Introduction

Another important feature of modern processing systems is the variety of offered services. Nowadays, in the same network they are different, often incompatible with communication services (eg. Isochronous and synchronous transfer). This issue requires a change of quality of provided services, through the dynamic allocation of independent communication channels to users or services present in the network specifically in particular, this applies to multimedia services rendered in real-time or services comprising critical infrastructure. Modern distributed systems are also characterized by high dynamics of changes in operating parameters. Load elements of computing and communications is changing rapidly, which prevents the design and execution of the network to meet even medium-term requirements of the users. Another disadvantage occurring in communication subsystems ubiquity of traffic is bursty traffic, obstructing, and sometimes preventing proper functioning of the network. Currently, the solution to the above problems is the use of load leveling, both communications and computing. Moreover, an effective solution to most of these problems can be also providing a flexible reconfiguration of connections, preferably at the logical level, without having to modify the hardware architecture. In this way, links can be dynamically adapted to the current traffic pattern.

Effective methods of reconfiguring connections should be seen in the use of modern communication technologies, especially those that allow to realize it at the logical level and which additionally improve the utilization of physical communication channels. An interesting issue is the construction of multi-channel network of bus-sharing bus logic dynamic range conversion of a set of buses to which the user is attached. Because of that it becomes possible to adapt to the existing network architecture in the traffic patterns. However, the use of such architecture requires solving a specific design task, which for obvious reasons should be characterized by an acceptable time complexity and memory. Because of the combinatorial nature of the task it is difficult to meet.

These issue may include the design task to build large class of system configuration tasks. This task is mostly decomposed into three basic subtasks: a. The selection of system components; b. their deployment; c. determining the connection between them. In previous work, component selection subtask is solved inter alia by implemented using for this purpose methods seeking the shortest path [1], [2] Backpack block [2], [3] the clustering multipartite graph [4], mullioned clique [5], morphological analysis. Subsequently, a solution subtasks arrangement of the components, currently is the most frequently used variants task assignment [2], [6], [7], [8]. To determine the connections between system components there is the most commonly used a method of agglomeration [9], [10] and the method solving the task of building the optimal hierarchy [11].

Architecture Connections and System Reliability Model

The Fig. 1 shows a distributed system consisting of K N node calculation -decoration, each of which has a K l retunes elements of the transceiver and the K B communication buses. Buses B i (i = 1, . . . , K B ) are logical and can be implemented on the basis of methods of reproduction of wave-go in one physical bus D F . The addition of logical channels to any node N i physical bus B F is done by using a physical connection channels l and distributors of bus channels C. to another logical bus. The system can operate in two modes: a. redundancy communication subsystem; b. the communication load sharing. To evaluate the operating characteristics of the system in one of these modes, the probabilistic model suggested combinatorial, and in particular evaluating the reliability R. In this model, the kit: the transceiver -receiving (≈), the physical connection cable (l), and a manifold physical channel (C) are treated as a single device connection. Let p io -the probability of performance transceiver -the receiving node computational p l -probability of physical fitness connecting channel; p c -the probability of the distributor channel efficiency Trunk, the p f k -probability of physical fitness BUS channel. Then, the probability of p ku efficiency of connecting the node to the logical channel BUS is defined as: p ku = p io p l p c and p uku probability of the merger selected node with other nodes calculation is equal to p uku = p io p l p c p f k .

Trunk consider the reliability of a distributed system with connections complete (each compute node is connected to each bus logic) and equal rights computational nodes, which is the most general example of this class of systems. The probability p we (k we ) efficiency connection sets providing connection to the bus channel not less than k min we compute nodes with their total number K N determined by the expression:

p we (k we ) = p f k K N i=k min we C i k p i ku (1 − p ku ) kwe−i(1)

Let K B to be the amount of bus logic (ie. The maximum multiplicity system interface), p sp we -likely performance computing node. Then, using expression (1), according to the proposed condition for the system in redundancy, reliability R is defined by the following formula:

R = K N j=k min we C j K N (p sp we ) j (1 − p sp we ) K N −j K B k=1 C k K B p we (j) k (1 − p we (j)) K B −k (2)

Consider the current system of equal rights computational nodes working in load sharing mode of communication. Let W (k we , k m , σ) to be the amount of system efficiency states consisting of k we compute nodes, connected with k m canals system, which can be selected with the existence of σ denials transceiver components. In order to determine the amount of W (k we , k m , σ) state performance of the system in the event of damage, etc., it is proposed to use the methods of include -exemption. H 1 (σ) number of states malfunction of the entire system in case of refusal not less than one minimum section for a system with equal rights nodes is equal to:

