# Patent

## Title
Multi-dimensional lattice network

## Abstract

An N-dimensional lattice network that scales to capacities of the order of a Yotta bits per second (1024 bits per second) includes a plurality of sub-nets of edge module switches interconnected by an agile switching core. The agile core may be distributed. In the N-dimensional lattice network, each edge module 408 is connected to N core stages, each core stage having an associated dimensional indicator. The input/output ports of each edge module are divided into (N+1) port groups. One of the port groups serves local sources/sinks while the remainder of the port groups are respectively connected to core stages in each of the N dimensions. This structure permits virtually unlimited capacity growth and significantly simplifies the routing and forwarding functions. The edge modules are addressed using logical coordinates, one coordinate being assigned for each of the N dimensions. This simplifies routing and permits each edge module to compute its own routing tables.

## Background
CROSS-REFERENCE TO RELATED APPLICATIONS
This is the first application filed for the present invention.
MICROFICHE APPENDIX
Not Applicable.
TECHNICAL FIELD
This invention relates generally to the field of the design and control of data networks. In particular, it is related to the architectural design and routing control in a very high-capacity data network adapted to provide service to a large geographical area.
BACKGROUND OF THE INVENTION
The architectural design of high-capacity data networks that provide quality of service is a challenging task that has inspired a great deal of inventive ingenuity. Network architectures which enable the construction of networks that scale to hundreds of Tera bits per second have been described in patent applications filed by the Applicant. For example, in U.S. patent application Ser. No. 09/286,431, filed on Apr. 6th, 1999 and entitled SELF-CONFIGURING DISTRIBUTED SWITCH, a network architecture is described in which a plurality of high-capacity electronic edge modules are interconnected by an agile wavelength-switching optical core. U.S. patent application Ser. No. 09/475,139, filed on Dec. 30, 1999 and entitled AGILE OPTICAL-CORE DISTRIBUTED PACKET SWITCH, describes an architecture for an optical-core network in which the optical switching latency is masked. In U.S. patent application Ser. No. 09/550,489, filed Apr. 17, 2000 and entitled HIGH CAPACITY WDM-TDM PACKET SWITCH, a network architecture is described in which a plurality of electronic edge modules are interconnected by electronic space switches which are operated in a time division multiplexed (TDM) mode. The use of TDM permits a channel (typically a wavelength in a WDM transport medium) to be split into several subchannels. This increases the number of edge modules that can be directly reached without a requirement for tandem switching.
Network architectures in Applicants' copending patent applications enable the construction of a network having edge control to satisfy quality-of-service requirements. Those networks can scale to about 1 Peta bits per second, i.e., 1015 bits per second. The number of edge modules in those networks is generally limited to about 1,000.
With the rapid growth of Internet traffic, and the potential for innovative applications that may require capacities that are orders of magnitude higher than current capacity requirements, a new approach to network design appears to be necessary. Backbone networks to support the potential expansion of the Internet require architectures adapted to support much wider coverage and higher capacity than the networks described to date. A global Internet can potentially include millions of edge modules with a combined user access capacity that approaches a Yotta bits per second (1024 bits per second). One well-known method for constructing networks of that magnitude is to use a hierarchical structure where traffic streams from source nodes are aggregated into larger streams that are switched at coarse granularities in higher levels of the hierarchy.
The control complexity of hierarchical networks prompts a search for a different architecture. A multi-dimensional structure appears to be a promising approach. One of the well-known two-dimensional architectures is the so-called Manhattan-street network described in U.S. Pat. No. 4,797,882 which issued on Jan. 10, 1989 to Maxemchuk, entitled MESH-BASED SWITCHING NETWORK. Another example is U.S. Pat. No. 5,606,551 which issued on Feb. 25th, 1997 to Kartalopoulos entitled BIDIRECTIONAL MESH NETWORK. Kartalopoulos describes a mesh network that is similar to the one described by Maxemchuk but uses intersecting bidirectional links.
A three-dimensional mesh network, known as a Torus network, in which each node can direct traffic to neighboring nodes along three dimensions is described in a paper by Banerjee et al. entitled “The Multi-Dimensional Torus: Analysis of Average Hop Distance and Application as a Multi-Hop Lightwave Network (IEEE, International Conference on Communications, 1994, pp. 1675-1680). The nodes in such networks are arranged in intersecting rings.
The mesh networks referred to above were designed to use bufferless nodes. Consequently, each node had to direct an incoming data unit to one of its neighboring nodes immediately upon arrival. The same architecture can be used with nodes capable of buffering incoming data units to resolve conflicting forwarding requirements. In either case, the mean number of hops from a source node to a sink node is proportional to the number of nodes in each of the rings. This dramatically reduces the efficiency of the network and limits its application to small-scale networks.
Another mesh architecture that uses intersecting buses is described in U.S. Pat. No. 5,499,239 which issued on Apr. 14, 1995 to Munter. Munter teaches a network architecture based on an implementation of a three-stage Clos network wherein each space-switching module is replaced by a bus. Each of the three stages is replaced by a set of parallel buses. The buses are interconnected by selectors for routing data between buses. This architecture has the same scalability limitations as a classical Clos network. It is, however, suitable for constructing a centralized switching node having a total capacity of several Tera bits per second.
Methods for constructing networks that scale virtually indefinitely are required to accommodate new specifications that may require capacities well beyond the Peta bits per second enabled by prior art network architectures. There therefore exists a need for a network architecture which enables the construction of a high-capacity network adapted to provide ensured quality-of-service over a very wide geographical area.
SUMMARY OF THE INVENTION
It is an object of the invention to provide an architecture for a data network that may be scaled to provide a high transfer capacity with a very large number of edge modules.
