RU2753147C1 - Method for organizing optimal fault-tolerant multidimensional tori based on low-port routers and duplex channel splitters - Google Patents

Abstract

FIELD: computer technology.

SUBSTANCE: invention relates to the field of computer technology, namely to the construction of optimal system networks of supercomputers with the topology of multidimensional toroid. The effect is achieved by the fact that a method is proposed for constructing a system network in the form of multidimensional tori with a large number of subscribers, with a low data transmission delay and with channel fault tolerance from low-port routers and duplex channel splitters with a multiplexer/demultiplexer function, while extended routers are used in the torus nodes duplex ports, composed of small port routers with duplex ports and duplex channel splitters.

EFFECT: possibility of constructing a toroid network of large dimension with the possibility of increasing the scalability of the network, the speed of the network and its channel fault tolerance.

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Description

The invention relates to the field of computing, namely, to the construction of optimal system networks of supercomputers with the topology of multidimensional tori. Optimization in the construction process is carried out according to such important functional characteristics of the network as the number of its subscribers (processors), transmission delays between them, set by the network diameter and its channel fault tolerance. The construction is carried out in the element base of low-port routers and duplex channel splitters using the topology of quasi-complete graphs as a template and preserving the routing properties of basic routers and duplex channels.

In the work “Podlazov B.C. Improving the characteristics of multidimensional tori // Control of large systems. M: IPU RAS. - 2014. - Issue 51. - S. 60-81. [Boosting Performance of Multidimensional Tores // Automation and Remote Control. - 2017. - V. 78. - No. 1. - P. 167-179] ”a method of reducing the diameter of a torus by introducing additional chordal bonds - transforming rings into multi-rings is considered. The problem of increasing the speed of the torus by reducing the measurement diameters and increasing their throughput due to their parallelization is solved. Both of these goals are achieved only by changing the topology of the ring pairs of each dimension without increasing the number of node ports used to connect to the rings. To do this, each duplex ring is replaced with a minimum switched multi-ring. However, the issues of constructing torus nodes from available low-port routers, the issues of torus scaling, and the possibility of introducing structural channel redundancy during construction to increase the fault tolerance of tori are not considered.

In the work “Simonov A.S. and others. High-speed network of the Angara. Architecture and application results // Cybersecurity issues. - 2019. - No. 4 (32). - P. 46-53 ”describes the construction of the Angara network in the form of a multidimensional torus. When creating large networks, it is important to have a multiport router in the form of an LSI, but there are currently no such routers in the Russian Federation. There is, given in the work, a functionally complete single-chip router EC8430 of the Angara network with 8 network duplex PCI-express ports and one PCI-express processor port. Initially, it was supposed to be used in a single-board version for building a system network in the form of a 4-dimensional torus on M = 4K processors and with a diameter of D = 16 hops (8 routers in rings of different dimensions). Then it was announced about the possibility of having M = 16K ÷ 32K on it with diameters D = 24 ÷ 32 hops (up to 16 routers in rings). The single-board option turned out to be not very economical for building small networks, because consumed one router to connect one processor to the network.

Then a single-frame 24-port EC8433 router was created by interlocking four 8-port EC8430 routers (all ports are duplex). The use of this router greatly simplifies the construction of networks of various sizes - from tens of processors to several thousand of them (in the topology of a 1-dimensional or 2-dimensional torus). In this form, the Angara network is considered a basic network for building domestic supercomputers. FIG. Figure 1 shows the structure of a single-case 24-port EC8433 router, assembled from single-chip 8-port EC8430 routers (the + and - indices on the port numbers indicate, in particular, the sequence of connecting the ports of the routers in the torus rings).

FIG. 2 shows the structure of the Angara network, built on 24-port EC8433 routers in the form of a two-dimensional torus (rings are formed using 4 duplex lines, grouped as in Fig. 1, 8 processors can be connected to each router of the torus).

In this case, the maximum number of network subscribers M is again achieved when 16 routers are placed in the rings. However, using more than 8 routers in a ring does not increase its throughput, but increases transmission delays over it. To increase the network throughput, 4 duplex rings were introduced in each dimension, which significantly reduces these delays. However, a 3-dimensional torus based on a 24-port switch can no longer be created in this way due to the insufficient number of ports, which makes it almost impossible to further increase the number of processors in the Angara network without increasing the number of nodes in the rings and transmission delays through them.

The method of building the "Angara" network was chosen as a prototype.

The main disadvantage of the method described in the prototype is the impossibility of further increasing the number of processors in the Angara network without increasing the number of nodes in the rings and transmission delays along them and in the absence of the possibility of reducing the diameter of the network. There is also no technique for introducing channel redundancy into the torus structure to increase fault tolerance.

The technical objective of the invention is to develop such a method for constructing a network or project management of the characteristics of a large-scale torus made of low-port routers, in which it is possible to improve its functionally important characteristics, namely, to increase the number of subscribers with constant delays, or to reduce delays by reducing the diameter of measurements with a constant number subscribers, either to increase the channel redundancy (which, it should be borne in mind, can lead to a decrease in the number of subscribers or to an increase in the number of ports of the basic routers), or to obtain network organization options that best combine the number of processors, network diameter and channel fault tolerance.

