RU2703351C1 - Method of organizing a system network in the form of a non-blocking self-routable three-dimensional p-ary multi-ring - Google Patents

Abstract

FIELD: information technology.

SUBSTANCE: invention relates to design of non-blocking self-routed system networks for multiprocessor systems. Non-blocking on random permutation of packets means possibility of their parallel transmission from sources to receivers via direct channels, which increases system speed. When constructing a network, a topology of a three-dimensional p-ary multi-ring is used, which enables to build a network with a large number of nodes compared to networks in form of two-dimensional p-ary multi-rings. Three-dimensional multi-ring is represented by a composition of two non-blocking two-dimensional multi-rings with addition of the required number of redundant rings sufficient for conflict-free transfer of packets at their arbitrary permutation. Multi-ring has a seed set of (p-1)-th arcs, which are nonuniformly distributed in three of its dimensions – a single set in dimension X, a four-set in measurement Y and a double set in dimension Z. Switches of network nodes in establishing connections for transmitting packets using seven route parameters loaded by processors into packets when transmitting them, or four of them can be calculated by switches during connection establishment.

EFFECT: wider range of tools.

1 cl, 14 dwg

Description

The invention relates to the construction of non-blocking self-routing system (NSS) networks for multiprocessor systems with hundreds and thousands of processor subscribers.

Non-blocking at arbitrary packet permutation means the possibility of their parallel transmission from sources to receivers via direct channels (without buffering in intermediate nodes), which increases the system performance. Self-routing involves the possibility of laying paths locally over nodes without the latter interacting with each other. In the invention, a non-blocking system network is constructed in the form of a 3-dimensional p-ary multi-ring having dynamic local self-routing for arbitrary permutation of data packets.

In the work “Podlazov B.C. P-p-tunability and fault tolerance of dual r-egg multirings and generalized hypercubes // Automation and Telemechanics. - 2002.-№7. - S. 138 - 148 "it is shown that a p-ary multiring of any dimension r with a doubled set of internode channels is tunable for p-p-permutations (simultaneously implemented p different permutations). However, in tunable networks, conflict-free routing involves the preliminary calculation of routes for each permutation separately, that is, there is no possibility of self-routing.

These calculations require much more time than the implementation of the permutation itself. Therefore, it is important to find such a way of organizing the network that provides conflict-free data transmission using self-routing.

In the work “Karavay MF, Podlazov BC Distributed full switchboard as an“ ideal ”system network for multiprocessor computing systems // Management of large systems. - 2011. - Issue. 34. - P. 92 - 116 "it is shown that a non-blocking self-routing network of N nodes can be constructed in the form of a two-dimensional p-ary multi-ring, with N = p ² , and each node contains a switch p × p and a subscriber (processor) with p input and output ports.

However, to obtain large rings of large dimension, switches with large p are required. For example, for a network of 1,000 and 10,000 nodes, 33 and 100 I / O switches are required, respectively, and the available network switch microcircuits have 8 × 8 I / O (almost inaccessible company ones have 64 × 64 I / O).

In the patent RU 2435295 C, November 27, 2011, a method is proposed for expanding the network by constructing a non-blocking multi-ring with N _R = p ³ nodes, in which two-dimensional multi-rings with N = p ² are used as nodes. In this method, multiplexers-demultiplexers are used, and although for this multi-ring switches of smaller dimension are required, its overall complexity is greater than that of a two-dimensional multi-ring with the same number of nodes.

Considered in chapter 2.1 of the work “Karavay MF, Podlazov B.C. Distributed full switch as an “ideal” system network for multiprocessor computing systems // Management of large systems. - 2011. - Issue. 34. - S. 92 - 116 "system network in the form of a two-dimensional p-ichnoto multi-ring selected as a prototype.

The main disadvantage of the non-blocking self-routing network described in the prototype is that the number of network nodes only quadratically depends on the size of the switch from which the network is built, which limits its scope to systems with dozens of subscribers (processors). This network uses a static method for constructing non-blocking routes, which is of limited use, as it is not suitable in networks with a more complex topology where dynamically arising conflicts must be taken into account.

An object of the invention is to develop a method for organizing a non-blocking self-routing system network with a large number of nodes N = p ³ to expand its field of applicability to systems with hundreds and thousands of nodes. In the proposed method, the dynamic local self-routing procedure integrated into the network must be taken into account, which ensures the achievement of the non-blocking property.

The technical result of the invention is a method of organizing a new non-blocking self-routing system network in the form of a 3-dimensional p-ary multiring, characterized by a cubic dependence of the number of network nodes N on the dimension of the switches p (N = p ³ ).

