashi H. - Field 03/06/2009. - Pub date 03/22/2011. - Appl. No. 12/399, 220. - 25 p.). A functional diagram of a system implementing the method is shown in FIG. 2. The method consists in the fact that as part of the system (12) there is one processor element - the main processor element (13) - the tasks of which include monitoring and controlling the level of system performance, determine a set of parameters of all elements of the system (14, 15, 16) that have attitude to performance assessment, on the basis of which a mathematical model is built to assess the performance value of a distributed multiprocessor system in the form of the target functional of the system, in the process of functioning of the system, data on enii functional in performance calculation portion (9), in case no functional predetermined minimum threshold value, produce a change in the system characteristics. Changing the characteristics of the system is due to the launch of self-organization mechanisms, according to which all processor elements of the system PE1, PE2 ... PEP (14, 15, 16) belong to one of the types of process elements T1, T2 ... Tm. The type of element strictly defines the function performed by the element. To improve system performance, based on the method chosen by the user from the database of methods for selecting changes in the structure of the system (7), the optimal proportion of the presence of elements of the type Ti in the system is determined in the block for determining the optimal types (10). For example, if there are 6 elements in the system (n = 6) that belong to one of 3 types (m = 3), the formed proportion can be 2: 1: 0, which means that the system recommends changing the structure so that it had 4 elements of the first type, 2 - of the second and the third would be absent. The resulting optimal proportion then goes to the unit responsible for generating signals for changing the types of elements (11) and the system changes the types of some elements depending on the specific application and execution. The described actions are repeated cyclically or can be caused by various interruptions, reflecting changes in the composition of the system elements. In addition, based on one or more criteria for evaluating system performance stored in the user preferences database (6), another model for evaluating performance can be selected. In this case, the target functionality of the system is changed in accordance with the newly selected model. The disadvantages of the method are low scalability in the case of the presence of a large number of elements with a large set of different types of elements, the absence of detailed recommendations in the general case for finding the optimal proportion, and the presence in the system of only one type of self-organization - self-organization of element types - to increase its productivity.

The technical result is to increase the performance of a distributed multiprocessor system.

To obtain the indicated technical result, one processor element is allocated in the method of self-organization of a distributed multiprocessor system, the tasks of which include monitoring and controlling the level of system performance, determine the set of parameters of all system elements related to performance evaluation, on the basis of which a mathematical model is built to evaluate the performance value distributed multiprocessor system in the form of the target functional of the system, in the process of functioning with The systems receive data on the value of the functional, if the functional does not reach the specified minimum acceptable threshold value, the system characteristics are changed, to change the characteristics of the system, the parametric self-organization mechanism is initially launched, during which the parameter values of the system elements are adjusted within the specified limits based on the cyclic coordinatewise descent method, then , in case of failure to achieve the minimum acceptable threshold value of the target functional by tuning parameters, they start the mechanism of functional self-organization of the system, during which the optimal functions for the system elements are selected from the set of functions realized by the elements, and then, if the minimum acceptable threshold value of the target functional is not achieved by changing the functions of the elements, they change the structure of the system, selecting first the optimal types of elements, then reconfiguring the system by determining the optimal location of elements in the topology without changing their quantitative composition, and q, adding elements of optimal types of optimum location.

Figure 3 presents an example of a structural diagram of a distributed multiprocessor system in the form of a tree, the vertices of which correspond to processor elements, and arcs - to the connections through which control signals and data are transmitted. Elements of the lower levels correspond to elementary objects (EO) of a distributed multiprocessor system (20, 21, 22, 24, 25), which operate according to some algorithm, performing some useful function. An elementary object can be a processor in a multiprocessor system, a computer as part of a local or global network, various autonomous devices, etc. Intermediate elements (EPs) (18, 19, 23) are elements of higher levels and generalize the obtained results of the functioning of elements of lower levels according to a previously known algorithm, realizing some convolution function

µ = f (el_one, el₂, ... el_p),

where el _i is the result of the operation of the element i controlled by the current ES, p is the total number of connected lower-level elements to the current ES, f is some operator (for example, the addition operator), and the results of the calculation of the performance estimate are transmitted to the element of the higher level.

The root of the tree (17) forms the value of the target functional J for evaluating the performance of the entire system based on the information received from the elements of the first hierarchy level and, in case of unsatisfaction with the assessment, corrects the system based on self-organization mechanisms.

