Showing papers on "Equal-cost multi-path routing published in 1992"

The turn model for adaptive routing

Abstract: We present a model for designing wormhole routing algorithms that are deadlock free, livelock free, minimal or nonminimal, and maximally adaptive. A unique feature of this model is that it is not based on adding physical or virtual channels to network topologies (though it can be applied to networks with extra channels). Instead, the model is based on analyzing the directions in which packets can turn in a network and the cycles that the turns can form. Prohibiting just enough turns to break all of the cycles produces routing algorithms that are deadlock free, livelock free, minimal or nonminimal, and maximally adaptive for the network. In this paper, we focus on the two most common network topologies for wormhole routing, n-dimensional mesh, just a quarter of the turns must be prohibited to prevent deadlock. The remaining three quarters of the turns permit partial adaptiveness in routing. Partially adaptive routing algorithms are described for 2D meshes, n-dimensional meshes, k-ary n-cubes, and hypercubes. Simulations of partially adaptive and nonadaptive routing algorithms for 2D meshes and hypercubes show that which algorithm has the lowest latencies and highest sustainable throughput depends on the pattern of message traffic. For nonuniform traffic, partially adaptive routing algorithms perform better than non-adaptive ones.

Planar-adaptive routing: low-cost adaptive networks for multiprocessors

Abstract: Network throughput can be increased by allowing multipath, adaptive routing. Adaptive routing allows more freedom in the paths taken by messages, spreading load over physical channels more evenly. The flexibility of adaptive routing introduces new possibilities of deadlock. Previous deadlock avoidance schemes in k-ary n-cubes require an exponential number of virtual channels, independent of network size and dimension. Planar adaptive routing algorithms reduce the complexity of deadlock prevention by reducing the number of choices at each routing step. In the fault-free case, planar-adaptive networks are guaranteed to be deadlock-free. In the presence of network faults, the planar-adaptive router can be extended with misrouting to produce a working network which remains provably deadlock free and is provably livelock free. In addition, planar adaptive networks can simultaneously support both in-order and adaptive, out-of-order packet delivery.Planar-adaptive routing is of practical significance. It provides the simplest known support for deadlock-free adaptive routing in k-ary n-cubes of more than two dimensions (with k > 2). Restricting adaptivity reduces the hardware complexity, improving router speed or allowing additional performance-enhancing network features. The structure of planar-adaptive routers is amenable to efficient implementation.

Synchronization mechanism for link state packet routing

Abstract: A method of providing loop free and shortest path routing of data packets in a network having a plurality of switches, routing messages for communicating network topology information between the switches, a plurality of links connecting the switches and a plurality of channels connecting the switches to the links. The loop free routing of data packets is achieved through modifications to known link state packet (LSP) routing protocols and permits each switch to inform adjacent switches in the network of the information in the switch's database used to compute forwarding tables. A switch uses a received LSP to compute a forwarding table and informs neighboring switches on attached links of the routing change. The switch discards any subsequent data packets whose path would be affected by the changed routing information. The discarding of data packets continues until the switch receives notification from each adjacent switch affected by the changed routing information that all affected routing paths have been recalculated and the forwarding table of each affected switch has been updated. Thus, while adjacent switches temporarily contain inconsistent LSP databases and possibly inconsistent forwarding tables, the looping of data packets is prevented. Shortest path routing for data packets from a source endnode to a destination endnode is achieved by assuring that the first switch to forward the packet is on the shortest path to the packet's destination endnode. A source endnode transmits a data packet with an appropriate destination header and the determination of the actual routing path is performed transparently to endnodes. A data packet reaches its destination endnode by following the shortest path possible based on the network topology as represented in the database of the first switch that forwards it.