The technical result is achieved by the fact that a new method of organizing a system network in the form of a non-blocking, self-routing three-dimensional p-ary multi-ring is proposed, characterized in that each i-th node of N = p ³ nodes, numbered from 1 to N, are connected by 3 groups of simplex transmission lines of network packets corresponding to the 3rd dimensions of the multi-ring, with m nodes, the numbers of which are calculated by the formulas i + m, i + mp, i + mp ^2, respectively, in the first, second and third dimensions, the value of m is 0, 1, 2 , ..., p-1 and sets the line number in the group (where p - atural number), with each node including a processor with 2p inputs and p outputs, as well as a switch with 5 (p-1) +1 inputs and 6 (p-1) +2 outputs connected by seven groups of lines, namely, a group lines X _O in the first dimension, groups of lines Y _I , Y _M , Y _D , Y _R in the second dimension and groups of lines Z _I , Z _M in the third dimension,

moreover, p lines of the group X _{O are} laid from p outputs of the processor of the i-th node to the inputs of p switches of the corresponding m nodes,

p lines of the group Y _{I are} laid from p outputs of the switch of the i-th node to the inputs of p processors of the corresponding m nodes,

p lines of group Z _{I are} laid from p outputs of the switch of the i-th node to the inputs of p processors of the corresponding m nodes,

p-1 lines of groups Y _M , Y _D , Y _R , Z _{M are} laid at the inputs of p-1 switches of the corresponding m nodes, the numbers of which are calculated for m = 1, 2, ..., p-1, namely,

p-1 lines of the group Y _{M are} laid from p-1 outputs of the switch of the i-th node to the inputs of p-1 switches of the corresponding m nodes,

p-1 lines of the group Y _{D are} laid from p-1 outputs of the switch of the i-th node to the inputs of p-1 switches of the corresponding m nodes,

p-1 lines of the group Y _{R are} laid from p-1 outputs of the switch of the i-th node to the inputs of p-1 of the switches of the corresponding m nodes, and in this group, when calculating the number of the next node, the values of m are set with a negative sign, that is, i-mp,

p-1 lines of the group Z _{M are} laid from p-1 outputs of the switch of the i-th node to the inputs of p-1 switches of the corresponding m nodes;

at the same time, inside each switch, full-switch communications are organized from inputs X _O to outputs Y _I , Z _I and Y _M , from inputs Y _M to outputs Z _I , from inputs Y _D to outputs Y _R and Z _M , from inputs Y _R to outputs Z _I , from inputs Z _M to outputs Y _I and direct connections from inputs X _O to outputs Y _D , and the choice of connections for transmitting network packets is established by the switch independently of other nodes, taking into account the route parameters in the packet header and the presence of conflicts on the lines groups Y _M and Y _R as follows:

the parameters of the shortest route m ₁ , m ₂ , m ₃ in the packet header generated by the processor, in the absence of conflicts, specify three stages of laying the direct path by the packet, namely, the source node transmits the packet along the line X _O (m ₁ ) to the next network node, the switch of which transmits a packet without buffering on the Y _M (m ₂ ) line to the next network node, the switch of which transmits a packet without buffering on the Z _I (m ₃ ) line to the receiving node;

if the switch detects a conflict when transmitting a packet on line Y _M (m ₂ ), then it establishes a connection for transmitting this packet on line Y _D (m ₂ ), and parameter m ₂ is taken equal to parameter m ₁ (that is, line number X _O ( m ₁ ) by which the switch receives the packet);

if the switch does not detect a conflict when transmitting a packet from input Y _D (m ₂ ) to line Y _R (m ₂ ^* ), then it establishes a connection for transmitting this packet to line Y _R (m ₂ ^* ) with number m ₂ ^* = m ₂ -m ₁ for m ₁ ≥m ₂ or to the line Y _R (m ₂ ^* ) with the number m ₂ ^* = m ₂ -m ₁ -p for m ₁ <m ₂ ,

if the switch detects a conflict when transmitting a packet from input Y _D (m ₂ ) to line Y _R (m ₂ ^* ), then it establishes a connection for transmitting this packet to line Z _M (m ₃ ^# ) with number m ₃ ^# = m ₃ -1 for m ₁ ≥m ₂ or to the line Z _M (m ₃ ^# ) with the number m ₃ ^# = m ₃ for m ₁ <m ₂ ;

if the switch receives a packet on the Y _R line (m ₂ ^* ), then it sends it to the receiving node on the Z _I (m ₃ ^* ) line with the number m ₃ ^* = m ₃ for m ₁ ≥m ₂ or on the Z _I line ( m ₃ ^* ) with the number m ₃ ^* = m ₃ +1 for m ₁ <m ₂ ;

if the switch receives the packet on the Z _M line (m ₃ ^# ), it transmits it to the receiving node on the Y _I (m ₂ ^# ) line with the number m ₂ ^# = m ₂ -m ₁ + p for m ₁ ≥m ₂ or along the line Y _I (m ₂ ^# ) with the number m ₂ ^# = m ₂ -m ₁ for m ₁ <m ₂ .

The spare line numbers m ₂ ^* , m ₃ ^* , m ₂ ^# , m ₃ ^# for packet transmission in case of conflict are calculated in the node processors and loaded into the headers of the forwarded packets along with the shortest route parameters m ₁ , m ₂ , m ₃ , while node switches establish connections using the already calculated spare line numbers received in the packet headers.