If it is necessary to use several criteria to evaluate system performance, then known methods are used to formulate the mathematical model of the target functional J: the main criterion method, the method of linear convolution of particular criteria into one, etc.

After a function is set in the root of the system to assess the overall performance of the system, at some points in time it is measured J _t and compared with some threshold minimum acceptable value J _min . If J _t ≥J _min , then it is believed that the system performance is at an acceptable level, no action should be taken. Otherwise, to increase the performance of the system, self-organization mechanisms are launched in the system. They start with parametric self-organization, during which an increase in productivity can be achieved by fine-tuning some parameters of the system elements. If after adjusting the parameters it is possible to achieve the fulfillment of the inequality J _t ≥J _min , it is believed that the parametric self-organization was successful, the system continues to function with the new values of the parameters. Otherwise, if it is impossible to adjust the parameters for inequality, the mechanism of functional self-organization is launched, during which an increase in system performance can be achieved by changing the functions implemented by the elements. After each change, the functions start the parameter selection mechanism. If the change in functions and parameters leads to the fulfillment of the inequality J _t ≥J _min , it is considered that the functional self-organization was successful, and the system continues to function with new implemented functions and their parameters. Otherwise, they start the mechanism of structural self-organization, during which they change the types of elements in the system, their location and quantitative composition. For each change in the structure of the system, the selection of the functions of the elements and their parameters is performed. If it is possible to achieve the fulfillment of the inequality J _t ≥J _{min by} changing the structure of the system, it is considered that structural self-organization was successful, and the system continues to function with a new structure, implemented functions and their parameters. If even in the process of structural self-organization it is not possible to achieve the fulfillment of the inequality J _t ≥J _min , they conclude that it is impossible to achieve the required performance level with this distributed multiprocessor system. If there is a block in the root of the system that accumulates the results of the conducted processes of self-organization, these results are first analyzed and make a more optimal decision about the need for a particular stage of self-organization. For example, it can be concluded that it is inadvisable to perform parametric self-organization, as a result, they immediately proceed to change the functions of the elements of the system, which speeds up the execution time of the method.

Next, each of the stages of self-organization is examined in detail to increase the performance of a distributed multiprocessor system.

At the first stage - the stage of parametric self-organization - a set of all parameters related to the calculation of system performance is initially determined. The performance of each elementary object is expressed by some function f _k depending on the selected set of parameters. The nature of the parameters can be fundamentally different. It can be any of its resources, the number of operations per unit time, the quality of data processing, etc. A function can consist of any combination of basic elementary mathematical functions (sin, cos, ln, etc.) and operations, in addition, processes in the system occur in real time, so all functions are also functions of time.

The implementation of a performance function by an element, in general, is always associated with the presence of certain restrictions imposed on its parameters. Most often, such restrictions are of the form:

a _i ≤x _i ≤b _i ,

where a _i , b _i ∈R, although more complex nonlinear constraints are possible. To eliminate these restrictions, use the operation of replacing variables, which consists in replacing variables in the original function in accordance with table 1.

Table 1 Replacing variables to remove parameter restrictions Limitation Conversion x _i > a _i x _i = a _i + exp (z _i ) x _i > x _j

$$x_i=a_i+z_i^2$$

x _i > x _j , i ≠ j x _j = z _j , $$x_i=z_j+z_i^2$$

a _i ≤x _i ≤b _i x _i = b _i + (a _i -b _i ) * sin ² z _i x _i = 0.5 * (a _i + b _i ) + 0.5 * (b _i -a _i ) * sinz _i a _i <x _i <b _i x _i = b _i + (a _i -b _i ) * (1 / π) * arctgz _i x _i = b _i + (a _i -b _i ) * exp (z _i ) / (1 + exp (z _i )) a≤x _i ≤b x _j = b + (ab) * sin ² z _j a≤x _j ≤bx _i > x _j , i ≠ j x _i = b + (ab) * sin ² z _j * sin ² z _i a <x _i <b x _j = b + (ab) * (1 / π) * arctgz _j a <x _j <bx _i > x _j , i ≠ j x _i = b + (ab) * (1 / π ² ) * arctgz _i * arctgz _i a _i (x _j ) ≤x _i ≤b _i (x _j ) x _j = z _j i ≠ j x _i = b _i (z _j ) + (a _i (z _j ) -b _i (z _j )) * sin ² z _i a _i (x _k ) ≤x _i ≤b _i (x _j ) x _j = z _j x _k = z _k i ≠ j, i ≠ k x _i = b _i (z _j ) + (a _i (z _k ) -b _i (z _j )) * sin ² z _i