The technical result of the invention is the possibility of constructing a large-scale torus network from low-port routers and channel splitters, in which, in various variants of their joint use, it is possible to increase the scalability of the network (increase the number of processors), the speed of the network (reduce its diameter) and its channel fault tolerance.

The technical result is achieved by the fact that a method is proposed for constructing a system network in the form of multidimensional tori with a large number of subscribers, with a low data transmission delay (with a small network diameter) and with channel fault tolerance from low-port routers and duplex channel splitters with a multiplexer / demultiplexer function, characterized by the fact that the nodes of the torus use extended routers with R duplex ports, formed from N small-port routers with K duplex ports and R duplex splitters of 1 × m channels using duplex communication channels, namely,

R taps are connected to R ports numbered from 1 to R of the extended router, m opposite ports of which are connected to K ports of N low-port routers according to the corresponding N × K connection table such that Rm≤KN, the lines of which specify different low-port routers with numbers from 1 to N, and the columns are different ports of the low-port routers numbered from 1 to K, and the table cells contain the port numbers of the extended router connected through duplex splitters to the ports of the low-port routers, the numbers of which are specified by the column number,

подтаблиц, пронумерованных от 1 до t, с N строками и m столбцами в каждой подтаблице, при этом, если Rem(K/m)=0, то R=(K/m)N, если Rem(K/m)=m-σ, то

-ю подтаблицу образуют N-m портов расширенного маршрутизатора и m-σ портов малопортовых маршрутизаторов,and the join table is split into

subtables numbered from 1 to t, with N rows and m columns in each subtable, and if Rem (K / m) = 0, then R = (K / m) N, if Rem (K / m) = m -σ, then

-th subtable consists of Nm ports of an extended router and m-σ ports of low-port routers,

in this case, the 1st subtable is obtained from the table of incomplete balanced symmetric block diagram B (N, m, σ) by replacing N blocks of the block diagram with N low-port routers with m first ports, N elements of the block diagram - with N first ports of the extended router , and the elements belong to the blocks - to connect the first N ports of the extended router to the first m ports of the N low-port routers through duplex splitters of 1 × m channels, and m different ports of the extended router are connected to each low-port router, each port of the extended router is connected to m ports of different low-port routers, and each port pair of the extended router is connected to σ low-port routers, so that N = m (m-1) / σ + 1,

равен М+iN, где М - номер порта расширенного маршрутизатора в той же ячейке первой подтаблицы, при этом последнюю подтаблицу с номером

при Rem(K/m)=m-σ получают из остаточной неполной уравновешенной симметричной блок-схемы B*(N-m, m-σ, σ) аналогичной заменой N-m блоков и m-σ элементов блок-схемы соответственно на N-m последних портов расширенного маршрутизатора и m-σ последних портов малопортовых маршрутизаторов;moreover, each subsequent subtable in the order of numbering is formed from the previous one, increasing the port numbers of low-port routers by m, and the port numbers of the extended router by N, that is, the port number of the extended router in the cell of the i-th subtable

is equal to M + iN, where M is the port number of the extended router in the same cell of the first subtable, while the last subtable with the number

for Rem (K / m) = m-σ is obtained from the residual incomplete balanced symmetric block diagram B * (Nm, m-σ, σ) by a similar replacement of Nm blocks and m-σ elements of the block diagram, respectively, by Nm of the last ports of the extended router and m-σ last ports of low-port routers;

the constructed extended routers are connected into torus rings in the traditional way, that is, in each of the numbered and ordered from 1 to P _r routers of each dimension r, along with the ports for subscribers, a pair of ports are reserved (let's call them the left and right ring ports, LC and PC ports) , which are connected into rings of r-th measurements, namely, the PC port of each router is connected by a full-duplex channel to the LAN port of the next router in the corresponding ring (for the last router, the first is the next),

or to reduce the delay in data transmission (reduce the diameter) and increase the channel fault tolerance in the proposed network, instead of traditional rings, sparse multi-rings are used, formed by several rings using 2P _r duplex channel splitters 1 × m _t , as follows:

to the LAN and PC ports of _{routers numbered and ordered from 1 to P r of} each dimension, single ports of the left and right duplex channel splitters 1 × m _{t are} connected, respectively, and the m _t duplex ports of the right splitter of each router are connected to the m _t duplex ports of the left splitters of the routers with large numbers according to a certain connection table, in the first column of which the numbers of the rings forming the multiring are set from 1 to N _t , and each row lists the routers that form the ring corresponding to the row by using a duplex channel connection of one of the ports m _{t of the} right splitter of each router of the row with one from the ports m _{t of the} left splitter of the router, following in ascending order of their numbers on the line (for the last router on the line, the first is the next),

in this case, if N _t ≤P _r , then P _r ordered routers and the connection table are divided into p _r numbered from 1 to p _r groups of N _t routers and sub-tables with N _t rows and m _t columns, respectively, in each of which one sets connecting the corresponding N _t routers to N _t rings of the same group,