The technical nature and principle of operation of the proposed network are illustrated by drawings.

In FIG. 1 and FIG. 2 shows the structure and node of the NSS network in the form of a 2-dimensional 3-egg multiring.

In FIG. Figure 3 shows the connection table for a 2-dimensional HCC network.

In FIG. 4 and FIG. Figure 5 shows the structure and switch of the NSS network in the form of a 3-dimensional r-ary multiring.

In FIG. Figure 6 shows the connection table for a 3-dimensional HCC network.

Figure 7 shows a diagram of a node of a 3-dimensional p-ary HSS network.

In FIG. 8 and FIG. Figure 9 shows the routing graphs in a 3-dimensional p-ary HSS network with │Y _D │≥│Y _M │ and │Y _D │ <│Y _M │.

In FIG. 10 and FIG. Figure 11 shows examples of routing in a 3-dimensional 3-ary NSS network with │Y _D │≥│Y _M │ and │Y _D │ <│Y _M │.

In FIG. 12 and FIG. 13 shows examples of routing in a 3-dimensional 4-ary NSS network with │Y _D │≥│Y _M │ and │Y _D │ <│Y _M │.

In FIG. Figure 14 shows a graph of conflict frequencies based on the results of modeling a 3-dimensional p-ary HSS network.

We describe a method for organizing the proposed system network.

One of the networks that is both non-blocking and self-routing is a network with the topology of a 2-dimensional p-ary multiring (we will call it a multiring). It consists of 2 (p-1) different simplex rings with steps {1, 2, ..., p-1} making up the dimension X, and with steps {p, 2p, ..., p (p-1)} making up the dimension Y, and has N = p ² nodes. Each ring consists of identical arcs, the length of which determines the step of the ring and is given by the difference modN of the numbers of incident nodes. In FIG. Figure 1 shows a 2-dimensional 3-element multiring of 9 knots with steps {1, 2} and {3, 6}. In it, the arcs of measurements X, Y are represented by solid and dashed lines, respectively (two rings of measurement Y with steps 3 and 6 are counter rings and are shown in FIG. 1 as one bidirectional ring). A network node with the topology of a 2-dimensional p-ary multi-ring is shown in FIG. 2, it consists of the subscriber A _i (processor) and the switch p × p; the communication lines corresponding to the measurement arcs X connect the outputs of the node subscriber to the inputs of the switches of other nodes, and the communication lines corresponding to the measurement arcs Y connect the outputs of the node switch to the inputs of the subscribers of other nodes. The interconnect diagram in a 2-dimensional r-ring multiring is defined by the incident table, in which the numbers of the incident nodes are in the cells. For the multi-ring in FIG. 1 wiring diagram is given in table. 1 in FIG. 2 (hereinafter “the network with the multi-ring topology” and “multi-ring” we will use as synonyms).

Self-routing is carried out using the table of incidents according to the numbers of the subscriber-source and subscriber-receiver. Let for example these be nodes 2 and 7, respectively, underlined in Table. 1. On the right side of the table are the numbers of the switches, of which there are arcs to the receiver. In the example, these are switches 1, 4, and 7, indicated by double underscores. On the left side of the table of these switches is the switch to which there is an arc from the source. In the example, this is switch 4. On the other hand, any path of length L ₂ in a 2-dimensional multiring is a sequence of no more than two arcs, the lengths of which are set as the values of the digits in the p-ary number system L ₂ = i + jp (0≤i, j≤p-1). Here i sets the length of the arc X, aj-arc Y.

Now we will build a network in the form of a three-dimensional full p-personal multiring containing N = p ³ nodes, as a composition of two non-blocking two-dimensional multirings.

In a three-dimensional full p-egg multiring, three types of arcs with lengths {1, 2, ..., p-1}, {p, 2p, ..., p (p-1)} and {p ² , 2p ² , ..., p ² (p-1)}, respectively. Such a multiring consists of simplex rings with different steps, each of which consists of arcs of the same length. The lengths of the component arcs specify the lengths of the steps of the rings. Rings with step lengths {1, 2, ..., p-1} define the dimension X (multi-ring X), rings with lengths {p, 2p, ..., p (p-1)} define the dimension Y (multi-ring Y) and rings with p lengths ^{{2, 2} 2p, ..., p ² (p-1)} - measurement Z (multikoltso Z).

In FIG. Figure 4 shows an example of a 3-dimensional 3-egg multi-ring of 27 nodes. In it, the rings of measurement X are denoted by solid arcs, measurements of Y by dashed arcs and measurements of Z by dashed arcs.

In FIG. 5 shows the minimum commutator of a 3-dimensional multi-ring (2p-1) × (3p-1), providing data transfer from p measurement inputs X _O to p measurement outputs Y _I and p measurement outputs Z _I , forming two two-dimensional multi-rings X _O , Y _I and X _O , Z _I , the communication lines in which are defined by table 2 in FIG. 6.