The parameters of the functions f _k can be either deterministic or stochastic. In the second case, the function f _k can be represented in the form f _k = F (x, ξ), where ξ is an indefinite vector. There are two main situations that are characteristic of distributed multiprocessor systems and reflect the nature of the vector ξ:

- ξ is a random vector with a known distribution law;

- the vector ξ changes in an unknown way, but is not random, or the statistical characteristics of ξ turn out to be unknown.

If there is uncertainty of the first kind, the mathematical expectation (MO) of the random vector ξ is used. The function f _k in this case takes the form

f _k = F (x, ξ ′)

в начале работы системы выбирается и устанавливается в соответствии с экспертными оценками, а затем, в процессе функционирования, уточняется по мере накопления системой информации:Value $${\xi }_0^{\text{'}\text{'}}$$

at the beginning of the system’s work, it is selected and installed in accordance with expert estimates, and then, in the process of functioning, it is specified as the system accumulates information:

where ξ _i are the values of the vector ξ at the ith moment of data acquisition.

If there is uncertainty of the second kind, this approach in some cases is ineffective due to the impossibility of predicting the MO value of the vector ξ. In this case, the worst case scenario is applied using the so-called “guaranteed result” principle. The function f _k takes the form:

f _k = F (x, max (ξ)), or

f _k = F (x, min (ξ)).

After all the parameters are determined and the target functional for evaluating the performance is formed, the parametric optimization operation is performed. The parametric optimization operation is set as a multi-criteria parametric optimization operation with restrictions and is formulated as follows:

f _i (x) → min (x), i∈ [l: k], x∈D⊂R ⁿ ,

where D = {x∈R ⁿ | g _i (x, δ) ≤0, i∈ [l: m]; g _i (x, δ) = 0, i∈ [m + l: s]} is the set of feasible solutions; x = {x ₁ , ..., x _z } is the vector of input parameters, y = {y ₁ , ..., y _k } is the vector of criteria output parameters; δ = {δ ₁ , ..., δ _w } is the vector of external parameters characterizing the uncertainty of the situation. Within the set D, direct, functional, and criteria constraints are fulfilled, which are presented as a general system of inequalities and equalities. Direct restrictions are imposed directly on the components of the vector of input parameters; functional limitations include working conditions, which are of fundamental importance in assessing the correct functioning of the optimization object, the implementation of functional limitations with a large margin is usually not required, it is important to simply ensure their implementation; criterial constraints reflect the requirements for the characteristics of the optimization object, their main difference from functional constraints is that for criterial constraints it is necessary to achieve the fulfillment of the corresponding inequalities with a maximum margin.

The stage of parametric self-organization is carried out by one of several methods of parametric optimization, the most universal of which is the method of cyclic coordinate-wise descent (DPS). Since it is necessary to select a set of parameters x that will ensure that the condition J _t ≥J _{min is} satisfied, then at each pass of the method, this inequality is checked, and if it is satisfied, the necessary data on the changes in the parameters are saved and the operation stops. The DSP method has high reliability in relation to various malfunctioning situations, and is also simple in the process of preparing a task for modeling on a computer, because has zero order, i.e. does not require the inclusion in the computational scheme of information about derivatives of the minimized functional.

определяется как:To construct the minimizing sequence {x ^k } of the functional J (x), the transition from the vector x ⁱ to the vector x ^{i + 1} by the DSP method is carried out as follows: for m∈ [l: n] component $$x_m^{i+\mathrm{one}}$$

defined as:

First, the vector of initial steps h = (h_one, ... h_n) advancements from the point x in the direction of the coordinate unit vectors e^one, e², ..., eⁿ. Next steps h_i modify from iteration to iteration. If the inequality J (x + h_ieⁱ) <J (x), then replace the current point x with x + h_ieⁱ, and the quantity h_i Triple: h_i= 3h_i. After that, go to the next number i. If J (x + h_ieⁱ)> J (x), then multiply h_i -0.5 and also carry out the transition to the next coordinate unit. Thus, the method adapts to specific optimization conditions by changing the values and signs of steps. If the initial values of the steps were not chosen correctly, then they are quickly adjusted to the necessary values.