и при Rem(P_r/N_t)>0, последняя группа маршрутизаторов содержит сокращенное количество маршрутизаторов Rem(P_r/N_t)<N_t, а последняя подтаблица имеет сокращенное количество заполненных ячеек,moreover

and for Rem (P _r / N _t )> 0, the last group of routers contains a reduced number of routers Rem (P _r / N _t ) <N _t , and the last subtable has a reduced number of filled cells,

the first subtable is obtained from the table of the incomplete balanced symmetric block diagram B (N _t , m _t , σ _t ) by replacing the blocks of the block diagram with N _t rings of a sparse multiring, elements of the block diagram by N _t extended routers of the first group of ordered routers P _r , and the elements belong to the blocks for connecting the routers of the first group to the corresponding rings through N _t left and N _t right duplex channel splitters 1 × m _{t , and m t} different routers from the first group of routers P _{r are} connected to each ring of the multi-ring, each router are connected to m _t rings, and each pair of routers is connected to σ _t rings, so that N _t = m _t (m _t -1) / σ _t +1,

in this case, each subsequent subtable in ascending order p _{r is} formed from the previous one, increasing the number of routers by N _t , that is, the number of the router in the cell of the i-th subtable (1 <i≤p _r ) is equal to L + iN _t , where L is the number of the router in the same cell of the first subtable, in the last subtable for Rem (P _r / N _t )> 0 routers with numbers greater than P _r are excluded.

If, when building an extended router, R <N and R = Nm, K = m-σ, then the corresponding connection table is obtained from the residual incomplete balanced symmetric block diagram B * (Nm, m-σ, σ) by replacing Nm blocks and m-σ elements of the block diagram, respectively, on the R ports of the extended router and K ports of the low-port routers.

If, when obtaining the corresponding sparse multiring connection table from the table of the incomplete balanced symmetric block diagram B (N _t , m _t , σ _t ) N _t > P _r , then only the first P _r elements of the block diagram are replaced with extended routers.

The technical essence of the proposed method for organizing optimal fault-tolerant multidimensional tori is illustrated by drawings.

FIG. 1 shows the structure of a single-frame 24-port EC8433 router, assembled from single-chip 8-port EC8430 routers.

FIG. 2 shows the structure of the Angara network built on 24-port EC8433 routers in the form of a two-dimensional torus.

FIG. 3 and FIG. 4 shows, respectively, Table 1, which represents the Connection Table, and the diagram of the simplest extended SS router (7, 4, 2).

FIG. 5 and FIG. 6 shows, respectively, Table 2, which represents the Connection Table, and the diagram of the extended PascM router (14, 8, 4, 2).

FIG. 7 and FIG. 8 shows, respectively, Table 3, which represents the Connection Table, and the diagram of the extended PascM router (18, 8, 3, 1).

FIG. 9 and FIG. 10 shows, respectively, Table 4, representing the Connection Table, and the diagram of the rarefied RazMk multiring (7, 4, 2).

FIG. 11 and FIG. 12 shows, respectively, Table 5, representing the Connection Table, and the diagram of the rarefied RazMk multiring (9, 3, 2, 1).

FIG. 13 and FIG. 14 shows, respectively, Table 6, representing the Connection Table, and the diagram of the rarefied RazMk multiring (9, 7, 3, 1).

FIG. 15 shows a diagram of a one-dimensional torus based on RasM (12, 8, 2, 1) and RazMk (3, 3, 2, 1) with D = 5.

FIG. 16 fig. 17 and FIG. 18 shows, respectively, Table 7, Table 8 and Table 9 with the characteristics of tori built, respectively, from the following pairs of routers and multicircles: RasM (12, 8, 2, 1) and RazMk (P _r , 3, 2, 1), RasM (18 , 8, 3, 1) and RazMk (P _r , 7, 3, 1), RasM (14, 8, 4, 2) and RazMk (7p _r , 7, 4, 2).

FIG. 19 shows Table 10 with comparative characteristics of the "Angara" network and the network built by the proposed method.

Let us describe the proposed way of organizing a multidimensional torus.

The proposed method includes two stages: building an extended router from low-port routers and an extended sparse multiring from the simplest multi-rings and, then, building a multidimensional torus from the extended routers obtained at the first stage using extended sparse multi-rings. In practice, the construction is reduced to connecting the initial routers for the stage into routers of a larger dimension at the first stage and into multidimensional tori at the second in some optimal way while preserving their routing properties and channel redundancy according to the corresponding connection table.

These tables are obtained on the basis of such a mathematical object as an incomplete balanced symmetric block diagram B (N, m, σ) (Hall M. Combinatorics // Chapters 10-12. - World. M. - 1970. - 424 p. [Hall Marshall Combinatorial Theory // Blaisdell Publishing Company. Waltham. - 1967.]). The block diagram B (N, m, σ) contains N blocks and N elements, which are arranged in blocks so that each block contains exactly m different elements, each element is included in exactly m different blocks, and each pair of elements is included in exactly σ blocks and N = m (m-1) / σ + 1. Moreover, B (N, m, σ) specifies the maximum N for given m and σ, and vice versa, the minimum m for given N and σ. The tabular representation of the block diagram consists of N rows and m + 1 columns, the first column indicates the block numbers, and the corresponding line lists the numbers of the elements included in this block, while observing the properties that define the block diagram. Many such tables are constructed and presented in the work of M.F. Karavay, P.P. Parkhomenko, B.C. Podlazov. Combinatorial Methods for Constructing Bipartite Homogeneous Minimal Quasicomplete Graphs (Symmetric Block Diagrams) // Autom. 2009. No. 2. S. 153-170.