Thus, the measurement pairs X _O , Y _I and X _O , Z _I are non-blocking 2-dimensional multirings in which any direct path consisting of no more than two arcs is laid through self-routing through only one switch, as was done above with using table 1. The switch supporting these transmissions is shown in FIG. 5.

For complete connectivity of the nodes of the three-dimensional multi-ring, p-1 lines of the multi-ring Y _{M are} directly connected to the switches Y with the measurement step Y in the measurement Y. Accordingly, the node switch (Fig. 5) is expanded with additional inputs and outputs Y _M , as well as intra-switch connections. Then any two nodes dimensional multikoltsa can be connected two-stage paths X _O, Y _I and X _O Z _I or a Three-Step X _O, Y _M, Z _I, consisting of arc X _O from the source to the switch, arc Y _M between switches and arc Z _I from the switch to the receiver (two-step paths in this case are a special case of three-step paths at Y _M = 0). At the same time, two-stage and three-stage routes cannot have conflicts at all, because arcs from sources and to receivers are uniquely specified during rearrangement, and in the middle of three-stage paths, arcs that are absent in two-stage paths are used.

However, in such a network, conflicts can occur on the Y _M lines.

To prevent all possible conflicts, the resulting three-dimensional multi-ring is introduced into the Y dimension in parallel with Y _M along p-1 of additional arcs Y _D and Y _R , and Y _R = -Y _M , that is, Y _R is a counter ring to the ring Y _M , and also p-1 of additional arcs Z _M between the switches in the Z dimension. The node of the obtained 3-dimensional HSS network is shown in FIG. 7. A suitably expanded switch with all its inputs and outputs as part of this node is also shown in FIG. 7, it has 5 (p-1) +1 inputs and 6 (p-1) +2 outputs (lines are marked by the lengths of the arcs corresponding to them). At the same time, inside each switch, full-switch communications are organized from inputs X _O to outputs Y _I , Z _I and Y _M , from inputs Y _M to outputs Z _I , from inputs Y _D to outputs Y _R and Z _M , from inputs Y _R to outputs Z _I , from inputs Z _M to outputs Y _I and direct connections from inputs X _O to outputs Y _D (in Fig. 7, these groups of connections are shown inside the switch by lines connecting the corresponding groups of inputs with the corresponding groups of outputs).

We show that in this way the extended three-dimensional multi-ring is a non-blocking self-routing network for arbitrary permutation of data packets.

In FIG. 8 and FIG. Figure 9 shows all the options for self-routing of any packet in conflict in a 3-dimensional p-ary NSS network, respectively, for │Y _D │≥│Y _M │ for │Y _D │ <│Y _M │. Moreover, these options do not require buffering, which proves the non-blocking nature of this network.

We will represent the traveling information by the numbers of the output arcs of the switches at each node, which should be a direct path. Arcs are numbered for each dimension in increasing order of their lengths by numbers from 0 to p-1. Number 0 specifies either an intra-node arc in the source node and in the destination node, or the absence of an arc between the switches of different nodes. Thus, arcs with a length of m ₁ measurements X are defined as numbers m ₁ (0≤m ₁ ≤р-1), arcs with a length m ₂ p of measurement Y are defined as numbers m ₂ (0≤m ₂ ≤p-1) and arcs with a length of m ₃ p ² measurements Z are defined as numbers m ₃ (0≤m ₃ ≤р-1).

To lay a direct path, the packet must contain at least three numbers m ₁ , m ₂ , m ₃ , which specify the shortest path between the source node and the destination node.

The number m ₁ defines an arc X _O (m ₁ ) of length m ₁ from the source node s to the intermediate node a (see Figs. 8 and 9). When m ₁ = 0, the nodes s and a coincide. The number m ₂ defines an arc Y _M (m ₂ ) of length m ₂ p from node a to intermediate node b. When m ₂ = 0, the nodes a and b coincide. The number m ₃ defines an arc Z ₁ (m ₃ ) of length m ₃ p ² from the switch of node b to the receiving node c. These numbers for each shortest path are calculated by each source node s in advance. The numbers m ₂ ^* and m ₃ ^* define the spare arcs Y _R (m ₂ ^* ) and Z _I (m ₃ ^* ) in case a conflict arises on the arc Y _M (m ₂ ). The numbers m ₂ ^# and m ₃ ^# define the spare arcs Y _I (m ₂ ^# ) and Z _M (m ₃ ^# ) in case a conflict arises on the arc Y _R (m ₂ ^* ). These spare arcs, along with Y _D , will be used by the switches of the network nodes to transmit packets bypassing conflicting arcs on the way to the receiving node c.

Let us consider in more detail the procedure for transmitting conflicting packets along spare arcs.