, где $$x_i^{\text{'}}=\left|x_i-x_i^0\right|/\min \left(x_i;x_i^0\right)$$

. При последующих запусках этапа параметрической самоорганизации изменение составляющих вектора x производят в порядке убывания значений вектора x′, который соответствует убыванию величины, показывающей, во сколько раз изменился каждый параметр после предыдущего этапа параметрической самоорганизации.To reduce the execution time of the method, the operation of comparing parameter changes can be used, in which at the end of each stage of parametric self-organization, a vector $$x\text{'}\text{'}=\left(x_{\mathrm{one}}^{\text{'}\text{'}},...,x_n^{\text{'}\text{'}}\right)$$

where $$x_i^{\text{'}\text{'}}=\left|x_i-x_i^0\right|/\min \left(x_i;x_i^0\right)$$

. At subsequent launches of the parametric self-organization stage, the components of the vector x are changed in the decreasing order of the values of the vector x ′, which corresponds to a decreasing value that shows how many times each parameter has changed after the previous parametric self-organization stage.

Next, we consider the implementation of the stage of functional self-organization. In the general case, EA can be attributed to a certain type of EA. We denote the set of all types of EO in the system S as T _s :

T _s = {T _{1, s,} T _{2, s} , ..., T _{n, s} },

where n is the number of different types of EO in the system S. Note that the type of EO determines the corresponding set of characteristic parameters and the set of realized EO functions.

EO of type i operates according to one of the predefined algorithms. The algorithm for each specific system can be defined differently and in many cases is quite complex and even “closed”. However, we are not interested in the details of the operation of the object, and we do not care about reproducing the exact model of its operation. For us, only the output function of this object is relevant, which is related to the formation of the target functional for assessing system performance. EO of type i at each instant of time implements the output function f _{k, i} ∈F _i , where F _i is the set of functions implemented by EO of type i:

F_i= {F_{1, i}, F_{2, I}, ..., F_mi},

where m is the number of different functions that an object of type i can implement.

In the general case, the effect of EO on the objective function can be expressed not by one, but by several independent functions at once:

зависит от набора параметров P, характеризующих ЭО типа i:where p is the total number of EO functions that affect the formation of the target functional of the system J (x). Every function $$f_{k,i}^j$$

depends on a set of parameters P characterizing the type I EO:

where q is the number of EA parameters of type i.

At the stage of functional self-organization, they select functions that implement system objects to achieve the desired level of performance, and not parameters. Based on the fact that it is difficult to study a complex function at an optimum with parameters that vary in an arbitrary range, the following operations are used to implement the stage.

Initially, they select the first in order function that the system sheet implements, and the optimal parameters are selected for it, i.e. start the phase of parametric self-organization. If, after completing the stage of parametric self-organization, the necessary results are not achieved, they select the next in order function that this element can implement, and for it the stage of parametric self-organization is launched. If all the functions of the element have been enumerated, and the functional of the system has not reached the desired value, they proceed to the next sheet element, and the described operations are repeated.

To speed up the implementation of the stage of functional self-organization, the operation of selecting the optimal function is used, based on the use of previous experience, in which, once having sorted all the functions of an element of this type, it is determined which one gives the maximum increase in the output function of the system. Thus, during subsequent launches of this stage of self-organization, it is known in advance which function will give the optimum for this type of object. Enumeration of all functions is carried out once for all types of objects that are in the system. Based on information about the optimal function, functional self-organization is carried out during subsequent launches in one step, choosing the found optimal function for each element.

At the stage of structural self-organization, the topology of the tree system, as well as the number of elements can change. Structural self-organization is a more powerful means of adaptation than parametric or functional, but requires much greater implementation costs.

Obviously, the addition of new facilities is associated with some financial and other costs. Therefore, at the stage of structural self-organization, some equivalent value is introduced into the system when new elements are added. As a result, each of the types of elements in the system is associated with a number, hereinafter referred to as price.

Due to the fact that intermediary elements perform the function of convolution of the results of values of children, as a rule, with an increase in the number of children, the value in the parent element also grows. Thus, we can distinguish from all intermediary elements that one adding an elementary object to which will give the maximum increase in the target functional, and add elements only to this intermediary element in the subsequent steps of self-organization. However, this will lead to unlimited growth of the descendants of this intermediary element.