H 1 (σ) = K N C σ−K B (K N −1)K B + C 2 K N C σ−K B (K N −1)K B K B−1 α=1 C α K B = C σ−K B (K N e −1)K B K N + C 2 K N K B −1 α=1 C α K B(3)

Then, the value of W is equal to

W (k we , k m , σ) = C σ kwekm + iσ i=1 (−1) i H i (σ),

where: C σ kwekm -total number of states σ denials system for transmitting elementsreceiving; i σ -the maximum number taken into account when assessing the minimum cross sections; H i (σ) -the number of states of a computing system failure, refusal to transmit elements -receiving no less than the minimum i sections. The probability P ku (k we , k m , σ), k wu ensures consistency nodes by k m bus for refusals σ is defined by the expression:

P ku (k we , k m , σ) = W (k we , k m , σ) p kwekm−σ ku (1 − p ku ) σ (4)

Using the expression (4), the likelihood of P ku (k we , k m ) ensures the consistency of computing nodes k we , k m buses, with denials of the existence of σ can be written as:

P ku (k we , k m ) = (kwe−1)km σ=0 P ku (k we , k m , σ)(5)

Using the expression ( 5), it will determine the likelihood of consistency P uku (k we ), k we compute nodes:

P uku (k we ) = K B l=k min m C l K B p l f k (1 − p f k ) K B −l P ku (k we , l),

where: k min m -the minimum required number of buses needed to provide the required bandwidth. In this way, the reliability of calculation system is equal to:

R = K N n=k min we C n K N (p sp we ) n (1 − p sp we ) K N −n P uku (n)(6)

For computing system client-server mode redundancy it will determine the likelihood of P ks (K K , K S ) efficiency BUS communication channel to which, through the operational elements transmitter -receiver including no less than k min k customers with their total number of K K and k min s servers with the total number of K S :

P ks (K K , K S ) = p f k K K i=k min k K S j=k min s C i K K p i ku (1 − p ku ) K K −i • C j K S p j ku (1 − p ku ) K S −j(7)

Let p sp k and p sp s be the likelihood of efficiency for clients and servers nodes, respectively. Then, using the expression (7), reliability Rcan be written as:

R = K K m=k min k C m K K (p sp k ) m (1 − p sp k ) K K −m • K S n=k min s C n K K (p sp s ) n (1 − p sp s ) K S −n • Km l=1 C l Km (P ks (K K , K S )) l (1 − P ks (K K , K S )) Km−l .(8)

Let's consider the reliability of client-server system with a complete blend of computing and communication subsystem working in load sharing mode. Let W (k s , k k , k m , σ)to be the number of states efficient system consisting of servers k s , k k clients, k m bus, in the presence of σ denials transceiver components. For the clientserver system, the number of failure conditions the H 1 (σ) no less than a minimum cross section can be determined using the expression:

H 1 (σ) = (k k + k s ) C σ−km km(k k +ks−1) + k k k s C σ−km km(k k +ks−1) = = C σ−km km(k k +ks−1) k k + k s + k k k s km−1 α=1 C α km ,(9)

a number of states proper functioning as:

W (k k , k s , k m , σ) = C σ km(k k +ks) + iσ i=1 (−1) i H i (σ) ,(10)

Where: C σ km(k k +ks) -the total number of computing system states that may occur at σ refusals. The probability P ks (k s , k k , k m , σ) ensures consistency k s servers and k k clients using k m bus in case of refusal elements σtransmitter -receiver can be written as:

P ku (k s , k k , k m , σ) = W (k s , k k , k m , σ) p (ks+k k )km−σ ku (1 − p ku ) σ . (11)

The probability of P ku (k s , k k , k m ) servers to ensure coherence k s and k k clients using k m bus in the event of a refusal elements transmitter -receiver has been defined as:

P ku (k s , k k , k m ) = (ks+k k )km s=0 P ku (k s , k k , k m , σ) ,(12)

and the probability P ku (k s , k m ) of consistency k s servers and k k clients as:

P ku (k s , k k ) = Km km=1 C k Km p km f k (1 − p f k ) Km−km P ku (k s , k k , k m ) . (13)

Using the expression (11), (12), and (13) the sought reliability R will be written as:

R = K k k=k min k C k K k (p sp k ) k (1 − p sp k ) K k −k • Ks s=k min s C s Ks (p sp s ) s (1 − p sp s ) Ks−s P ku (s, k)(14)

The above-described methodology we will use for further connections to network design measuring system.