At an arbitrary permutation p-1 of node s to p-1 X _O arcs to the node and receives p-1 packets. They can follow the p-1 arcs Y _M at p-1 nodes b without conflict. And then along the corresponding p-1 arcs Z _I in p-1 nodes c (in Fig. 8 and 9, for simplicity, the transmission of one packet from node s to node c is shown). However, with certain permutations, there may be a situation in which several packets from p − 1 nodes s pretend to transmit along one arc Y _M. This situation is considered a conflict of the first type on this arc. A conflict of the first type occurs when the paths from different p-1 source nodes s passing through node a coincide on the same arc Y _M leading to node b, and then diverge along different arcs to different nodes c. Such intersections of paths, therefore, can be any number from 2 to p-1.

The resolution of the conflict for each packet of the source node s in conflict is as follows (see Figs. 8 and 9): from node a , a path to node d is laid along the arc Y _D (m ₂ = m ₁ ) of length m ₁ p where the number of the arc m ₂ is equal to the number m _{1 of} that arc X _O (m ₁ ) by which this packet arrived at node a . The further course of self-routing depends on the ratio of the lengths │Y _D │ and │Y _M │ (the module operation determines the line length), as well as on the presence of a conflict on the arc Y _R.

If │Y _D │≥│Y _M │ (i.e., m ₁ ≥m ₂ ) and there is no conflict on the arc Y _R (m ₂ ^* = m ₂ -m ₁ ), it returns from node d to node b and then to receiver node with an arc Z _I (m ₃ ^* = m ₃ ) of length m ₃ p ² . When │Y _D │ <│Y _M │ (i.e. m ₁ <m ₂₎ and there is no conflict on the arc Y _R (m ^* = m ₂ -m ₁ -p ₂₎ reduced to p ² length │Y _R (m ₂ ^* ) │ = (m ₂ -m ₁ ) solution ² is used to return from node d to node b ^* and then to the receiving node with an arc Z _I (m ₃ ^* = m ₃ +1) of length m ₃ p ² + p ² .

However, conflicts can occur on Y _R packets received on arcs Y _D , these conflicts will be called conflicts of the second kind. Then the message from the source node s, having fallen into conflict on Y _R , for │Y _D │≥│Y _M │ will be transmitted from the node d "bypassing" along the arc Z _M (m ₃ ^# = m ₃ -1) of length m ₃ p ² -p ² to node e and further along the arc Y _I (m ₂ ^# = m ₂ -m ₁ + p) of length (m ₂ -m ₁ ) p + p ² to node c. And the message from the source node s, having fallen into conflict on Y _R , with │Y _D │ <│Y _M │ will be transmitted from the node d "bypassing" along an arc Z _M (m ₃ ^# = m ₃ ) of length m ₃ p ² to node e and further along the arc Y _I (m ₂ ^# = m ₂ -m ₁ ) of length (m ₂ -m ₁ ) p to node c.

Summarize. In FIG. Figures 8 and 9 show the paths that arise during packet self-routing in the process of forwarding it from node s to c (s → c), for any node s and c as part of an arbitrary permutation of packets of all nodes.

Self-routing paths with │Y _D │≥│Y _M │.

The path in the absence of conflict is sabc: X _O (m ₁ ), Y _M (m ₂ ), Z _I (m ₃ ).

The path in the conflict on the arc Y _M (m ₂ ≤m ₁ ) - sadbc: X _O (m ₁ ), Y _D (m ₂ ), Y _R (m ₂ ^* = m ₂ -m ₁ ), Z _I (m ₃ ^* = m ₃ ).

Conflict path on arcs Y _M (m ₂ ≤m ₁ ) and Y _R (m ₂ ^* ) - sadec: X _O (m ₁ ), Y _D (m ₁ ), Z _M (m ₃ ^# = m ₃ -1 ), Y _I (m ₂ ^# = m ₂ -m ₁ + p).

Self-routing paths for │Y _D │ <│Y _M │

The path in the absence of conflict is sabc: X _O (m ₁ ), Y _M (m ₂ ), Z _I (m ₃ ).

The path in the conflict on the arc Y _M (m ₂ > m ₁ ) is sadb ^* c :): X _O (m ₁ ), Y _D (m ₁ ), Y _R (m ₂ ^* = m ₂ -m ₁ -р) , Z _I (m ₃ ^* = m ₃ +1).

The path in conflicts on the arcs Y _M (m ₂ > m ₁ ) and Y _R (m ₂ ^* ) is sadec: X _O (m ₁ ), Y _D (m ₁ ), Z _M (m ₃ ^# = m ₃ ), Y _I (m ₂ ^# = m ₂ -m ₁ ).

As you can see, the route parameters m ₂ *, m ₃ *, m ₂ ^# , m ₃ ^# are derived from the parameters of the shortest path given by the numbers m ₁ , m ₂ , m ₃ , and are calculated in two versions, depending on the relation │Y _D │ and │Y _M │ (or m ₁ and m ₂ ), that is, all possible packet transmission routes, taking into account conflicts, are determined by a set of seven parameters: m ₁ , m ₂ , m ₃ and m ₂ ^* , m ₃ ^* , m ₂ ^# , m ₃ ^# . Spare line numbers for conflict-free packet delivery can be calculated by the processor and loaded into the packet header along with the parameters m ₁ , m ₂ , m ₃ , or they can be calculated by the switch when establishing a connection if you endow it with this function.