The invention therefore provides an N-dimensional lattice network that comprises a plurality of edge modules having respective identities. Each edge module is identified by N coordinates for addressing the edge module in the network. The edge modules are organized in a plurality of sub-nets, each sub-net including at least two edge modules having N−1 corresponding identical coordinates. Each of the edge modules in each sub-net is directly connected to N core stages for switching connections between edge module pairs. The number of edge modules in each sub-net is less than or equal to an upper-bound Qd, 0<d≦N.
The core stages may be a cross-connector or data packet switch, for example. Alternatively, the core stage may comprise a plurality of core switch modules. If so, the core modules may be geographically distributed. Regardless of whether the core switches are modular, the core may comprise agile switches that reconfigure to adapt to changing traffic loads in response to fluctuating traffic patterns. The core stage may also comprise a TDM space switch, and the TDM space switch may be an agile switch. Alternatively, the core stage may comprise an optical wavelength switch, and the optical wavelength switch may be an agile optical wavelength switch.
The invention further provides a method for computing route-sets for an edge module in a N-dimensional lattice network. The method comprises a first step of assigning a unique identity to each of the N dimensions of the network. The unique identities are then arranged in a starting order, and (N−1) of the unique identities are permuted to derive (N−1) mutually exclusive routes. For routes to another edge module that has at least one coordinate which corresponds identically to coordinates of the edge module for which routes are being computed, the method further comprises a step of reducing the number of the unique identities permuted by one for each corresponding identical coordinate.
After the (N−1)! routes are generated, each of the routes is evaluated to determine a merit index associated with each of the routes. The evaluation is performed by rotating each permutation to produce a set of N rotations of each permutation. After the rotations are completed, another edge module in the network is selected and the coordinates of the other edge module are used to construct a set of N routes using the N rotations of each permutation. The merit of each of the N rotations of each permutation is then computed using some known merit measure, and the computed merit of each permutation is compared with the computed merit of the other permutations. The permutation with the greatest merit is selected, and the selected permutation is associated with the coordinates of the other edge module so that the rotations of the selected permutation are used as a route-set for setting up connections to the other edge module. Thereafter, connection setup messages are routed to the other edge module by selecting a one of the rotations and associating coordinates of the other module with respective ones of the unique identities using a connection array.
The N-dimensional lattice network in accordance with the invention is adapted to support high speed data transport over a large geographical area. In the network, a plurality of edge modules are connected to local data sources/sinks. Each edge module is identified by N coordinates that define a relative position of the edge modules in the N-dimensional lattice network. A plurality of the core stages switch data packets between the plurality of edge modules, each edge module being connected to N core stages. The edge modules are switching nodes that have a plurality of input/output (dual) ports and the dual ports are divided into N+1 port groups. One of the port groups is connected to the local sources/sinks, and a remainder of the port groups are connected to the respective N core stages. The N+1 port groups are substantially, but not necessarily, equal in size. Edge modules that have N−1 common coordinates form a sub-net, each of the edge modules in the sub-net being connected to a same one of the core stages.
The invention also provides a method of routing through an N-dimensional lattice network comprising a plurality of edge modules and a plurality of core stages, in which each edge module is connected to N core stages. The method comprises a first step of identifying each edge module in the network using N coordinates, the N coordinates defining a relative position of each edge module in the network with respect to other edge modules in the network. The N coordinates assigned to each edge module are arranged in a predetermined order of a first through an Nth dimension of the network. The coordinates of an edge module are used, in combination with dimension identifiers uniquely associated with the first through the Nth dimensions, to route through the network from a first edge module to a second edge module by associating the respective coordinates of an edge module with the respective dimension identifiers, arranged in a predetermined order, to define a path from the first to the second edge modules.
The method further comprises a step of storing the respective coordinates and the dimension identifiers in a routing array that is forwarded in a connection request message sent towards the second node as a connection is routed through the network. As the connection request message progresses across the network, the routing array is shortened at each intervening edge module in the path to the second edge module by deleting a coordinate and a dimension identifier from the array at the intervening edge module. The coordinate and the dimension identifier deleted are ones that define the next node to which the connection request message is to be sent. The predetermined order of the dimension identifiers used for routing to the second node is determined by computing rotations of a route-set consisting of the dimension identifiers arranged in a predetermined order selected during the route-set generation process.
The invention therefore provides a network structure that can be scaled to a very large number of edge modules having a very high access capacity. Due to the unique method of addressing edge modules in the network, and setting up connections between nodes, routing through the network is extremely simple and efficient. This permits nodes to operate autonomously without direction from a central controller. The edge modules calculate their own routing tables and negotiate connections autonomously. Signaling overhead is thereby reduced and network throughput is correspondingly improved. The N-dimensional network in accordance with the invention therefore provides a network model that can be scaled to support the next generation Internet, and provide a network structure adapted to support many new and innovative telecommunications services.