At the first stage, we will use the connection tables of the simplest schemes of extended SS routers (N, m, σ), which are isomorphic to the block schemes B (N, m, σ), by interpreting blocks as initial basic low-port routers, elements as ports of an extended router, and occurrences element in m different blocks as connections of the input port of the extended router with m ports of various low-port routers through splitters of duplex channels 1 × m.

The use of block diagrams for such circuit design interpretations allows us to assert that the network diagrams obtained using the described connection tables are optimal, since the block diagram B (N, m, σ) sets the maximum N for given m and σ, and vice versa, the minimum m for given N and σ.

In this interpretation, the obtained simplest extended router scheme isomorphic to B (N, m, σ) is given by a bipartite graph, one part of which contains N initial low-port routers RxM (m), the other part contains N nodes (subscribers) connected by m edges (duplex channels) with different source low-port routers. Between any users there are σ different paths of length 2 edges, and any path passes through only one ExM (m). We call this graph a quasicomplete graph, in which the subscriber has degree m due to connection to ExM (m) through a splitter of 1 × m duplex channels.

An example of a connection table and the corresponding simplest scheme of an extended router built from the original routers ExM (m) based on the block diagram B (N, m, σ) with N = 7, m = 4, and σ = 2 are shown in Figs. 3 and FIG. 4 (for meaningful clarity, the ports of the extended router and the subscribers connected to them will be identified in what follows).

In routers extended in this way, the connection between any two subscribers can be carried out through σ low-port routers with a delay of one router. If ExM (m) is an m × m non-blocking router, then the MS (N, m, σ) is an N × N non-blocking router composed of m × m routers and 1 × m duplex link taps. In this case, PacM (N, m, σ) has static self-routing, in which subscribers specify conflict-free routes independently of each other. These routes are laid between subscribers via direct channels (without intermediate packet buffering). Therefore, the SS (N, m, σ) has a diameter D = 1 and is (σ-1) -fault-tolerant across links and source routers.

подтаблиц по m столбцов. Первая подтаблица N×m (в порядке возрастания номеров портов ИсхМ(K)) получается из табличного представления ПС(N, m, σ) также как было описано выше. Она задает соединение первых N портов расширенного маршрутизатора с первыми m портами исходных N в виде простейшей схемы ПС(N, m, σ). Каждую последующую подтаблицу (включающую очередную группу m столбцов) получаем копированием предыдущей с увеличением номеров портов расширенного маршрутизатора на N, то есть, если L это номер порта в какой-то ячейке первой подтаблицы (1<L≤N), то номер порта в той же ячейке i-й подтаблицы (1≤i≤t) будет равен L+(i-1)N. Таким образом i-я подтаблица задает соединения в i-й ПС(N, m, σ) между i-й группой N портов расширенного маршрутизатора и i-й группой из Nm портов исходных маршрутизаторов. Для размножения линий с N портов i-й группы расширенного маршрутизатора также используются N разветвителей дуплексных каналов 1×m. Расширенные маршрутизаторы построенные из исходных согласно такой таблице будем обозначать PacM(R, K, m, σ), где R - число портов (абонентов) расширенного маршрутизатора, K - число портов исходных малопортовых маршрутизаторов, m и σ - параметры простейшей схемы ПС(N, m, σ) (напомним, N=m(m-1)/σ+1), тиражируемой при построении расширенного маршрутизатора. Пример таблицы соединения и соответствующей схемы расширенного маршрутизатора PacM(R, K, m, σ), построенной из исходных маршрутизаторов ИсхМ(m) на основе ПС(N, m, σ) при R=14, K=8, N=7, m=4 и σ=2 приведены соответственно на фиг. 5 и фиг. 6.There may be a situation when the source routers have K> m ports. In this case, the connection table of the extended router with the required properties is obtained from the table representation of the simplest SS scheme (N, m, σ) as follows. The table consists of N + 1 rows and K + 1 columns, the first column and the first row indicate the numbers of the source routers and their ports, respectively, and each line corresponding to the source router lists the port numbers of the extended router connected to the ports of this source router. We split the table into

subtables with m columns. The first N × m sub-table (in ascending order of the numbers of ports Ref (K)) is obtained from the table representation of the PS (N, m, σ) as described above. It defines the connection of the first N ports of the extended router with the first m ports of the original N in the form of the simplest PS scheme (N, m, σ). Each subsequent subtable (including the next group of m columns) is obtained by copying the previous one with increasing the port numbers of the extended router by N, that is, if L is the port number in some cell of the first subtable (1 <L≤N), then the port number in that the same cell of the i-th subtable (1≤i≤t) will be equal to L + (i-1) N. Thus, the i-th subtable defines the connections in the i-th SS (N, m, σ) between the i-th group of N ports of the extended router and the i-th group of Nm ports of the source routers. To multiply lines from N ports of the i-th group of the extended router, N splitters of 1 × m duplex channels are also used. Extended routers built from the original ones according to such a table will be denoted by PacM (R, K, m, σ), where R is the number of ports (subscribers) of the extended router, K is the number of ports of the original low-port routers, m and σ are the parameters of the simplest SS scheme (N , m, σ) (recall, N = m (m-1) / σ + 1), replicated when building an extended router. An example of the connection table and the corresponding scheme of the extended router PacM (R, K, m, σ), built from the original routers ExhM (m) based on the SS (N, m, σ) with R = 14, K = 8, N = 7, m = 4 and σ = 2 are shown in FIG. 5 and FIG. 6.