To implement the proposed self-routing, the wormhole method is most suitable - a method in which the packet route set by its header is reserved until the packet shank passes through it. Each packet can be represented as a worm that makes its way through the network through switches. The packet, as it were, is stretched along the intermediate network nodes, sequentially occupying the channels from the sender to the receiver. If the channel is busy transmitting, then the packet arriving again is blocked and awaits its release. In this case, the transmission of this packet is suspended, but it is not lost and does not release the already occupied network channels. Packet traffic resumes after the corresponding network channel becomes free. Thus, the entire package is stored only at the time of sending at the source node and at the time of receipt at the destination node. Note that the proposed method of networking eliminates the intersection of "wormholes."

We illustrate non-blocking and self-routing using specific multirings as examples.

In FIG. 10 and 11 are examples of routing in a 3-dimensional 3-ary HSS network shown in FIG. 4, respectively, with │Y _D │≥│Y _M │ and │Y _D │ <│Y _M │ (node numbers for recording the route are taken from Fig. 4).

In FIG. Figure 10 shows the routes s ₁ → c ₂ (2 → 3 → 6 → 24) and s ₂ → c ₁ (1 → 3 → 6 → 15), conflicting on the arc 3 → 6, the first of the conflicting paths can remain on the arc 3 → 6, and the second one is “bypassed” in the case of one conflict along the route 1 → 3 → 9 → 6 → 15, if the second type gets into the conflict on the arc 9 → 6, the packet bypasses the arc 9 → 6 along the route 1 → 3 → 9 → 9 → 15.

In FIG. 11 shows two routes s ₂ → с ₂ (27 → 2 → 8 → 26) and s ₁ → c ₁ (1 → 2 → 8 → 17) conflicting on an arc 2 → 8, the first of the conflicting paths remains on an arc 2 → 8 and the second one is “bypassed” in the event of one conflict along the route 1 → 2 → 5 → 26 → 17, if the second type gets into a conflict on the arc 5 → 26, the packet bypasses the arc 5 → 26 along the route 1 → 2 → 5 → 14 → 17.

Let us consider in more detail the reasons for the occurrence of conflicts of the second type and their resolution using the example of a 3-dimensional 4-egg multiring containing 81 nodes (Figs. 12 and 13).

In FIG. 12 shows the routes s ₃ → c ₂ (79 → 1 → 9 → 41) and s ₂ ^* → s ₁ (3 → 5 → 9 → 25). The first packet conflicts with the first type on the arc Y _M with a message from node s ₁ and is bypassed using the arc Y _D and Y _R along the route 79 → 1 → 13 → 9 → 41. The second packet conflicts with the first type on the arc Y _M with the packet from node s ₁ ^* and is bypassed using the arc Y _D and Y _R along the route 3 → 5 → 13 → 9 → 25. However, these routes intersect on the arc Y _R (13 → 9), which causes a conflict of the second type. The first packet is bypassed along the route 79 → 1 → 13 → 29 → 41, thereby resolving the conflict.

In FIG. Figure 13 shows the routes s ₂ → c ₁ (80 → 1 → 13 → 29) and s ₃ ^* → c ₂ (2 → 5 → 13 → 45). The first packet conflicts with the first type on the arc Y _M with the packet from node s ₁ and is bypassed using the arc Y _D and Y _R along the route 80 → 1 → 9 → 78 → 29. The second packet conflicts with the first type on the arc Y _M with the packet from node s ₁ ^* and is bypassed using the arc Y _D and Y _R along the route 2 → 5 → 9 → 78 → 45. However, these routes intersect on the arc Y _R (9 → 78), which causes a conflict of the second type. The first packet is bypassed along the route 80 → 1 → 9 → 25 → 29, thereby resolving the conflict.

Thus, conflicts of the first type that arose at nodes a are resolved with the help of an additional multiring Y _D. Arising in different nodes a , they can have different or identical following nodes d. In the first case, they are resolved, and in the second they can lead to conflicts of the second type at nodes d; these conflicts are resolved in a different way using the additional multi-ring Z _M There are no other options for the occurrence of conflicts, which allows us to argue that the constructed 3-dimensional rye multiring with 7 (p-1) simplex rings is a non-blocking network for which a procedure of local dynamic self-routing is proposed; this multi-ring in each node has (Fig. 7) output arcs X _O from subscribers, input arcs Y _I , Z _I to subscribers and arcs Y _M , Y _D , Y _R and Z _M between the switches.

The considered procedure defines a general scheme for laying conflict-free direct paths through dynamic self-routing, which is carried out only on the basis of local information about conflicts within each node.

We present an algorithm for dynamic local self-routing when laying direct paths in a 3-dimensional r-ring multiring (route parameters m ₂ ^* , m ₃ ^* , m ₂ ^# , m ₃ ^# are calculated as described above; in a specific implementation, for example, using the method wormholes routes for all N nodes of the HCC network are laid in parallel).