Obviously, in real systems this situation is unacceptable. In this regard, the system introduces restrictions on the number of child nodes for each parent. Each type is associated with the number of slots — a non-negative integer that restricts the maximum number of child element nodes for this type. The number of slots of an elementary object is zero. It is the number of slots, and not the number of existing child nodes that characterizes the node as an intermediary element or elementary object. So, in a particular case, the intermediary element can be a sheet and have no children, but this does not become an elementary object.

Structural self-organization includes three operations: selecting the optimal types for leaf elements of the system tree (typical self-organization), reconfiguring the tree at the level of elementary objects (changing the tree topology without changing the composition of elements) and adding new elements to the system.

Initially, they start the operation of selecting the optimal types - typical self-organization. Further, if the system still does not meet the set criteria, the system is reconfigured. Finally, new elements are included in the system. If the last operation fails to achieve the desired value of the target functional, the system stops and a request is issued to change the goals of functioning.

The following is a detailed description of the three operations of the structural self-organization stage. The first is typical self-organization, during which the optimal types for the elements of the system are selected. It is the type of element that determines the set of functions that an element of the system can implement.

The selection of the optimal type for each element of the system is a exhaustive task and has a number of features. It is important to remember that the type of the element not only determines the set of functions implemented by this node, but also shows whether the given node is an elementary object or an intermediary element. So, an elementary object can only be a leaf of a tree, while an intermediary element can occupy any position (except the root), however, it can affect the target functional only if there are child nodes.

Thus, when enumerating types, it is important not to allow the situation when some intermediary element having child nodes gets the type of an elementary object, since in this case the system’s performance is impaired. On the other hand, an elementary object can change the type to the type of an intermediary element, however, obviously, in this case, the increase in the target functional of the system will be negative, since a hanging (without child nodes) intermediary element does not affect the target functional.

Based on the above limitations, typical self-organization is carried out only at the level of elementary objects. Such a restriction significantly speeds up the operation time, reducing the number of search options. An exception is an intermediary element that does not have child nodes. Such an intermediary element does not affect the system, and if it is replaced by an elementary object, it is possible to obtain some positive increase in the target functional.

In this regard, typical self-organization is understood as the process of self-organization, as a result of which the optimal type is selected for each leaf of the tree of the system.

In the course of a typical self-organization, a system tree is traversed, while for each leaf element, all possible types are enumerated. After changing the type of one object, they start first parametrically, and in case of its inefficiency - functional, self-organization. After all possible types have been enumerated, the type in which the value in this sheet is maximum in comparison with the values for other types is selected as the final type for the element.

After the optimal type is selected for one sheet element, the system is checked for compliance with the set criteria. If the system satisfies those, the stage of structural self-organization is considered successful and self-organization is completed. If the system does not meet the set criteria, go to the next element of the system. If optimal types are selected for all leaves of the tree, and the system still does not meet the set criteria, typical self-organization is considered unsuccessful.

Based on the foregoing, it can be seen that as a result of typical self-organization, it may turn out that not all sheets will be matched with the optimal type. This approach increases the speed of the operation, significantly reducing the power of many search options, but does not guarantee that the increase in the target functional obtained at the stage of typical self-organization will be as possible.

If typical self-organization has not succeeded, they proceed to launch the system reconfiguration operation, during which the location of the elements in the hierarchy is changed. Reconfiguration is carried out in several stages, at each of which one elementary object is transferred to a place more favorable from the point of view of increasing the target functional of productivity. Reconfiguration is completed if the resulting system meets the criteria or analysis of the functioning of the system shows that its further optimization is impossible.

At each stage of reconfiguration, for each type of elementary object represented by one or more elements in the system, two positions are determined: the "worst" element of this type existing in the system (its position means the parent element of this elementary object) and the "best" place for adding an element of this type to the system.

By the “worst” type element is understood such an element, when removing it from the system, the target functional is more important than when removing any other element of this type.

By “best” place is meant such an intermediary element, when adding an elementary object of a given type to which the target functional will be greater than when adding an elementary object of this type to any other intermediary element. It is important that adding an object as a child node of one or another intermediary element is possible only if the selected intermediary element has free slots.