By construction, the connection between any two subscribers whose numbers do not coincide in modN can be carried out through the original low-port routers with a delay of one router. On the contrary, any two subscribers whose numbers coincide in mod N are connected to each other in parallel through m different initial RxM (K). These properties ensure that the routing properties of ExhM (K) are saved in RasM (R). In this case, N subsets of t subscribers are formed, with the capacity between them increased by a factor of m. Thus, if ExxM (K) has diameter D, then PacM (R, K, m, σ) has diameter D + 1.

However, dividing K by m may result in a remainder equal to m-σ, that is, K = tm + m-σ, then the (t + 1) -th subtable sets the residual simplest PS scheme * (Nm, m-σ, σ) with subscribers whose numbers are specified as tN + j (1≤j≤Nm). This (t + 1) -th subtable is obtained from the residual block diagram B * (Nm, m-σ, σ) (Hall M. Combinatorics // Chapter 10, p. 114 - Mir. M. - 1970. - 424 p. .), where Nm = (m-1) (m-σ) / σ, similarly to how the connection table for PS (N, m, σ) was obtained from the block diagram B (N, m, σ). As a result, the extended router contains either R = tN or R = tN + N-m subscribers. An example of a connection table and a diagram of an extended router for such a case when constructing PASM (18, 8, 3, 1), when K = tm + m-σ (where t = ⎣K / m⎦, that is, the integer part of dividing K by m ) are shown in Fig. 7 and in FIG. eight.

At the second stage, using the constructed extended routers, we organize multidimensional tori. This can be done in the traditional way by placing extended routers at the nodes of the torus. To include the routers in the ring r of the torus dimensions, it is necessary for each dimension to select a pair of ports in the routers, which, when traversing the ring in ascending order of node numbers, will be called the left port and the right port.

To reduce the diameter of the torus, increase the fault tolerance and increase the throughput when organizing the torus in each of its dimensions, we will use sparse multi-rings. In a sparse multiring, instead of one ring connecting the routers of the ring, several shorter rings are used that form a multiring, which in the described method of invariant extension are the initial for the multiring. The table of the connection of the simplest sparse multiring with N _t nodes (we denote it by RTMk (N _t , m _t , σ _t )), which specifies the inclusion of routers in the nodes of the original rings, as at the first stage, we obtain from the incomplete balanced block diagram B (N _t , m _t , σ _t ), in which N _t = m _t (m _t -1) / σ _t +1, interpreting it as follows: the blocks are interpreted as N _t initial for the extended sparse multiring of duplex rings of m _t numbered nodes, the elements - as N _t numbered routers of the extended sparse duplex multi-ring, and the occurrence of each element in m _t different blocks as the inclusion of the corresponding router in m _t different initial rings using a pair of duplex channel splitters 1 × m _t . In this case, the splitters (left and right) are connected respectively to the left and right ports of the router, allocated for its inclusion in the ring, the sequence of connecting the routers in the ring coincides with the sequence of their placement in the table, the last router is connected to the first. In this interpretation, σ _t is the number of original rings through which any two routers in the multi-ring can communicate. The presence in the structure of the multiring σ _{t of} parallel circuits between any nodes makes it (σ _t -1) -fail-safe along the channels. Note that the index t in the parameters of the block diagram B (N _t , m _t , σ _t ) indicates the possibility of using (when constructing sparse multi-rings for organizing a torus) block diagrams with parameters that differ from those selected at the stage of constructing extended routers.

скачков, заменяющим кольцо с N_t узлами и диаметром

The sparse multiring RazMk (N _t , m _t , σ _t ), by construction, is a ring with N _t nodes and the minimum diameter

jumps replacing a ring with N _t nodes and diameter

An example of a connection table and the corresponding scheme of a sparse multiring RazMk (N _t , m _t , σ _t ) for N _t = 7, m _t = 4 and σ _t = 2 are shown in Fig. 9 and FIG. 10. The rows of the RazMk connection table (7, 4, 2) contain the numbers of the original rings ExhK (4) and the numbers of routers connected to its nodes.

In the diagram in FIG. 10 multi-ring with 7 nodes, composed of 7 original duplex rings with 4 nodes, 14 duplex splitters 1 × m, has a diameter of D = 2 and is 1-fault tolerant in parallel rings, for example, between nodes 1 and 6 two chains on rings 1 and 3.

подтаблиц N_tm_t. Первую подтаблицу получаем для первой группы N_t маршрутизаторов первых P_r узлов, также как выше была получена таблица для простейшего разреженного мультикольца РазМк(N_t, m_t, σ_t) из неполной уравновешенной блок-схемы B(N_t, m_t, σ_t). Затем каждую следующую подтаблицу в порядке возрастания ее номера образуем из предыдущей, увеличивая номера маршрутизаторов на N_t, то есть номер маршрутизатора в ячейке i-ой подтаблицы (1<i≤p_r) равен L+(i-1)N_t, где L - номер маршрутизатора в той же ячейке первой подтаблицы. В последней подтаблице при N_t>Rem(P_r/N_t)>0 маршрутизаторы с номерами больше P_r исключаем, при этом