BRIEF DESCRIPTION OF THE DRAWINGS
Further features and advantages of the present invention will become apparent from the following detailed description, taken in combination with the appended drawings, in which:
FIG. 1. is a schematic diagram of a prior art mesh network;
FIG. 2 is a schematic diagram of a Clos network, well known in the prior art;
FIG. 3 is a schematic diagram of an implementation of the Clos network shown in FIG. 2 that uses buses as space switches;
FIG. 4 is a schematic diagram of a sub-net of edge modules interconnected by a core switch in accordance with an embodiment of the invention;
FIG. 5a is a schematic diagram showing the connection of an edge module to N core sub-nets in an N-dimensional lattice network in accordance with the invention;
FIG. 5b is a schematic diagram of a two-dimensional network in accordance with the invention;
FIG. 6 is a schematic diagram of a three-dimensional network in accordance with the invention;
FIG. 7 is a schematic diagram illustrating interconnection of certain of the edge modules shown in FIG. 6 to construct a three-dimensional network in accordance with the invention;
FIG. 8 is a schematic diagram of the partitioning of ports of an edge module in the network in accordance with the invention, the ports being partitioned into port groups, the respective port groups being respectively assigned to serve local traffic, and each of the dimensions in an N-dimensional lattice network;
FIG. 9 is a schematic diagram illustrating a coordinate system used for addressing the edge modules in a three-dimensional network in accordance with the invention;
FIG. 10 is a schematic diagram illustrating route-sets in a three-dimensional network which define mutually exclusive paths referred to as “parallel routes” between two edge modules in the N-dimensional lattice network in accordance with the invention;
FIG. 11 is a schematic diagram illustrating route-sets for a three-dimensional network in which an intersection occurs because the route-sets do not follow a “rotation”;
FIG. 12 schematically illustrates a method of constructing route-sets consisting of non-intersecting routes in a three-dimensional network in accordance with the invention;
FIG. 13 is a schematic diagram that illustrates a method of constructing route-sets consisting of non-intersecting routes in a four-dimensional network in accordance with the invention;
FIG. 14 illustrates the route construction process shown in FIG. 13 when the source and sink nodes have one or more identical coordinates in a network in accordance with the invention;
FIG. 15 is a schematic diagram illustrating a step of evaluating route-sets to determine their respective merit;
FIG. 16 is a schematic diagram illustrating the generation of a route-set used for connection setup in an N-dimensional lattice network;
FIG. 17 is a schematic diagram of a portion of a connection request message as it traverses a four-dimensional lattice network in accordance with the invention;
FIG. 18 is a flow diagram illustrating how connection requests are handled at an origination edge module in accordance with the invention; and
FIG. 19 is a flow diagram illustrating how connection requests are handled at a terminating edge module or an edge module serving as a tandem switch in accordance with the invention.