Task Design and Its Solution

We will consider hypergraph H = (V, E) comprising a set V = {v} of vertices and a set of E = {e} of edges, which represent a subset of the set V, i.e. e ⊆ V . Hypergraph H is a k-regular if each of its edge e ∈ E consists of k vertices. On the other hand, hypergraph H is l-partite graph, if the set of its vertices is divided into l subsetsV 1 , V 2 , . . . , V l , in such a manner that the vertices of each of the edges e = (v 1 , v 2 , . . . , v l ) ∈ E belong to different parts of the graph, ie. v i ∈ V i , where i = 1, . . . , l. For the determination of l-partite hypergraphs we will use record form

H = (V 1 , V 2 , . . . , V l ).

Let's consider the l-partite hypergraph H = (V 1 , V 2 , . . . , V l ). In this graph, the part a = V A 1 , . . . , V A i , . . . , V A l , E A , for i = 1, . . . , l and V A l ⊆ V l , where any two edges e 1 , e 2 ∈ E A overlap in one and the same vertex v ∈ V A 1 and do not overlap at any vertex v ∈ V A l , will be called star. This means that the cardinality of V A 1 is 1, and the vertex v ∈ V A 1 , will be called the center of the star. We distinguish the simple and complex stars. If any pair of edges e 1 , e 2 ∈ E A covers only in one vertex v ∈ V A 1 , then the star is called simple. Otherwise, a star will be called complex. The number of edges of the star will be called degree. For the edge e = (v 1 , v 2 , . . . , v l ) ∈ E of the star verticesv 1 and v l we will call end. In turn, the vertices v 2 , . . . , v l−1 will be determined as internal. Vertices set of the part of graph V 2 , . . . , V l−1 are composed of empty pairs of disjoint sets V i (v j ), v j ∈ V j , where: i = 2, . . . , l − 1, j = i + 1.

For hypergraph H = (V, E) its subhypergraph H 1 = (W, U ) we'll be called hypergraph for which set of the vertices W is the vertices subset V of hypergraph H, ie. W ⊆ V and the edge set U is the edges subset E of the hypergraph H, wherein if the (x, y) ∈ E and x, y ∈ W , then (x, y) ∈ U . Hypergraph cohesion component will be called the set of its vertices, such as any of two of its elements there is a path between them, but there is no path leading from the vertex of belonging to this collection to any other vertex outside. If there is in the subhypergraph

H 1 = (V 1 , E 1 )

of hypergraph H consistency of each component there is a star with center at some vertex v ∈ V 1 , the H 1 we will call the coverage of hypergraph H stars.

Fixed design task was to find such a connection structure that will ensure the maximization or minimization of operating parameters, such as communication delay, errors in access to the communication medium as a result of his occupation, performance computational processing nodes and others. Such a task can be solved by seeking the cover at least the stars of trigeminal graph. Let's consider the task.

Input data. As an input data we use the design task:

1. B = {b} -A set of logical communication bus dedicated by physical channel under communication using any of the methods of reproduction communication; 2. F = {f } -A set of access protocols, which describes the functioning logical BUS communication [12]; 3. N = {n} -A set of customers of the system, using BUS communication channels. The definition of design task. Each of the compute nodes n ∈ N should be assigned a set of M bus b, which is a subset of B, ie. M ⊆ B, each of which will operate on the basis of one of the access protocols f ∈ F .

The mathematical model. The task design is iteratively solved. In each of the steps and for each of the compute nodes there is sought one bus b ∈ B providing for node communication services using Access Protocol f ∈ F . To avoid multiple of includes a node on the same bus at each successive step from the available buses the client is excluded from those for whom it has already been connected.

The mathematical model is based on the 3-partite hypergraph H = (V, E) = (X, Y, Z, E). Busses from the set B = {b} correspond to the vertices of the first part x (x ∈ X). Each of them (at the same time each logical bus) is assigned to the label η (x) determining the transmission characteristics of the bus, in the simplest case, the number of nodes measured, that it can handle.