However, in the general case, the number of nodes P _r in the dimensions of the torus can be greater than N _t . The join table for such extended sparse multiring with P _r > N _t (which we will denote as RTMk (P _r , N _t , m _t , σ _t )) will be constructed as follows. In the first column of the table, we set the ring numbers from 1 to N _t , and in each row we list the routers that form the source ring corresponding to the row by using a duplex connection of one of the m ports of the right splitter of each router in the row with one of the m ports of the left splitter of the router that follows in in ascending order of their numbers on the line (for the last router on the line, the first is the next). Divide the table into p _r numbered from left to right from 1 to p _r

subtables N _t m _t . We obtain the first subtable for the first group N _{t of} routers of the first P _r nodes, just as above we obtained a table for the simplest sparse multiring RazMk (N _t , m _t , σ _t ) from an incomplete balanced block diagram B (N _t , m _t , σ _t ). Then each subsequent subtable in ascending order of its number is formed from the previous one, increasing the number of routers by N _t , that is, the number of the router in the cell of the i-th subtable (1 <i≤p _r ) is equal to L + (i-1) N _t , where L - router number in the same cell of the first subtable. In the last subtable, for N _t > Rem (P _r / N _t )> 0, we exclude routers with numbers greater than P _{r, while}

На фиг. 11 и фиг. 12 приведены соответственно таблица соединения и схема расширенного разреженного мультикольца РазМк(9, 3, 2, 1), построенные описанным способом из первой подтаблицы и схемы простейшего мультикольца РазМк(3, 2, 1).The diameter of such a multiring RZMk (P _r , N _t , m _t , σ _t ) is defined by construction as

FIG. 11 and FIG. 12 shows, respectively, the connection table and the diagram of the extended sparse multiring RazMk (9, 3, 2, 1), constructed in the described way from the first subtable and the diagram of the simplest multiring RazMk (3, 2, 1).

FIG. 11 clearly shows the result of the described replication of the first subtable, when the router numbers in the next subtable differ from the previous one by N = 3, and in FIG. 12 a way of combining the simplest sparse multiring RazMk (3, 2, 1) of 3 nodes corresponding to the first subtable, when the original rings of the simplest sparse multiring RazMk (3, 2, 1) of 3 nodes are broken and connected into common initial rings for 9 knots. The diameter of this multiring is D = 3.

(при N_t>Rem(P_r/N_t)>0 в последнем мультикольце маршрутизаторы с номерами больше P_r исключаются). При этом диаметр расширенного разреженного мультикольца задается как

Thus, the process of constructing an extended sparse multiring with the number of nodes P _r > N _t can be considered as a union of homogeneous original rings in p _r simplest sparse multi- _{rings with N t} nodes, where

(for N _t > Rem (P _r / N _t )> 0, routers with numbers greater than P _r are excluded in the last multi-ring). In this case, the diameter of the expanded sparse multiring is given as

An example of constructing a multiring for the case when P _{r is} not a multiple of N _t , that is, for N _t > Rem (P _r / N _t )> 0, is shown in Fig. 13 and FIG. 14. The simplest sparse multiring in this example is RazMk (7, 3, 1), the join table of which is specified in the first subtable. If we want to construct a multiring RazMk (9, 7, 3, 1) from it, then the next subtable includes connections for only 8 and 9 nodes and has a reduced number of cells.

FIG. 13, the original rings 1, 2, 3, 4 and 5 were expanded to connect nodes 8 and 9 in the same way as nodes 1 and 2 in the first simplest multiring were connected to the same rings. The diameter of the resulting multi-ring is D = 2.

Similarly, multi-rings RazMk (16, 7, 3, 1) with p _r = 3 and diameter D = 4 or RazMk (24, 7, 3, 1) with p _r = 4 and diameter D = 6 can be constructed.

The real diameter between the subscribers connected to the routers of the nodes, in addition to the diameter of the multi-ring, also includes the delays in the routers. For example, in FIG. 15 shows a one-dimensional torus based on RasM (12, 8, 2, 1) and RazMk (3, 3, 2, 1). Its diameter, taking into account 2 hops in extended routers (input port - no hop, low-port router, output port) is 5. For example, the route between subscribers 7 and 23 includes the input port, low-port router 2 and the output port of extended router 1, the source ring 3 of the sparse multi-ring, ingress port, low port router 1, and egress port of extended router 3, that is, D = 5 (routers are counted from top to bottom).

Similarly, from the same routers RasM (12, 8, 2, 1) and multicircles RazMk (P _r , 3, 2, 1), one can construct r-dimensional tori with r = 2, 3, 4. To connect routers in rings of different dimensions it is enough to disconnect from each router two subscribers for each measurement. The freed duplex ports must be used to connect to neighboring routers in the + and - directions in each dimension. The characteristics of the created tori are specified in table. 7 in FIG. 16 (M is the number of subscribers). Here

The characteristics of the created tori when using routers RasM (18, 8, 3, 1) and multicircles RazMk (P _r , 7, 3, 1) are shown in Table 8 in Fig. 17. In this torus, routes of the same length in each dimension are split along three different paths, which significantly reduces the average transmission delays.

Somewhat weaker characteristics have 1-fault-tolerant tori, which are built from routers PacM (14, 8, 4, 2) and multicircles RazMk (P _r , 7, 4, 2) in each dimension (shown, respectively, in Fig. 6 and Fig. ten). However, in this torus, routes of the same length in each dimension are split along four different paths, which further reduces average transmission delays. The characteristics of these tori are given in table. 9 in FIG. 18. The values of M for table. 9 are calculated by the formula M = P _r ^r (14-2r).