It will be noted that throughout the appended drawings, like features are identified by like reference numerals.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT
This invention relates to a multi-dimensional lattice network in which a plurality of edge modules (i.e., switching nodes connected to data sources/sinks) having unique identities are identified by N coordinates, N representing the number of dimensions in the network. The N coordinates are used for addressing the edge modules within the network. The network includes a plurality of sub-nets, each sub-net including at least two edge modules. The edge modules of each sub-net have N−1 corresponding identical coordinates. The edge modules of each sub-net are also connected directly and exclusively to at least one core switch associated with the sub-net. Every edge module in the multi-dimensional lattice network is connected to a core switch in each of the N-dimensions of the network. The number of dimensions in a network is limited only by the number of ports of the edge modules in the network. The network is therefore scalable to global proportions and the throughput capacity of the network may be scaled to Yotta bits per second, i.e., 1024 bits per second.
FIG. 1 is a schematic diagram of a grid-based mesh network 100 in which a plurality of switching nodes 102 are connected by even numbers of directed rows and columns of links 106, 108. The switching nodes 102 are connected to packet sources and sinks by input/output links 110. This network structure is frequently referred to as a Manhattan street network. While this network structure works well for small networks, it becomes increasingly inefficient as the size of a network increases because the mean number of hops between a source and a sink increases proportionally with the number of nodes per row and the number of nodes per column. Consequently, this network structure is not suited for use as a model for large capacity networks.
FIG. 2 is a schematic diagram of a three-stage network in which input (first-stage) switches 206 are connected to output (third stage) switches 216 by center stage switches 210. Input links 202 are connected to the input switches 206 by input buffers 204. The input switches 206 are connected to the center stage switches 210 through alignment buffers 208. Likewise, the center stage switches 210 are connected to the output switches 216 through alignment buffers 212, and the output switches 216 are connected to output links 220 through output buffers 218. As is well known in the art, the three-stage switch 200 is prone to blocking unless there is a capacity expansion of about 2 to 1 in the center stage switches 210. The three-stage switch 200, commonly referred to as a Clos network, can be geographically distributed and can be scaled to about one Tera bits per second.
FIG. 3 is a schematic illustration of a bus arrangement 300 for a large-capacity Asynchronous Transfer Mode (ATM) switch described by Munter in U.S. Pat. No. 5,499,239. In the bus arrangement 300, the buses are arranged in a mesh pattern with cross-point nodes 302 at each intersection of input and output buses. The buses are arranged in parallel groups of vertical bus lines called the “V” data buses 306, horizontal bus lines called the “H” data buses 304, and a third group of vertical bus lines referred to as the “W” data buses 308. Each “V” bus, or “W” bus has as many channels as the number of nodes 302 per column. Each “H” bus has as many channels as the number of nodes 302 per row. Each node 302 transfers data to a designated channel in a respective “V” bus 306 and receives data from any of the channels of a “W” bus 308. A channel selector 314 transfers ATM cells from any one of the channels of a “V” bus to a designated channel in a respective “H” bus. A channel selector 318 transfers ATM cells from any channel in an “H” bus, to a designated channel in a respective “W” bus. A channel selector 312 permits a node 302 to receive ATM cells from any of the channels of the W buses. This bus structure has the same performance as the three-stage network shown in FIG. 2, because the input switches 206 are functionally equivalent to the V buses, the center stage switches 210 are functionally equivalent to the H buses, and the output switches 216 are functionally equivalent to the W buses.
The N-dimensional lattice network (N>1) in accordance with the invention is constructed of a plurality of sub-nets 400 schematically illustrated in FIG. 4. In each sub-net 400, input/output links 402 interconnect data sources and sinks (not illustrated) with edge switches, hereinafter referred to as “edge modules” 408. The edge modules 408 are in turn connected to N core stages 414 (only one is shown) by core links 412. A core stage may be a circuit switch of coarse granularity, switching 10 Gb/s channels for example, conventionally called a cross connector. A core stage may also be a circuit switch of fine granularity, switching time slots of a channel for example, or even a packet switch switching data packets of arbitrary size. The N core stages 414 may be agile sub-networks, for example, as described in Applicant's copending patent application entitled AGILE OPTICAL-CORE DISTRIBUTED PACKET SWITCH filed Dec. 30, 1999 and assigned U.S. patent application Ser. No. 09/475,139, the specification of which is incorporated herein in its entirety. Each agile sub-network may include a plurality of agile core modules 416 (FIGS. 4 and 7). Agile core modules 416 are respectively connected to each of the edge modules 408 in the sub-net 400 by at least one link 412.
Another form of an agile network that may serve as a sub-net in the multi-dimensional structure 500 is based on the use of time-division-multiplexed (TDM) switches in the core in which the time-slot allocation in a predefined time frame may change to follow the traffic variation. The adaptation of the time-frame allocation to traffic variation is realized by coordination with respective edge modules, as described in U.S. patent application Ser. No. 09/550,489, filed Apr. 17, 2000 and entitled HIGH CAPACITY WDM-TDM PACKET SWITCH.