Multihop lightwave networks: a comparison of store-and-forward and hot-potato routing

Abstract: The achievable aggregate capacity for a variant of the basic multihop approach in which minimum distance store-and-forward routing is replaced by a hot-potato routing algorithm is determined. With hot-potato routing, all packets simultaneously arriving at a given node and not intended for reception at that node are immediately placed onto the outbound links leaving that node; if two or more packets contend for the same outgoing link to achieve a minimum distance routing, then all but one will be misrouted to links which produce longer paths to the eventual destination. Attention is confined to the development of an analytical methodology for finding the probability distribution of the number of hops with hot potato routing for symmetric networks under uniform traffic load. Results show that the maximum throughput achievable with hot-potato routing can be as low as 25% of that for store-and-forward routing, and that the relative degradation increases as the number of nodes grows larger. This implies that the link speed up needed to produce a significant overall capacity advantage with hot potato should be at least a factor of 10. >

Analysis of shortest-path routing algorithms in a dynamic network environment

Abstract: In a dynamic network environment under heavy traffic load, shortest-path routing algorithms, particularly those that attempt to adapt to traffic changes, frequently exhibit oscillatory behaviors and cause performance degradation. In this paper we first examine the problems from the perspective of control theory and decision making, and then analyze the behaviors of the shortest-path routing algorithms in details.

Adaptive deadlock- and livelock-free routing with all minimal paths in Torus networks

Abstract: Luis Gravano, Gustavo D. PifarrC, Pablo E. Berman, and Jorge L. C. Sanz, Fellow, ZEEE Abstract-This paper consists of two parts. In the first part, two new algorithms for deadlock- and livelock-free wormhole routing in the torus network are presented. The first algorithm, called *-Channels, is for the n-dimensional torus network. This technique is fully-adaptive minimal, that is, all paths with a minimal number of hops from source to destination are available for routing, and needs only five virtual channels per bidirectional link, the lowest channel requirement known in the literature for fully-adaptive minimal worm-hole routing. In addition, this result also yields the lowest buffer require- ment known in the literature for packet-switched fully-adaptive minimal routing. The second algorithm, called 4-Classes, is for the bidimensional torus network. This technique is fully-adaptive minimal and requires only eight virtual channels per bidirectional link. Also, it allows for a highly parallel implementation of its associated routing node. In the second part of this paper, four worm-hole routing techniques for the two-dimensional torus are experimentally evaluate'd using a dynamic message injection model and different tr&c patterns and message lengths.

Dynamic multi-path routing and how it compares with other dynamic routing algorithms for high speed wide area network

Abstract: In this paper we describe briefly a dynamic multi-path routing scheme that has been considered for connection oriented homogeneous high speed networks. The fundamental objective of the scheme is to bridge the gap between routing and congestion control as the network becomes congested. Because propagation delay far out shadows queueing and transmission delay in high speed networks, the proposed routing scheme works as a shortest path (minimum hop) first algorithm under light traffic conditions. However as the shortest path becomes congested, the source node uses multiple paths when and if available in order to distribute the load and reduce packet loss. The scheme is a cross between Alternate Path routing and Trunk Reservation.We compare the performance of the proposed scheme with the Shortest Path Only algorithm, the Alternate Path routing algorithm, the Random Routing algorithm, and the Trunk Reservation scheme. The throughput and packet loss performance are compared via simulations. These have been carried out concentrating on a 5 node network with varying traffic patterns, the intention being to gain insight into the strengths and weaknesses of the various schemes.

Optimal routing algorithms for mesh-connected processor arrays

Abstract: We show that there is a randomizedoblivious algorithm for routing any (partial) permutation on ann ?n grid in 2n +O(logn) parallel communication steps. The queues will not grow larger than ź(logn/log logn) with high probability. We then modify this to obtain a (nonoblivious) algorithm with the same running time such that the size of the queues is bounded by a constant with high probability. For permutations withlocality, where each packet has to travel a distance at mostL, a generalization of the algorithm routes in time proportional toL with high probability. Finally, we identify a class of meshlike networks that have optimal or near-optimal diameter. These meshes have the potential of being adapted to run existing sorting and routing algorithms with corresponding reduction in their running times.

Resource pooling in queueing networks with dynamic routing

Abstract: In this paper we investigate dynamic routing in queueing networks. We show that there is a heavy traffic limiting regime in which a network model based on Brownian motion can be used to approximate and solve an optimal control problem for a queueing network with multiple customer types. Under the solution of this approximating problem the network behaves as if the service-stations of the original system are combined to form a single pooled resource. This resource pooling is a result of dynamic routing, it can be achieved by a form of shortest expected delay routing, and we find that dynamic routing can offer substantial improvements in comparison with less responsive routing strategies.