1. If m ₁ = 0, then the path is laid along a local arc at node s from the source processor to the switch. Go to step 3.

If m ₁ > 0, then the path is laid from the source processor in node s along the arc X _O (m ₁ ) to the switch of node a . Go to step 2.

2. If m ₃ = 0 and m ₂ = 0, then the path is laid along the local arc in node a from the switch to the processor-receiver. The end of the algorithm.

3. If m ₂ = 0 and m ₃ ≠ 0, then the path is laid along the arc Z _I (m ₃ ) from the switch of node a to the processor in node c. The end of the algorithm.

If m ₂ ≠ 0 and m ₃ = 0, then the path is laid along the arc Y _I (m ₂ ) from the switch of node a to the processor-receiver in node c. The end of the algorithm.

If m ₃ > 0 and m ₂ > 0, then the presence of a conflict on the arc Y _M (m ₂ ) is checked.

If there is no conflict, then the path is laid along the arc Y _M (m ₂ ) from the switch of node a to the switch of node b. Go to step 4.

If there is a conflict on the arc Y _M , then the path is laid along the arc Y _D (m ₁ ) unique to the node from the switch of node a to the switch of node d. Go to step 5.

4. The path is laid along the arc Z _I (m ₃ ) from the switch of node b to the processor in the receiving node c. The end of the algorithm.

5. Conflicts the path conflict along the arc Y _R (m ₂ ^* ).

If there is no conflict, then the path is laid along the arc Y _R (m ₂ ^* ) to the switch of the node bm ₁ ≥m ₂ or node b ^* for m ₁ <m ₂ . Go to step 6.

If the conflict on the arc Y _R takes place, then go to step 7.

6. The path is laid along Z _I (m ₃ ^* ) from the switch of node b or node b ^* to the processor in the receiving node c. The end of the algorithm.

7. The path is laid along the arc Z _M (m ₃ ^# ) from the switch of node d to the switch of node e. Go to step 8.

8. The path is laid along the arc Y _I (m ₂ ^# ) from the switch of node e to the receiver in node c. The end of the algorithm.

An experimental check was made of the non-blockability of the proposed 3-dimensional p-ary multi-ring. Its simulation model was created, and it implements the algorithm of local dynamic self-routing. A frequency check of the conflict of the algorithm was carried out on arbitrary permutations of packets. The frequencies ƒ ₁ and ƒ _{2 of the} occurrence of permutations with at least one conflict of the first type and the second type (after the resolution of the first) were measured, respectively. In FIG. 14 shows their values for different values of p.

Of course, the main goal of the experiments was to measure the frequency ƒ _{3 of the} occurrence of any conflicts after resolving conflicts of the first and second types. Experiments were carried out at each p for several million (up to ten) random permutations. In all cases, the value ƒ ₃ = 0 (!) Was fixed. The latter value confirms with a high degree of certainty the non-blocking nature of the considered multi-ring. Naturally, exhaustiveness of all permutations would give full certainty. However, it is practically unrealizable at p> 5 even on supercomputers. Therefore, it was not carried out even at p <5 due to the incompleteness of the achieved result.

The application proposed a new system network structure in the form of a 3-dimensional full multirings based on 2-dimensional non-blocking multirings with a minimum number of arcs. The proposed structure provides the possibility of laying conflict-free paths through their local dynamic self-routing in the nodes of the multi-ring. This allows data packets to be transmitted along direct paths without delay for their buffering in intermediate nodes. The constructed multi-ring has a seven-dimensional set of (p-1) -th arcs that are unevenly distributed over its dimensions — a single set in the dimension X, a quadruple set in the dimension Y, and a double set in the dimension Z.

Compare the complexity of the 2-dimensional and the new 3-dimensional multirings with the same number of nodes N ₂ = N ₃ . Since N ₂ = p ₂ ² and N ₃ = p ₃ ^3, then p ₂ = p ₃ ^3/2 . The complexity S _{2 of a} 2-dimensional multiring is defined as S ₂ = N ₂ p ₂ ² = p ₂ ⁴ = p ₃ ⁶ . The complexity S _{3 of a} 3-dimensional multi-ring is set (the complexity of the intra-node switchboard s = 8р ₃ ² ) as S ₃ = 8N ₃ p ₃ ² = 8р ₃ ⁵ . Therefore, S ₂ > S ₃ for p ₃ > 8. Thus, with the same number of nodes, the transition from a 2-dimensional to a 3-dimensional multi-ring not only increases the number of nodes for any p, but also reduces the comparative complexity of the latter for p> 8.