The sub-nets 400 are arranged in an N-dimensional lattice network 500 shown in FIG. 5a. FIG. 5a is a schematic diagram showing a portion of an N-dimensional lattice network in which only a single edge module 408 and a plurality of core stages 414 are illustrated for the sake of clarity. The N-dimensional lattice network 500 includes a number (Q1×Q2× . . . ×QN) of edge modules 408, and a number of core stages 414, each core stage 414 being logically oriented along one of the N-dimensions and associated with one sub-net 400. The sub-nets 400 of all edge modules 408 connected the same core stage preferably include the same number of edge modules 408. Each core stage 414 is assigned a unique dimension identifier according to its logical orientation in the network. Such core stage may comprise one or more core modules 416. The sub-nets 400 are independent and non-intersecting. The sub-nets 400 are likewise identified in accordance with a corresponding dimension with which they are associated. Thus, each sub-net oriented in the first dimension is a first-dimension sub-net, each sub-net oriented in a second dimension is a second-dimension sub-net, and so on. In FIG. 5a a group of N core stages are represented in different logical orientations, along with one edge module 408 having N links, numbered 1 to N. A link leading to the jth-dimension sub-net is called a j-dimension link, 1≦j≦N. Two-dimensional and three-dimensional implementations of N-dimensional lattice network 500 are illustrated in FIGS. 5b and 6, respectively.
FIG. 5b illustrates a two-dimensional lattice network 500 in accordance with the invention. In the two-dimensional lattice network shown in FIG. 5b, a plurality of edge modules 408 are interconnected by a plurality of core stages 414 which may be, for example, cross-connections, optical switches, or electronic packet switches. The core stages may also be, as described in Applicant's copending patent applications referred to above, distributed switches. The core stages 414 may likewise be agile core switches, as described above. The edge modules 408 connected to any one core stage 414 are collectively referred to as a sub-net 400 although each edge module 408 is a member of N sub-nets in an N-dimensional lattice network 500. The number of edge modules 408 in each sub-net is arbitrary, as is the geographical location of the respective edge modules 408 in any given sub-net. Although the edge modules 408 are interconnected in a logical, juxtaposed relationship as shown in FIG. 5b, the physical relationship between the edge modules 408 and the core stages 414 is preferably governed by traffic patterns and other factors which are beyond the scope of this disclosure. For the purposes of the invention, the edge modules 408 in the N-dimensional lattice network 500 in accordance with the invention are interconnected in logical rows and columns to form sub-nets 400. The number of sub-nets 400 in an N-dimensional lattice network 500 is likewise arbitrary, and the N-dimensional lattice network in accordance with the invention appears to be scalable without practical constraint. It should be noted that the structure of the N-dimensional network shown in FIGS. 5a and 5b facilitates routine through the network, as will be explained below with reference to FIG. 12.
FIG. 6 is a schematic diagram of a three-dimensional arrangement of the N-dimensional network 500 in accordance with the invention. For the sake of simplicity, only the edge modules 408 which appear at the side, top and end “surfaces” of the three-dimensional network are shown. It should be understood, however, that the three-dimensional network includes many more sub-nets 400 which are not illustrated. Each edge module 408 in the three-dimensional lattice network shown in FIG. 6 is connected to three core stages 414. The number of edge modules, Q1, Q2, or Q3, in the three dimensions is, as noted above, substantially arbitrary, though for purposes of addressing and ease of control within each sub-net, is preferably limited to about 256 edge modules 408. This is not a restrictive limit, however, and each sub-net may scale to about 1000 edge modules with a combined user-access capacity per sub-net of about 1 Peta bits per second given today's switching technology.
FIG. 7 is a schematic diagram of the three-dimensional network shown in FIG. 6, illustrating the connection of three core stages 414 (labelled core 1, core 2 and core 3) with respective edge modules 408 in three of the sub-nets in the network. As is apparent, each edge module 408 is connected to a respective core switch module 416 by at least one input/output link 402. If the core stages 414 are modular core stages as shown in FIG. 7, each edge module 408 is connected to each of the core modules 416 by at least one input/output link 402. As will be explained below in more detail with reference to FIG. 9, each of the edge modules 408 is addressed using its logical position in the N-dimensional network 500. For example, the edge module 408c at the lower left corner of the three-dimensional network shown in FIG. 7 has an address of (0, 0, 0). The edge module 408d shown at the top left corner of FIG. 7 has an address of (0, Q2−1, 0). Whereas the edge module 408e at the top right hand corner of FIG. 7 has an address of (Q1−1, Q2−1, Q3−1), and the edge module 408f at the bottom right hand corner of FIG. 7 has an address of (Q1−1, 0, 0).
FIG. 8 is a schematic diagram illustrating the allocation of input/output ports (dual ports) of an edge module 408 in an N-dimensional lattice network 500 in accordance with the invention. The dual ports are divided into N+1 groups. The edge module 408 shown in FIG. 8 is an edge module in the three-dimensional lattice network shown in FIGS. 6 and 7. Input links 802 and output links 804 are connected to input/output port group m0, while input links 806 and output links 808 are connected to port group m1. Likewise, input links 812 and output links 814 are connected to port group m2, while input links 816 and output links 818 are connected to port group m3. The number of input/output ports allocated to each port group is dependent on the number of switching modules 416 in each of the core stages 414 that serve the respective sub-nets of which the edge module 408 is a member. The number of switching modules 416 in each core stage 414 is in turn related to the number of edge modules 408 in the sub-net served by the core stage 414. The ports in port group m0 are connected to local data sources and sinks. The ports of port group m1, are connected to the core stage 414 in the first dimension of the three-dimensional network, while the ports in port groups m2 and m3 are respectively connected to core stages 414 in the second and third dimensions. The values of m1, m2, . . . , mN are preferably, but not necessarily, selected to be comparable to the value of m0 to ensure high performance under diverse spatial traffic distributions.
The access capacity of the network is the sum of the capacities of the input ports allocated to receiving traffic from traffic sources. The access capacity is determined by the number of input/output ports, the capacity per port, and the number of edge modules in each of the N dimensions. In an N-dimensional lattice network having identical edge modules, with each edge module having m0 input/output ports allocated to traffic sources and sinks, each input/output port having an input capacity of R bits per second, and with qj edge modules in dimension j, 1≦j≦N, the total capacity C of the network is determined by:

C=R×m0×(Q1×Q2× . . . ×QN)

where:

    
    
        C=total capacity of the N-dimensional network;
        R=capacity of a link;
        m0=number of links per edge module; and
        Qn=number of edge modules in dimension N.
    
    


Thus, with N=4, R=10 Gb/s, m0=100, and Q1=Q2=Q3=Q4=256, the capacity C is roughly 4×1021, i.e., 4 Zeta bits per second. With N=5, m0=80, and Q1=Q2=Q3=Q4=Q5=256, the capacity C is 0.8×1024, i.e., 0.8 Yotta bits per second.
FIG. 9 is a schematic diagram showing the addressing scheme used in the N-dimensional lattice network 500 in accordance with the invention. The N-dimensional lattice network 500 shown in FIG. 9 is a three-dimensional network. Only two edge modules 408c and 408g are illustrated for the sake of clarity. Edge module 408c has a network address of (0, 0, 0). Edge module 408g has a network address of (120, 83, 86). The address is derived from the logical position of each edge module 408 in the respective sub-nets to which it belongs. For example, edge module 408c is in the 0 position of each of the first, second and third dimensions of the N-dimensional lattice network 500. Edge module 408g, on the other hand, is the 120th position on the first dimension, the 83rd position on the second dimension and the 86th position on the third dimension with respect to edge module 408c. This addressing scheme forms the basis for a simple, autonomous, decentralized routing algorithm in accordance with the invention as will be explained below with reference to FIGS. 10-14.
In the N-dimensional lattice network in accordance with the invention, preferably only one route-set is used to establish connections for each pair of edge modules 408. Routes in the route-set are attempted in a predetermined order when a connection between a pair of edge modules 408 is required. In order to minimize the probability of blocking during connection attempts using a route-set in accordance with the invention, the route-set preferably includes only mutually-exclusive paths between the edge modules 408 in each edge module pair. Mutually-exclusive paths are paths between the pair of edge modules 408 that do not intersect at any point on the route. FIG. 10 schematically illustrates two route-sets in a three-dimensional lattice network between edge modules 408j and 408k having respective coordinates (A1, B1, C1) and (A2, B2, C2). Paths between the edge modules 408j, 408k are called “mutually-exclusive” paths if the paths do not traverse any common links. Paths are not mutually-exclusive if any link in the path is traversed by another path in the same route-set. The advantage of using a route-set consisting of mutually-exclusive paths is that the connection setup process is more likely to succeed because the same links are not retried.
FIG. 11 illustrates two more route-sets between edge modules 408j, 408k in which the routes are not mutually-exclusive. In the example shown in FIG. 11, route-set 3 includes routes generated by rotations BCA and CBA which intersect between edge modules having address (A1, B2, C2) and (A2, B2, C2). In route-set 4 shown in FIG. 11, routes generated by rotations ACB and CAB also have intersecting paths. (Following a rotation BCA means that the route from a source edge module to a sink edge module progresses along the B direction first, then along the C direction, and finally along the A direction.)
In order to facilitate an understanding of routing in accordance with the invention, reference is made once more to FIG. 5b. FIG. 5b illustrates two routes in a two-dimensional network between edge modules 408a and 408b. Route 1 passes through core stages 414a and core stages 414b while route 2 passes through core stages 414d and 414c. These two routes are representative of the two-hop routes which exist between any two pairs of edge modules 408 in a two-dimensional lattice network in accordance with the invention. As will also be apparent, the switching between successive edge modules in each route is direct switching through the core stages 414.
FIG. 12 illustrates a method of determining mutually-exclusive paths for route-sets in an N-dimensional network 500 in accordance with the invention. In accordance with the method, each dimension in the network is assigned a unique identifier. This is conveniently a binary code of ([log2 N]) bits ([log2 N] is the nearest integer not less than log2 N). For a network of four dimensions, for example, two bits are used to identify the four dimensions. The unique identifiers are then arranged in any order, their logical order of “00, 01, 10, 11”, for example, and (N−1) of the unique identifiers are permuted to yield (N−1)! permutations, each of which is further rotated to generate N mutually-exclusive paths for any pair of edge modules in the network. This operation is so simple that each edge module preferably computes its own route-sets, as will be explained below in more detail. FIG. 12 shows an example of the method based on the three-dimensional lattice network 500 shown in FIG. 6. For any given N-dimensional network in accordance with the invention, the number of route-set generating permutations is factorial (N−1). Therefore, in a three-dimensional lattice network, the number of route-set generating permutations is two factorial (2!), i.e., 2. In FIG. 12, the letters A, B and C are used to uniquely identify the three dimensions in the three-dimensional network rather than the binary codes, in order to facilitate the description. As shown in FIG. 12 and discussed above with reference to FIGS. 10 and 11, the two route-generating permutations for a three-dimensional network are ABC and ACB wherein the respective letters represent switching along a dimension of the network as illustrated in FIGS. 10 and 11 wherein the first dimension is represented by A, the second dimension is represented by B and the third dimension is represented by C. As shown in FIG. 12, the route-generating permutation ABC generates three routes between edge modules 408 having addresses (A1, B1, C1) and (A2, B2, C2). The route-generating permutation ACB also generates three routes between edge modules 408 having those respective addresses. The method of selecting a single route-set to be used between the edge modules 408j, 408k (FIGS. 10, 11) is explained below with reference to FIG. 15.
FIG. 13 illustrates a method of determining mutually-exclusive paths in a four-dimensional lattice network in accordance with the invention. The paths are routes from a first edge module 408 having an address (A1, B1, C1, D1) and a second edge module 408 having an address (A2, B2, C2, D2). As noted above, the number of route-set generating permutations is factorial (N−1), i.e., 3!=6 for a four-dimensional lattice network. As shown in FIG. 13, the six route-generating permutations are ABCD; ABDC; ACBD; ACDB; ADBC; and, ADCB. Each in turn generates four alternate routes for mutually-exclusive paths between the respective edge modules 408. It is noted that the generation of the permutations is a well-known procedure.
In an instance where an origination edge module and termination edge module share identical corresponding coordinates, the route-set generation process is facilitated by reducing the number of dimensions for which route-generating permutations are required by the number of identical corresponding coordinate pairs. For example, FIG. 14 illustrates a method of determining mutually-exclusive routing paths for a four-dimensional lattice network in which a first edge module 408j has an address (A1, B1, C1, D1) and a second edge module 408k has an address (A2, B2, C2, D2) and the mutual coordinates B1 and B2 are identical. The dimensions of the network for the purpose of determining mutually-exclusive paths is therefore reduced by one. Consequently, the number of route-generating permutations is reduced from 6 to 2 ((3−1)!=2). As a result, the only route-generating permutations that need be considered in selecting mutually-exclusive paths between the addresses of the edge modules 408j, 408k in a four-dimensional network in which the corresponding coordinates B1 and B2 are identical, are the permutations in which the B coordinates are in the same position in the permutation. As shown in FIG. 14, those two permutations are ABCD and ABDC, respectively. Each permutation generates three alternate routes, as shown in FIG. 14.
In accordance with the invention, the route-sets are preferably computed by each edge module 408 as required. The route-sets need be derived only when topological changes are introduced in the N-dimensional lattice network 500. Since the network is multi-dimensional and the core stages 414 are preferably agile and reconfigure as required, as explained in Applicant's copending patent applications incorporated by reference above, route-sets need not be recomputed in the event of failed links unless very large sectors of the network fail simultaneously, which is highly improbable. In addition, the provision of N parallel mutually-exclusive routes per node pair facilitates re-routing if one of the routes fails. As noted above, each edge module 408 preferably retains only one set of routes to each of the other edge modules 408 in the N-dimensional lattice network 500. Only the generating permutation of the route-set, rather than the routes' description, need be stored. The retained route-set is preferably selected based on merit. Merit can be defined in any number of ways. For example, the propagation delay of the links in the route-set can be used as a measure of merit. The shorter the propagation delay, the higher the merit of the link. FIG. 15 shows an example of route-set selection based on a merit criteria. In this example, the propagation delay is computed for each of the respective links in the mutually-exclusive paths between the edge modules 408 having respective addresses (A1, B1, C1) and (A2, B2, C2). By summing up the propagation delay of the links in each route-set, the edge module 408j determines which route-set is preferred. Accordingly, route-set 1 yields a merit index of 89 in the example shown in FIG. 15, while route-set 2 yields a merit index of 95. Since the merit index is based on propagation delay and is therefore related to cost, route-set 1 has the highest merit and is selected as the route-set to be used between edge module (A1, B1, C1) and edge module (A2, B2, C2).