The f elements of the set F bus access protocols correspond to the vertices y of the second part of hypergraph H (y ∈ Y ), and the elements n from N compute nodes correspond to the vertices zof the third part of hypergraph (z ∈ Z).The set of edges E = {e} includes all three vertices (x, y, z)such that x ∈ X_, y ∈ Y , z ∈ Z. There are permitted only those edges, for which a selected bus the client can handle b i ∈ X using a communication protocol f l ∈ Y 2 . Collection E = {e} of all edges is determined essentially by a set of all admissible triples e = (x, y, z). Taking account of the value of the parameter n (x) for x ∈ Xin hypergraph H = (V, E) = (X, Y, Z, E) permissible step design task solution will be any of his sub hypergraph β = (V β , E β ) forV β ⊆ V and E β ⊆ Eof which each component represents the simple consistency star of stage with the center in the apex x ∈ X. As S = S (H) = {s}we denote the set of all feasible solutions of tasks covering hypergraph H stars.

Each of edges e ∈ E of hypergraph H = (V, E) there is assigned three scales describing the following characteristics solutions:

1. ω (e) = φ (x, y, z) -Expected customer conversion processing performance in a system in which the client is supported in communication with the bus X, which uses a communication protocol y. To evaluate the performance characteristics of the proposed process there were used in [13], [14], [15]. Described measures therein are modified so that they reflect the change in performance which are due to changes in the architecture of calls. Because of the nature of the bus network connecting the primary measure of performance is the number of nodes, for which there is available transportation network [16]. 2. ξ (e) = φ (x, y, z) -Expected change in the communication delay on demand of the customer for these conditions. The level of changes in the delay is determined on the basis of the stochastic model using the method described in [17]. 3. ψ (e) = φ (x, y, z) -Expected change in system reliability for client-server preserved the conditions of point. 1. To determine the reliability of the method was applied changes presented in §2.

Solution design task. The rating of the solutions will be shown as a multi-criteria. The proposed set of criteria is obviously exemplary, and his selection depends on the needs of the designer, in particular concerning the nature of the future operation of the network merger. For the case of under consideration there are the three functions described below.

Let's consider the set A = {a} of acceptable solutions of design task. For each of them we define the following characteristics assessing the quality of solutions: The possibilities of the above method is not limited to the application of the summation as a min or max. To assess the quality of solutions it can be used any of the method of folding (convolution) parameters, including methods taking the weight of each sub-parameters into account. These sub-criteria are related by a function to form Φ (a) = (Φ 1 (a) , Φ 2 (a) , Φ 3 (a)). Multi-criteria objective function Φ (a)defines a set A feasible solutions, a set of Pareto A p composed of Pareto optima a p . If two solutions a 1 , a 2 ∈ A vector objective function Φ (a) are equivalent, then the set of A p is secreted full set of alternatives A A , which is, in fact, a maximum system vectorially different optima Pareto.

The Research, Results and Further Work

The work approach used to create a multi-channel design methodology destined for fieldbus communication service systems, client-server computing. The existing methodology is focused on providing definite level of computing capacity of the entire system, regardless of its reliability parameters. In the presented in the work version, methodology seeks the optimal solution with respect to multi-criteria objective function that one of the criteria is reliability. Depending on how sub-criteria ties and a set of restrictions proposed methodology also allows you to specify the connection architecture, characterized by: a. maximum reliability with certain: the minimum efficiency and maximum delay network communication links; b. the minimum communication delay with the reduction in the minimum reliability and performance; c. maximum computing performance of a specified acceptable level of reliability and delays. There was also tested solution, the aim of which was to design load leveling various communication buses. For each of the solutions sought there are limited the maximum cost of construction. We analyzed the network of connections complete and partial, flat and hierarchical.

Simulation studies of obtained architectures for computing model client-server based on the methodology presented in [16] showed that the use of multi-channel communication systems can flexibly adapt to the current needs of the computing system. Increasing performance computing system with unchanging resources, obtained by reconfiguring its connections reached 260%. Deviations in terms of the burden of communication channels does not exceed 31% and the probability of rejecting a service request has fallen nearly 8-fold. The algorithm of the interconnection network is characterized by polynomial time complexity, which can react in real time to any change in traffic patterns.

Further research will focus on finding effective methods of searching for coverage of celebrities simple multipartite hypergraph, which will allow the use of graphs in the design process of any of valor, and this will introduce further design criteria.