Adaptive routing in mesh-connected networks

Abstract: It is shown that wormhole routing in mesh-connected networks can be deadlock free and adaptive without the addition of channels to the basic topology. Several partially adaptive routing algorithms for 2-D and 3-D meshes are described and simulated for a variety of conditions. Simulations of policies for selecting input channels show that transmitting extra information in the header flits can reduce communication latencies at high network throughputs. Simulations of policies for selecting output channels show that avoiding turns reduces latencies at high throughputs. Unrestricted nonminimal routing is found to reduce latencies slightly at low throughputs but increase latencies significantly at high throughputs. For nonuniform traffic patterns, a partially adaptive routing algorithm performs better than a nonadaptive one. >

A theory of wormhole routing in parallel computers

Abstract: Virtually all theoretical work on message routing in parallel computers has dwelt on packet routing: messages are conveyed as packets, an entire packet can reside at a node of the network, and a packet is sent from the queue of one node to the queue of another node until its reaches its destination. The current trend in multicomputer architecture, however, is to use wormhole routing. In wormhole routing a message is transmitted as a contiguous stream of bits, physically occupying a sequence of nodes/edges in the network. Thus, a message resembles a worm burrowing through the network. The authors give theoretical analyses of simple wormhole routing algorithms, showing them to be nearly optimal for butterfly and mesh connected networks. The analysis requires initial random delays in injecting messages to the network. They report simulation results suggesting that the idea of random initial delays is not only useful for theoretical analysis but may actually improve the performance of wormhole routing algorithms. >

Separable routing: a scheme for state-dependent routing of circuit switched telephone traffic

Abstract: Separable routing is the first of a number of routing schemes for circuit switched telephone traffic invented at Bellcore. These routing schemes are state dependent, in the sense that, for each call attempt, a routing decision is made on the basis of the state of the network (defined in terms of the numbers of busy and idle trunks in the various trunk groups at the moment of the call attempt). In this paper, we describe separable routing and its mathematical background. Simulation results we have presented elsewhere show that the family of state-dependent routing schemes, of which separable routing is a member, is very attractive in terms of blocking rate, built-in network management features, and behavior in the presence of traffic forecast error.

State dependent routing for multirate loss networks

Abstract: An approach to adaptive routing in multirate networks using a Markov decision theoretic framework which maintains low computational complexity while still providing quite accurate routing information is proposed. In this approach, each link is modeled as a birth-death process to reduce the state space size and a policy iteration applied to achieve better network performance. The results show that routing algorithms based on this approach yield better performance than least-load path routing (LLP) without incurring any significant increase in computational complexity. >

Shipment routing algorithms with tree constraints

Abstract: Routing shipments efficiently on less-than-truckload trucking networks represents an important subproblem of the general network design problem that arises when designing a service network. The objective of the LTL shipment routing problem is to minimize the total transportation and handling costs subject to two key constraints: (i) service between two terminals must always satisfy a given minimum frequency (measured in trailers per week) and (ii) the paths from all origins into a destination should form a tree. This second constraint reflects a practical limitation on the types of instructions that can be implemented in the field. A solution approach is developed using a shortest path based formulation with additional routing constraints imposed to refine the routing in response to minimum frequency constraints. A local improvement heuristic is presented which manipulates the routing constraints. A separate set of primal-dual algorithms are also developed which provide both upper and lower bounds. Numeri...

Requirements for deadlock-free, adaptive packet routing

Abstract: This paper studies the problem of deadlock-free packet routing in parallel and distributed architectures. We present three main results. First, we show that the standard technique of ordering the queues so that every packet always has the possibility of moving to a higher ordered queue is not necessary for deadlock-freedom. Second, we show that every deadlock-free, adaptive packet routing algorithm can be restricted, by limiting the adaptivity available, to obtain an oblivious algorithm which is also deadlock-free. Third, we show that any packet routing algorithm for a cycle or torus network which is free of deadlock and which uses only minimal length paths must require at least three queues in some node. This matches the known upper bound of three queues per node for deadlock-free, minimal packet routing on cycle and torus networks.