Edge modules 408 in accordance with the invention, preferably store route-set generating permutations very economically in N times ┌log2 N┐ bits per permutation. For example, in a 4-dimensional lattice network, one byte is needed per permutation. That byte of information is divided into adjacent unique dimension identifiers that are used for selecting a route to a termination edge module. The unique dimension identifiers are used in conjunction with the address of the termination edge module to select a path to the termination edge module when a connection between the origination edge module and the termination edge module is requested. That assignment of the unique dimension identifiers is consistently used throughout an N-dimensional network in accordance with the invention. The axis with which a dimension identifier is associated is immaterial provided that the identifier is consistently used in instructions sent to other edge modules in the network. As shown in FIG. 16, a plurality of route-sets 1610 are stored in an edge module 408 in a 4-dimensional lattice network. The route-sets are used to set up connection s by generating a rotation of the route-set. A rotation 1630 of route-set 1620 is shown in FIG. 16. Rotation 1630 is used to select a route to the termination edge module, as will be explained below with reference to FIG. 18.
FIG. 17 shows the use of the rotations 1630 for setting up a connection across an N-dimensional lattice network 500 in accordance with the invention. At the origination edge module (A1, B1, C1, D1) the 0th rotation is selected and used to formulate a connection setup message that includes the dimension identifiers in the 0th rotation of the rotation set 1630 shown in FIG. 16. Associated with each dimension identifier is the corresponding coordinate of the termination edge module (A2, B2, C2, D2). These are respectively stored in routing arrays 1740A, 1740B of the connection setup message. Arrays 1740A and 1740B may be viewed as a single array of records, each record having two fields, the first containing a dimension identifier, and the second containing an edge module identifier within the respective dimension. The message further stores a bit-rate (not illustrated) requested by the source, for which the connection is being set up. As will be explained below in more detail, the routing arrays in the connection setup message are progressively shortened as the message traverses the network, so that only the requested bit-rate is passed to the termination edge module 408. The actions of the termination edge module 408 during connection setup are explained below in greater detail. Thus, before sending the connection setup message, the origination edge module deletes the address of the first edge module (in this example A2) from array 1740B and substitutes the dimension identifier in the first column of array 1740A with a binary number indicating the number of remaining records (i.e., binary “11”, which equals 3). The array 1742A, along with the shortened address array 1742B, are forwarded to the next edge module, as will also be explained below in more detail. This process continues as the connection setup request traverses the network as shown in arrays 1744A, 1744B and 1746A, 1746B. If the 0th rotation fails at any of the intervening edge modules because of lack of capacity on any of the links in the route-set, a connection request rejection message is returned and the origination edge module 408 selects another rotation. The right-hand side of FIG. 17 illustrates a second rotation of the route-set in which connection messages shown in arrays 1750A-1756B traverse the network as explained above.
FIG. 18 is a flow chart that shows the principal steps of a connection setup procedure executed by the edge modules 408 on receipt of a connection request from a source node (not shown). In step 1810, the edge module 408 receives the requested bit-rate and coordinates (e.g., A2, B2, C2, D2) of a terminating edge module 408 that serves the intended sink. As will be understood by those skilled in the art, the coordinates of the termination edge module 408 that serves the sink identified in the connection setup request may not be known to the subtending source. If so, the originating edge module 408 may perform any one of a number of translation procedures to determine the coordinates of the terminating edge module. In step 1812, the originating edge module selects a route-set using the coordinates of the terminating edge module. The originating edge module thereafter generates the N rotations of the selected route-set (step 1814) and selects a first rotation (step 1816). The first route-set rotation and the coordinates of the terminating edge module are used to generate a connection array (step 1818). The dimension identifier and the edge module identifier in the first record of the connection array are used to determine a first hop destination for a connection request message. Before the request message is formulated and forwarded to the first hop destination, the first record is deleted from the connection array (step 1820) as explained above with reference to FIG. 17. The available capacity to the first edge module in the specified dimension is checked in step 1822. If capacity is available to the first hop edge module, a connection request message is formulated (step 1824) and forwarded to the first hop edge module in the specified dimension. In step 1825, the origination edge module places the connection request in a queue and waits for a confirmation of request acceptance or denial. If the request is accepted, the source node is notified in step 1828 and the procedure ends. Otherwise, the origination edge module determines whether all rotations have been tried (step 1830) and, if not, a next rotation is selected (step 1816), and the process of steps 1818-1824 are repeated. Likewise if it is determined in step 1822 that adequate capacity is not available to the first hop edge module in the specified dimension, a determination is made in step 1830 as to whether all rotations have been attempted. If not, the process returns to step 1816 and steps 1818-1822 are repeated. If, however, all rotations have been selected, the connection request is rejected in step 1832 and the process ends.
The process of selecting rotations for routing is preferably based on a scheme that will tend to balance loads on the respective routes. A round-robin method of selection may therefore be used. Some other distribution method that attempts to equalize the capacity allocations to the mutually-exclusive routes of a route-set may also be used.
FIG. 19 is a flow diagram showing the principal steps in the connection setup process performed by edge modules downstream of an originating edge module 408. In accordance with the procedure, a connection request message is received in step 1910. In step 1912, the length of the routing array received in the message is examined to determine whether the routing array is longer than one record. If not, downstream edge module 408 is the terminating edge module and the requested bit-rate is forwarded to a subtending sink in step 1914. Thereafter, a connection acceptance message is formulated and returned to the originating edge module in step 1916 and the procedure ends. If the length of the routing array is greater than one record, the downstream edge module is not the terminating edge module. The process therefore continues in step 1918 in which the downstream edge module 408 extracts the dimension identifier from the first record of the routing array and the coordinates of the next edge module and determines whether capacity is available to the specified edge module in step 1920. If the capacity is available, the downstream edge module deletes the first record from the connection array (step 1922) and forwards the connection request (step 1924) to the next downstream edge module. A connection array length indicator may be inserted before the message is forwarded, as explained above. If it is determined in step 1920 that the required capacity is not available to the next downstream edge module, the connection request is rejected in step 1926 by sending a connection rejection message back (step 1825, FIG. 18) to the originating edge module using any one of a number of protocols well known in the art.
The invention therefore provides a highly-efficient network that can be expanded to provide a global data network. The N-dimensional lattice network in accordance with the invention is an adaptive, robust network of autonomous edge modules that effect connection setup with a minimum of delay and signaling overhead. The N-dimensional lattice network in accordance with the invention employs a simple addressing scheme that enables the coordinates of an edge module, in combination with a dimension identifier array, to be used as a routing map for enabling connection setup. The requirement for extensive translation tables and complex route-sets is therefore eliminated. Consequently, the N-dimensional lattice network operates with exceptional efficiency.
The embodiment(s) of the invention described above is(are) intended to be exemplary only. The scope of the invention is therefore intended to be limited solely by the scope of the appended claims.