To determine the "worst" element of each type, a tree is traversed, i.e. passing through all the elements of the tree elements. If the current tree element is an intermediary element and among its child nodes there is at least one element of the required type, any (first found) child node of this type is temporarily removed from the system. After that, the target functional of the resulting system is calculated and evaluated, and then the deleted item is returned to the system.

To determine the "best" place to add an element, a repeated traversal of the tree is performed. If the current tree element is an intermediary element and has free slots, they temporarily add to it an element of a given type with initial parameters - the first function from the list of functions of this type is used as an element function, all parameters are reset to the minimum allowable values. Next, they launch functional self-organization, which carries out the adjustment of the functions of the new system. We also note that at each step of functional self-organization, a parametric one is launched, which selects the optimal parameters for the selected functions. At the end of the work of functional self-organization, the elements of the system contain optimal functions and parameters for this structure. They calculate and evaluate the performance functional of the resulting system and delete the temporary object. After the removal of an element, the system does not return to its original state, since the functional and structural self-organization is irreversible. However, this does not matter, since only the structure of the system is important for reconfiguration, and the parameters and functions are selected again at each step in order to obtain the maximum output functional.

Thus, for each type, they find the “worst” element (and the value of the functional when removing it from the system), as well as the best position for adding an element of this type (and the corresponding value of the functional). After that, determine the type whose movement of the element will give the maximum increase in the functionality of the system. Choose the type for which the value of the expression J _b -J _w is the maximum, where J _b is the maximum value of the functional when adding an element of a given type to the system, J _w is the maximum value of the functional when removing an element of a given type from the system.

If the maximum value of the expression is non-negative, the “worst” element of the corresponding type is removed and the element of the corresponding type is added to the “best place”. If, after the reconfiguration step, the system still does not meet the set criteria, a second reconfiguration step is started, and the described steps are repeated.

The negative value of the expression J _b -J _w for all types indicates that the optimal structure has been achieved for a given set of system elements and further reconfiguration is irrational.

If the reconfiguration is unsuccessful, they perform the operation of adding system elements in order to obtain the maximum increase in the productivity functional. Note that the stage of structural self-organization is launched after parametric and functional, provided that they could not adjust the system so that it satisfies the set criteria. Then, by the beginning of the stage of structural self-organization, the functions and parameters of the elements of the system are optimal for the existing structure, i.e. each object gives a positive increase in the target functional, and when an element is removed from the system, the value of the functional decreases. Based on this, we can talk about the inexpediency of removing existing elements from the system.

The add operation is divided into several stages, at each of which one element is added. If at the end of the stage the system still does not meet the set criteria, the next stage of addition is carried out, otherwise self-organization is completed.

The most important point when adding an element to the system is determining the type of this element. In this case, the function being implemented, as well as its parameters, are not fundamental, since they will be subsequently adjusted.

Adding an elementary object to the system with subsequent functional self-organization can give a significant increase in the target functional, however, the number of free slots in the system decreases by one unit. Adding a certain number of elementary objects can lead to a situation where there are no free slots in the system. Obviously, this situation is unacceptable, since it makes the system incapable of further increasing the number of elements, and the possibilities for reconfiguring the system are limited.

On the other hand, adding an intermediary element to the system does not reduce the number of free slots in the system, but, on the contrary, increases their number by n-1 + k, where n is the number of free slots in the system before adding an element, k is the number of own slots The added mediation item. However, the addition of a hanging (i.e., having no child nodes) intermediary element does not change the target functionality of the system.

In addition to the number of slots in the system, it must be taken into account that adding an element of any type involves some economic, material and / or other costs, i.e. Each item has a price tag. In this regard, structural self-organization should provide the maximum increase in the target functionality at the lowest price. To account for this fact, the concept of utility coefficients is introduced.

The coefficient of utility for an intermediary element of a certain type is determined by the formula:

where n is the number of free slots in the system before self-organization; k is the number of own slots of the intermediary element of this type; price - the cost of adding an element of this type.

As can be seen from the formula, the utility coefficient of the intermediary element is inversely proportional to its value and directly proportional to the relative increment of the free slots of the system.

The utility coefficient for an elementary object of a certain type is determined by the formula:

where n is the number of free slots in the system before self-organization; J _old - the value of the target functional before self-organization; J _new - value of the target functional after adding the object; price - the cost of adding an element of this type.