Let us compare the characteristics of the constructed multidimensional tori and tori of the Angara system network. FIG. 19 Table 10 shows the characteristics of the tori of the "Angara" network and tori composed of routers PAC (18, 8, 3, 1) and sparse multicircles RazMk (P _r , 7, 3, 1).

It can be seen that the 1-dimensional torus constructed above has a diameter 1.3-2 times smaller than the 1-dimensional torus of the Angara network with a close number of subscribers. The constructed 2-dimensional torus has a diameter 1.5-2 times smaller than the 2-dimensional torus of the Angara network with a slightly larger number of subscribers. In other cases, the constructed tori have a smaller diameter and a significantly larger number of subscribers than can be provided by the Angara network in any case.

We note two more special cases that can arise when constructing an extended router and an extended sparse multiring.

If, when building an extended router, R <N and R = Nm, K = m-σ, then the corresponding connection table is obtained from the residual incomplete balanced symmetric block diagram B * (Nm, m-σ, σ) by replacing Nm blocks and m-σ elements of the block diagram, respectively, on the R ports of the extended router and K ports of the low-port routers. If, upon obtaining the corresponding connection table of the extended sparse multiring from the table of the incomplete balanced symmetric block diagram B (N _t , m _t , σ _t ) N _t > P _r , then only the first P _r elements of the block diagram are replaced with extended routers.

We consider the multidimensional tori constructed above to be optimal, since they are based on the optimal parallelization of a network structure based on a quasicomplete graph. It allows you to build extended routers with the maximum number of subscribers given the initial routers. Conversely, it allows you to have a minimum network diameter through the use of sparse multi-rings.

Such parallelization of network structures is accompanied, of course, by an increase in its hardware and cable costs. Let's evaluate them.

Let's assume that the complexity of a router is proportional to the square of the number of ports. Then the complexity s _{K of the} single-chip Angara EC8430 router is s _K = c64, where c is the proportionality coefficient. The complexity s _{X of} one 1 × 3 splitter can be estimated as s _X = c6 (multiplexer + demultiplexer).

The complexity of the 1-one-dimensional "Angara" torus with 8 frames of EC8433 routers in the ring is set as S _{A, 1} = с2048. The complexity of the 2-one-dimensional "Angara" torus with 8 cases of EC8433 routers in the ring of each dimension is set as S _{A, 2} = c16384. They contain M _{A, 1} = 128 and M _{A, 2} = 502 subscribers, respectively. Therefore, their specific complexity is s _{A, 1} = S _{A, 1} / M _{A, 1} = 16s and s _{A, 2} = S _{A, 2} / M _{A, 2} = 32s.

Router RasM (18, 8, 3, 1) contains 7 routers EC8430 of complexity sK and 18 splitters 1 × 3 of complexity s _X. As a result, the complexity S _{P of the} extended router is S _P = 7c64 + 18c6 = 556s.

The 1-dimensional torus contains 7 such routers and 14 more splitters to form sparse multi- _{rings with a total of S P, 1} = 3976 s. It contains M _{R, 1} = 112 subscribers. Therefore, its specific complexity is s _{P, 1} = 35.5 s.

A 2-dimensional torus contains 49 such routers and 4 more splitters at each router to form sparse multi- _{rings of total S P, 2} = 28420s. It contains M _{P, 2} = 686 subscribers. Therefore, its specific complexity is s _{P, 2} = 41.4 s.

Let us introduce a complex characteristic of tori ℵ (specific with respect to the number of channels and speed) as the product of the diameter and the specific complexity. Then ℵ _{A, 1} = 128s and ℵ _{P, 1} = 177.5s, similarly ℵ _{A, 2} = 416s and ℵ _{P, 2} = 331.2s. Hence, we can conclude that the increased complexity of tori from extended routers ensures their small diameters are comparable in dimensions. At the same time, a greater number of subscribers are provided at the same time. However, sparse multi-ring routers have 7/4 times the cable consumption.

In conclusion of the description of the invention, we note that the proposed method for constructing optimal system networks with the topology of multidimensional tori in an extended circuit basis. In the proposed controlled design, optimization is carried out according to such important functional characteristics of the network as the number of its subscribers and transmission delays set by the network diameter. Optimization is carried out in the element base of low-port routers and splitters by building or using networks with a quasi-complete graph topology, which also allows at the design stage of a multidimensional torus structure to specify channel redundancy to increase fault tolerance. The method of network expansion invariant in terms of routing properties is used to increase the number of subscribers in them and reduce their diameter in a given element base, as well as introduce channel redundancy. Optimization in terms of the number of subscribers and transmission delays is accompanied by some complication of the network in terms of circuit and cable costs, the measure of which (in times) is less than the measure (in times) of improving both characteristics.