## Claims

1. In an N-dimensional lattice network comprising a plurality of edge modules, a method for routing a connection setup message from a first edge module to a second edge module, the method comprising steps of:
a) assigning N unique identities, one unique identity for each of the N dimensions of the network; 
b) permuting (N−1) of said unique identities to derive factorial (N−1) route-set generating permutations, each route-set generating permutation specifying an ordered sequence of said N unique identities; 
c) assigning N coordinates for each of said edge modules, each of said coordinates associated with one of said unique identities; 
d) rotating said ordered sequence of a selected one of said route-set generating permutations to determine directions of N mutually exclusive routes; 
e) defining a selected route set according to said directions and the N coordinates of said second edge module; and 
f) selecting one of the rotations and associating coordinates of said second edge module with respective ones of the unique identities.

2. A method as claimed in claim 1 wherein when said first edge module and said second edge module have at least one common coordinate, the method comprises a further step of reducing the number of the unique identities permuted by the number of said at least one common coordinate.

3. A method as claimed in claim 1 further comprising a step of determining a merit index associated with said route-set by summing up link merits associated with each link in each route of said selected route set.

4. A method of routine through an N-dimensional lattice network comprising a plurality of edge modules and a plurality of core stages, each edge module being connected to N core stages, comprising steps of:
a) identifying each edge module using N coordinates associated with N dimension identifiers and arranged in a predetermined order; and 
b) generating a route set from a first edge module to a second edge module by associating the coordinates of said second edge module with respective dimension identifiers and performing a process comprising steps of: 
i) permuting N−1 of the dimension identifiers to determine factorial (N−1) route-sets, each route-set having non-intersecting paths from the first edge module to the second edge module; 
ii) evaluating each of the factorial (N−1) route-sets to determine a preferred route set; and 
iii) discarding the remainder of the factorial (N−1) route-sets.

5. The method as claimed in claim 4 wherein the step of evaluating comprises further steps of determining a merit index of each route-set and selecting the route-set with the highest merit index.

6. A method as claimed in claim 5 wherein the merit index is related to a propagation delay on each link in each route of each route-set.

7. A method of generating route sets each comprising mutually exclusive routes from a first edge module to a second edge module in a multi-dimensional network comprising a plurality of edge modules arranged into sets of edge modules, said sets further grouped according to a predefined number of dimensions and each edge module identified by a coordinate in each of said dimensions, the method comprising steps of:
permuting selected dimensions of said predefined number of dimensions to obtain a number of route-set generating permutations, each including a number of dimension identifiers equal to said predefined number of dimensions, wherein said number of route-set generating permutations does not exceed the factorial of a number equal to said predefined numbered of dimensions minus one; 
rotating each of said dimension identifiers of each of said route-set generating permutations to yield a set of rotated dimension identifiers; and 
associating each rotated dimension identifier with a coordinate of said second edge module to generate a route set comprising mutually-exclusive routes from said first edge module to said second edge module.

8. The method of claim 7 wherein said selected dimensions excludes at most one dimension of said predefined number of dimensions.

9. The method of claim 7 wherein said selected dimensions exclude any dimension corresponding to any common coordinate in said first edge module and said second edge module.

10. A method of generating route sets comprising mutually exclusive routes from a first edge module to a second edge module in a multi-dimensional network comprising plurality of edge modules arranged into sets of edge modules, said sets further grouped according to a predefined number of dimensions and each edge module identified by a coordinate in each of said dimensions, the method comprising steps of:
permuting selecting dimensions of said predefined number of dimensions to obtain a number of route-set generating permutations, each including a number of dimension identifiers equal to said predefined number of dimensions; 
rotating said dimension identifiers of each of said route-set generating permutations to yield a set of rotated dimension identifiers; 
associating each rotated dimension identifier with a coordinate of said second edge module to generate a route set comprising mutually-exclusive routes from said first edge module to said second edge module; 
associating a link merit with each link along a dimension from said first edge module to said second edge module; and 
determining a merit index for each route set by summing up said link merit associated with each link said each route set.

11. The method of claim 10 further including a step of determining a preferred route set based on said merit index.