Method and system for correcting routing errors due to packet deflections

Abstract: A distributed and adaptive method and system are provided for correcting routing errors due to packet deflections in a dual-shuffle exchange network (DSN). The DSN includes a shuffle-exchange network (SN) and an unshuffle-exchange network (USN). A packet that cannot be routed correctly will be temporarily "deflected" to a wrong route. This deflection, or routing error, is then registered and encoded in a routing tag of the header of the packet. Using this information, an error-correcting routing algorithm is then used to correct the error at a different part of the network. The method and system can be used either as the basis of a switch architecture of a ultra high-speed local-area network or metropolitan area network. Also, the method and system can be used in circuit switching. The DSN can achieve the Shannon's lower bound N log N on switch complexity with arbitrarily small packet-loss probability.

System for determining communication routes in a network

Abstract: A network system capable of speedily selecting an intermediate system which can provide a shortest route of data communication among various intermediate systems even if routing information is not stored on the end system side, and in which the wasteful routing information is not held on the end system side, thereby minimizing an amount of routing information stored. In the network system, each packet for broadcast communication sent from each intermediate system is imparted to an intermediate system-address extracting unit 6 via a reception unit 2 and a packet processing unit 4 in the end system. The management-address extracting unit 6 extracts addresses of the intermediate systems from the packets, and stores these addresses in the management-address storage unit 8. When the packet is transmitted from this end system, the packet processing unit 4 obtains addresses in the management-address storage unit 8 via a route request unit 9, and sends a request of routing information to the intermediate systems having these addresses via a transmission unit 10. When the respective routing information is sent from the intermediate systems to the end system in response to that request, a route selecting unit 5 determines a shortest route to the destination on the basis of each routing information. The packet processing unit 4 request the intermediate system providing the shortest route to relay the packet.

Provably good algorithms for performance-driven global routing

Abstract: The authors propose a provably good performance-driven global routing algorithm for both cell-based and building block design. The approach is based on a new bounded-radius minimum routing free formulation, which simultaneously minimizes both routing cost and the longest interconnection path, so that both are bounded by small constant factors away from optimal. The authors' method generalizes to Steiner global routing in arbitrary weighted graphs, and to the case where varying wirelength bounds are prescribed for different source-sink paths. Extensive simulations confirmed that the approach gave very good performance, and exhibited a smooth tradeoff between the competing requirements of minimum delay and minimum total wirelength. >

Balanced gamma network-a new candidate for broadband packet switch architectures

Abstract: The gamma network is enhanced to derive a balanced gamma network with the addition of an additional link. The performance of the proposed network is analyzed in comparison with the existing networks. The performance of replicated networks and of networks with one internal buffer are investigated. These networks are studied using two assumptions: the common assumption that each destination can accept only one packet in a given cycle and the assumption that any number of packets can be accepted by a destination. Balanced gamma networks exhibit good performance, enable simple routing schemes, and are modular. >

A Unified Approach to Inter-Domain Routing

Abstract: This memo is an informational RFC which outlines one potential approach for inter-domain routing in future global internets The focus is on scalability to very large networks and functionality, as well as scalability, to support routing in an environment of heterogeneous services, requirements, and route selection criteria

Rooted routing in linear lightwave networks

Abstract: The authors propose a new scheme for optical signal routing within linear lightwave network (LLN) subnets. They study the synchronization problem that exists in these subnets which prevents efficient implementation of time division multiple access schemes for sharing a common broadcast medium. A solution for this problem is proposed, based on a new optical agent signal routing scheme, called rooted routing. The impact of the rooted routing on power losses is analyzed, and an approach for optimizing the power losses in LLNs with rooted routing is presented. It is shown that when the link and excess losses are small, the optimal power budget is close to that when the original, shortest path routing scheme is used. It is also shown that the power budget in LLNs with rooted routing can be significantly improved using a single optical amplifier. >

Multipath E-cube algorithms (MECA) for adaptive wormhole routing and broadcasting in k-ary n-cubes