As can be seen from the formula, the utility coefficient of an elementary object is inversely proportional to the cost of an element of a given type and is directly proportional to the relative increment of free slots of the system, and also directly proportional to the increment of the target functional of the system.

It should be noted that the value of the target functional after adding an element of a certain type depends on the position of this new element, that is, on which intermediary element it is added to. In the second expression, the new functional of the system is understood to mean the maximum possible functionality when adding an element of this type, taking into account the implementation of functional and structural self-organization.

In the process of calculating the utility coefficient for the type of elementary object, the best intermediary element is also determined, to which it should be added.

Based on the foregoing, at each of the stages an element of this type is added, the utility coefficient of which is currently the maximum.

To calculate the utility coefficient of an elementary object, a tree is traversed starting from the root. At each step of the traversal, a temporary elementary object of this type is added to the current node of the tree, in case it is an intermediary element that has free slots. As a function, the first function is selected from the list of possible functions for this type, and all parameters are reset to the minimum allowable. After that, the functional self-organization of the system is launched and the target functional of the system is recalculated and evaluated. If the value of the functional is better compared to the previous steps, its value, as well as the node to which it was added, is stored. After that, delete the added temporary element and move to the next tree node.

Thus, at the end of the tree traversal, the maximum value of the functional that is possible when adding one elementary object is obtained, and the utility coefficient is calculated. The optimal position for adding it is also determined.

Due to the fact that the intermediary element, which does not have child nodes, cannot affect the value of the target functional of the system, it is difficult to calculate the optimal position for adding it, however, since the intermediary element has some function of convolving the results of its child elements, with some approximation can be considered the best place to add it; the best place to add an elementary object. If a decision is made to add an intermediary element, it is added to the position calculated as the best for adding an elementary object with a maximum utility coefficient among elementary objects.

After adding one element, it is checked whether the resulting system meets the set criteria. If not, go to the next step and add another element. It should be noted that several elements added to the system do not necessarily constitute a single subtree, but can be added to various nodes of the original system tree.

If there is a unit in the system that is responsible for accumulating experience, based on the accumulated information, it can be concluded that it is inexpedient to conduct an operation at the stage of structural self-organization. In this case, some of the three operations may be skipped. So, for example, if it is concluded that it is inappropriate to conduct typical self-organization and reconfiguration, after the failure of functional self-organization, they immediately proceed to add new elements.

In case of failure of all types of structural self-organization, they conclude that the system cannot complete the task, the system with its resources is not able to provide the required level of performance.

This method can be implemented using a system whose functional diagram is shown in Fig. 4, where (26) is a block of parametric self-organization that implements the operations of the stage of parametric self-organization, (27) is a block of functional self-organization that implements the operations of the stage of functional self-organization, (28) - a block of structural self-organization that implements the operations of the stage of structural self-organization, (29) - a memory block that implements storing the results of the stages of self-organization for their subsequent accounting. This scheme can be implemented on the basis of hardware and software.

It can be seen that the technical result, which consists in increasing the performance of a distributed multiprocessor system, is achieved by carrying out three stages of self-organization in the system - parametric, functional and structural, with greater universality, scalability and efficiency.

Claims (1)

The method of self-organization of a distributed multiprocessor system, which consists in the fact that the system allocates one processor element, the tasks of which are to monitor and control the level of system performance, determine the set of parameters of all system elements related to performance evaluation, on the basis of which a mathematical model is constructed for estimating the performance value of a distributed multiprocessor system in the form of the target functional of the system, in the process of functioning of the system they take into account the data on the value of the functional, in case the functional does not reach the specified minimum acceptable threshold value, make a change in the characteristics of the system, characterized in that, to change the characteristics of the system, the mechanism of parametric self-organization is initially launched, during which the values of the parameters of the elements of the system are adjusted within the specified limits based on the cyclic method coordinate descent, then, in case of not achieving the minimum acceptable threshold value of the target functional path m parameter adjustment, start the system’s functional self-organization mechanism, during which the optimal functions for the system elements are selected from the set of functions realized by the elements, and then, if the minimum acceptable threshold value of the target functional is not achieved by changing the functions of the elements, they change the structure of the system, selecting first the optimal types elements, then reconfiguring the system by determining the optimal location of elements in the topology without changing their quantitative composition va, and finally adding elements of optimal types of optimum location.

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