Claims (14)

1. A method of building a system network in the form of multidimensional tori with a large number of subscribers, with a low data transmission delay (with a small network diameter) and with channel fault tolerance from low-port routers and duplex channel splitters with the function of a multiplexer or demultiplexer, characterized by the fact that in the nodes of the torus use extended routers with R duplex ports, formed from N small-port routers with K duplex ports and R duplex 1 × m channel splitters using duplex communication channels, namely R taps are connected to R ports numbered from 1 to R of the extended router, m opposite ports of which are connected to K ports of N low-port routers according to the corresponding N × K connection table such that Rm≤KN, the lines of which specify different low-port routers with numbers from 1 to N, and the columns are different ports of the low-port routers numbered from 1 to K, and the table cells contain the port numbers of the extended router connected through duplex splitters to the ports of the low-port routers, the numbers of which are specified by the column number, and the join table is split into

subtables, numbered from 1 to t, with N rows and m columns in each subtable, and if Rem (K / m) = 0, then R = (K / m) N, if Rem (K / m) = m- σ, then

-th subtable consists of Nm ports of an extended router and m-σ ports of low-port routers, in this case, the 1st subtable is obtained from the table of incomplete balanced symmetric block diagram B (N, m, σ) by replacing N blocks of the block diagram with N low-port routers with m first ports, N elements of the block diagram - with N first ports of the extended router , and the elements belong to the blocks - to connect the first N ports of the extended router to the first m ports of the N low-port routers through duplex splitters of 1 × m channels, and m different ports of the extended router are connected to each low-port router, each port of the extended router is connected to m ports of different low-port routers, and each port pair of the extended router is connected to σ low-port routers, so that N = m (m-1) / σ + 1, moreover, each subsequent subtable in the order of numbering is formed from the previous one, increasing the port numbers of low-port routers by m, and the port numbers of the extended router by N, that is, the port number of the extended router in the cell of the i-th subtable

is equal to M + iN, where M is the port number of the extended router in the same cell of the first subtable, while the last subtable with the number

for Rem (K / m) = m-σ is obtained from the residual incomplete balanced symmetric block diagram B * (Nm, m-σ, σ) by a similar replacement of Nm blocks and m-σ elements of the block diagram, respectively, by Nm of the last ports of the extended router and m-σ last ports of low-port routers; the built extended routers are connected into torus rings in the traditional way, that is, in each of the numbered and ordered from 1 to P _r routers of each dimension r, along with the ports for subscribers, a pair of ports are reserved (let's call them the left and right ring ports, LC and PC ports) , which are connected into rings of r-x dimensions, namely, the PC port of each router is connected by a duplex channel to the LAN port of the next router in the corresponding ring (for the last router, the first is the next), or to reduce the delay in data transmission (reduce the diameter) and increase the channel fault tolerance in the proposed network, instead of traditional rings, sparse multi-rings are used, formed by several rings using 2P _r duplex channel splitters 1 × m _t , as follows: to the LAN and PC ports of _{routers numbered and ordered from 1 to P r of} each dimension, single ports of the left and right duplex channel splitters 1 × m _{t are} connected, respectively, and the m _t duplex ports of the right splitter of each router are connected to the m _t duplex ports of the left splitters of the routers with large numbers according to a certain connection table, in the first column of which the numbers of the rings forming the multiring are set from 1 to N _t , and each row lists the routers that form the ring corresponding to the row by using a duplex channel connection of one of the ports m _{t of the} right splitter of each router of the row with one from the ports m _{t of the} left splitter of the router, following in ascending order of their numbers on the line (for the last router on the line, the first is the next), moreover, if N _{t ≤P r} , then P _r ordered routers and the connection table are divided into p _r numbered from 1 to p _r groups of N _t routers and sub-tables with N _t rows and m _t columns, respectively, in each of which a connection is specified corresponding N _t routers in N _t rings of the same group, moreover

and for Rem (P _r / N _t )> 0, the last group of routers contains a reduced number of routers Rem (P _r / N _t ) <N _t , and the last subtable has a reduced number of filled cells, the first subtable is obtained from the table of the incomplete balanced symmetric block diagram B (N _t , m _t , σ _t ) by replacing the blocks of the block diagram with N _t rings of a sparse multiring, elements of the block diagram by N _t extended routers of the first group of ordered routers P _r , and the elements belong to the blocks for connecting the routers of the first group to the corresponding rings through N _t left and N _t right duplex channel splitters 1 × m _{t , and m t} different routers from the first group of routers P _{r are} connected to each ring of the multi-ring, each router are connected to m _t rings, and each pair of routers is connected to σ _t rings, so that N _t = m _t (m _t -1) / σ _t +1, in this case, each subsequent subtable in ascending order p _{r is} formed from the previous one, increasing the number of routers by N _t , that is, the number of the router in the cell of the i-th subtable (1 <i≤p _r ) is equal to L + iN _t , where L is the number of the router in the same cell of the first subtable, in the last subtable for Rem (P _r / N _t )> 0 routers with numbers greater than P _r are excluded. 2. The method according to claim 1, characterized in that if, when building an extended router R <N and R = Nm, K = m-σ, then the corresponding connection table is obtained from the residual incomplete balanced symmetric block diagram B * (Nm, m -σ, σ) by replacing Nm blocks and m-σ elements of the block diagram with R ports of the extended router and K ports of low-port routers, respectively. 3. The method according to claim 1, characterized in that if, when obtaining the corresponding sparse multiring connection table from the table of incomplete balanced symmetric block diagram B (N _t , m _t , σ _t ) N _t > P _r , then extended routers are replaced only the first P _r elements of the block diagram.

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