Claims (17)

1. A method of organizing a system network in the form of a non-blocking, self-routing three-dimensional p-ary multi-ring, characterized in that each i-th node of N = p ³ nodes, numbered from 1 to N, is connected by 3 groups of simplex transmission lines of network packets corresponding to To the 3rd dimensions of the multi-ring, with m nodes, the numbers of which are calculated by the formulas i + m, i + mp, i + mp ^2, respectively, in the first, second and third dimensions, the value of m is 0, 1, 2, ..., p-1 and sets the line number in the group (where p is a natural number), with each node turning on the processor with 2p inputs and p outputs, as well as a switch with 5 (p-1) +1 inputs and 6 (p-1) +2 outputs connected by seven groups of lines, namely a group of lines X _O in the first dimension, group of lines Y _I , Y _M , Y _D , Y _R in the second dimension and groups of lines Z _I , Z _M in the third dimension, moreover, p lines of the group X _{O are} laid from p outputs of the processor of the i-th node to the inputs of p switches of the corresponding m nodes, p lines of the group Y _{I are} laid from p outputs of the switch of the i-th node to the inputs of p processors of the corresponding m nodes, p lines of group Z _{I are} laid from p outputs of the switch of the i-th node to the inputs of p processors of the corresponding m nodes, p-1 lines of groups Y _M , Y _D , Y _R , Z _{M are} laid at the inputs of p-1 switches of the corresponding m nodes, the numbers of which are calculated for m = 1, 2, ..., p-1, namely, p-1 lines of the group Y _{M are} laid from p-1 outputs of the switch of the i-th node to the inputs of p-1 switches of the corresponding m nodes, p-1 lines of the group Y _{D are} laid from p-1 outputs of the switch of the i-th node to the inputs of p-1 switches of the corresponding m nodes, p-1 lines of the group Y _{R are} laid from p-1 outputs of the switch of the i-th node to the inputs of p-1 of the switches of the corresponding m nodes, and in this group, when calculating the number of the next node, the values of m are set with a negative sign, that is, i-mp, p-1 lines of the group Z _{M are} laid from p-1 outputs of the switch of the i-th node to the inputs of p-1 switches of the corresponding m nodes; at the same time, inside each switch, full-switch communications are organized from inputs X _O to outputs Y _I , Z _I and Y _M , from inputs Y _M to outputs Z _I , from inputs Y _D to outputs Y _R and Z _M , from inputs Y _R to outputs Z _I , from inputs Z _M to outputs Y _I and direct connections from inputs X _O to outputs Y _D , and the choice of connections for transmitting network packets is established by the switch independently of other nodes, taking into account the route parameters in the packet header and the presence of conflicts on group lines Y _M and Y _R as follows: the parameters of the shortest route m ₁ , m ₂ , m ₃ in the packet header generated by the processor, in the absence of conflicts, specify three stages of laying the direct path by the packet, namely, the source node transmits the packet along the line X _O (m ₁ ) to the next network node, the switch of which transmits a packet without buffering on the Y _M (m ₂ ) line to the next network node, the switch of which transmits a packet without buffering on the Z _I (m ₃ ) line to the receiving node; if the switch detects a conflict when transmitting a packet on line Y _M (m ₂ ), then it establishes a connection for transmitting this packet on line Y _D (m ₂ ), and parameter m ₂ is taken equal to parameter m ₁ (that is, line number X _O ( m ₁ ) by which the switch receives the packet); if the switch does not detect a conflict when transmitting a packet from input Y _D (m ₂ ) to line Y _R (m ₂ ^* ), then it establishes a connection for transmitting this packet to line Y _R (m ₂ ^* ) with number m ₂ ^* = m ₂ -m ₁ for m ₁ ≥m ₂ or to the line Y _R (m ₂ ^* ) with the number m ₂ ^* = m ₂ -m ₁ -p for m ₁ <m ₂ ; if the switch detects a conflict when transmitting a packet from input Y _D (m ₂ ) to line Y _R (m ₂ ^* ), then it establishes a connection for transmitting this packet to line Z _M (m ₃ ^# ) with number m ₃ ^# = m ₃ -1 for m ₁ ≥m ₂ or to the line Z _M (m ₃ ^# ) with the number m ₃ ^# = m ₃ for m ₁ <m ₂ ; if the switch receives a packet on the Y _R line (m ₂ ^* ), then it sends it to the receiving node on the Z _I (m ₃ ^* ) line with the number m ₃ ^* = m ₃ for m ₁ ≥m ₂ or on the Z _I line ( m ₃ ^* ) with the number m ₃ ^* = m ₃ +1 for m ₁ <m ₂ ; if the switch receives the packet on the Z _M line (m ₃ ^# ), it transmits it to the receiving node on the Y _I (m ₂ ^# ) line with the number m ₂ ^# = m ₂ -m ₁ + p for m ₁ ≥m ₂ or along the line Y _I (m ₂ ^# ) with the number m ₂ ^# = m ₂ -m ₁ for m ₁ <m ₂ . 2. The method according to claim 1, characterized in that the spare line numbers m ₂ ^* , m ₃ ^* , m ₂ ^# , m ₃ ^# for transmission of a packet in case of conflict are calculated in the node processors and loaded into the headers of the forwarded packets along with the shortest parameters route m ₁ , m ₂ , m ₃ , while the node switches establish connections using the already calculated spare line numbers received in the packet headers.

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