Abstract: Introduces and evaluates the multipath E-cube algorithm (MECA) for adaptive and fault-tolerant wormhole routing in k-ary n-cubes. This algorithm provides multiple shortest paths between any source and destination node of a multicomputer using only a constant number of virtual channels for every physical channel, and with little added overhead at the router. Consequently, it is able to improve network throughput and reduce latency while maintaining the deadlock-free property that is critical for circuit-switched routing mechanisms. MECA also allows multiple broadcast trees to be used concurrently without incurring deadlock. Simulation results highlight the advantages of MECA over other circuit-switched routing techniques. >

Over-the-cell channel routing for high performance circuits

Abstract: The authors present a new three-layer over-the-cell channel routing algorithm, WILMA3 (wire length minimization algorithm 3), for high-performance circuits. This router not only minimizes the channel height by OTC routing but also minimizes the net lengths. They have also developed a two-layer router, WILMA2. Both WILMA2 and WILMA3 achieve reduction in channel height while maintaining the net length greater than its length in the two-layer channel routing. Experimental results with WILMA2 indicated that WILMA2 can produce routings that are comparable to existing two-layer over-the-cell routers. Both WILMA2 and WILMA3 achieved these results, while maintaining the net length bound. >

Simple path selection for optimal routing on processor arrays

Abstract: In this paper, we consider the problem of permutation routing in twoand three-dimensional mesh-connected processor arrays. We present new on-line and off-line routing algorithms, all of which are optimal to within a small additive term. In particular, our results include the following: 1. An off-line algorithm for routing a permutation in an n x n mesh in time 2n – 1 using buffers of size 4. 2. An off-line algorithm for routing a permutation in an n x n x n mesh in time 372– 1 using buffers of size 10. 3. An on-line randomized algorithm for routing a permutation in an n x n x n mesh in time 3n + O(log n) time using constant sized buffers, ●Supported in part by NSF Grant NSF-CCR-87-04513. This work was done while visiting NEC Research Institute. E-mail: kakl@harvard.harvard .edu t This work was done while visiting N EC Research Institute. E-mail: krizanc@cs. rochester.edu t E-mail: satish@research .nj.nec.com Permission to copy without fee all or part of this material is granted provided that the copies are not made or distributed for direct commercial advantage, the ACM copyright notice and the title of the publication and its date appear, and notice is given that copying is by permission of the Association for Computing Machinety. To copy otherwise, or to republish, requires a fee and/or speeitic permission. SF’AA ’9261921CA @1992 ACM O-89791-484-8192K)O0610023. . . . . .. $1.50 23 4. An on-line randomized algorithm for routing a permutation in an n x n torus in time n + O(log n ) time using constant sized buffers. Also, while optimal algorithms for routing on two-dimensional meshes were known, we give new algorithms that are simpler and/or require smaller buffers.

Distributed routing with labeled distances

Abstract: The author presents, verifies, and analyzes a new routing algorithm called the labeled distance-vector routing algorithm (LDR), that is loop-free at every instant, eliminates the counting-to-infinity problem of the distributed Bellman-Ford (DBF) algorithm, operates with arbitrary link and node delays, and provides shortest paths a finite time after the occurrence of an arbitrary sequence of topological changes. In contrast to previous successful approaches to loop-free routing, LDR maintains DBF's row-independence property and does not require internodal coordination spanning multiple loops. The new algorithm is shown to be loop-free and to converge in a finite time after an arbitrary sequence of topological changes. Its performance is compared with the performance of other distributed routing algorithms. >

Improving FPGA routing architectures using architecture and CAD interactions

Abstract: The interactions between the CAD tools that are used to configure the routing resources of a field-programmable gate array (FPGA) and the design of the routing architecture itself are examined. Such an understanding is used to determine where to reduce the number of routing switches in the FPGA while maintaining routability. Experiments are used to study a switch block that was previously thought to have unacceptably low flexibility. It is shown that the performance of this switch block can be improved by adapting the global router to require less flexibility in the architecture, and by careful placement of physical pins on the logic blocks. It is demonstrated that the fewest routing switches are required when each logical pin appears on only one side of the logic cell rather than two or more. >