Showing papers on "Destination-Sequenced Distance Vector 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.

The Vehicle Routing Problem with Time Windows: Minimizing Route Duration

Abstract: We investigate the implementation of edge-exchange improvement methods for the vehicle routing problem with time windows with minimization of route duration as the objective. The presence of time windows as well as the chosen objective cause verification of the feasibility and profitability of a single edge-exchange to require an amount of computing time that is linear in the number of vertices. We show how this effort can, on the average, be reduced to a constant. INFORMS Journal on Computing, ISSN 1091-9856, was published as ORSA Journal on Computing from 1989 to 1995 under ISSN 0899-1499.

Provably good 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 tree formulation. The authors first present several heuristics with good performance, based on an analog of Prim's minimum spanning tree construction. Next, they give an algorithm which simultaneously minimizes both routing cost and the longest interconnection path, so that both are bounded by small constant factors away from optimal. They also show that geometry helps in routing: in the Manhattan plane, the total wire length for Steiner routing improves to 3/2*(1+(1/ epsilon )) times the optimal Steiner tree cost, while in the Euclidean plane, the total cost is further reduced to (2/ square root 3)*(1+(1/ epsilon )) times optimal. The method generalizes to the case where varying wire length bounds are prescribed for different source-sink paths. Extensive simulations confirm that this approach works well. >

Multicasting for multimedia applications

Abstract: The authors investigate multicast routing for high-bandwidth delay-sensitive applications in a point-to-point network as an optimization problem. They associate an edge cost and an edge delay with each edge in the network. The problem is to construct a tree spanning the destination nodes, such that it has the least cost, and so that the delay on the path from the source to each destination is bounded. Since the problem is computationally intractable, the authors present an efficient approximation algorithm. Experimental results through simulations show that the performance of the heuristic is near optimal. >

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.

An O(log N) deterministic packet-routing scheme

Abstract: A deterministic O(log N)-time algorithm for the problem of routing an aribitrary permutation on an N-processor bounded-degree network with bounded buffers is presented.Unlike all previous deterministic solutions to this problem, our routing scheme does not reduce the routing problem to sorting and does not use the sorting network of Ajtai, et al. [1]. Consequently, the constant in the run time of our routing scheme is substantially smaller, and the network topology is significantly simpler.

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.

Exact analysis of hot-potato routing

Abstract: The authors consider a form of packet routing known as hot potato routing or deflection routing. Its striking feature is that there are no buffers at intermediate nodes. Thus packets are always moving (possibly in the 'wrong' direction), giving rise to the term 'hot potato'. They give a simple deterministic algorithm that on a n*n torus will route a random instance in 2n+O(log n) steps with high probability. They add random delays to this algorithm so that it solves the permutation routing problem on the torus in 9n steps with high probability, on every instance. On a hypercube with N=2/sup n/ nodes, they give a simple deterministic algorithm that will route a random instance in O(n) steps with high probability. Various other results are discussed. >

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.

Routing technique for a hierarchical interprocessor-communication network between massively-parallel processors.

Abstract: A new routing process for a single-instruction-multiple-data (SIMD) multi-level hierarchical network or nodes, (N111-N113, N121-N123, N131-N133, N141-N143, N211, N212, N221, N222, N311 and N312), which are arranged in clusters and interconnected by dual, unidirectional channels, are used to send data packets including routing address information during a succession of routing cycles from transmitting ones to receiving ones of a larger number of parallel processors (e.g., 4096 processors arranged in a hierarchy of 8 cabinets, each of which contains a cluster of 8 circuits boards, with each circuit board containing a cluster of 64 processors). Each of the nodes (N111-N113, N121-N123, N131-N133, N211, N212, N221, N222, N311 and N312) includes a storage buffer having a capacity equal to one more than the number of channels at that level. This new routine process guarantees prevention of deadlock between levels and buffer overflow, and offers high-speed, low-cost interprocessor communication for SIMD computer.

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.

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. >

Optimal routing and buffer allocation for a class of finite capacity queueing systems

Abstract: The problem of routing jobs to K parallel queues with identical exponential servers and unequal finite buffer capacities is considered Routing decisions are taken by a controller which has buffering space available to it and may delay routing of a customer to a queue Using ideas from weak majorization, it is shown that the shorter nonfull queue delayed (SNQD) policy minimizes both the total number of customers in the system at any time and the number of customers that are rejected by that time The SNQD policy always delays routing decisions as long as all servers are busy Only when all the buffers at the controller are occupied is a customer routed to the queue with the shortest queue length that is not at capacity Moreover, it is shown that, if a fixed number of buffers is to be distributed among the K queues, then the optimal allocation scheme is the one in which the difference between the maximum and minimum queue capacities is minimized, ie becomes either 0 or 1 >

Scalable inter-domain routing architecture

Abstract: As internets grow, both in size and in the diversity of routing requirements, providing inter-domain routing that can accommodate both of these factors becomes increasingly crucial. We propose a scalable inter-domain routing architecture consisting of two major components: source-demand routing (SDR) and node routing (NR).The NR component pre-computes and installs routes that are shared by a significant number of sources. These generic routes are commonly used and warrant wide propagation. The SDR component provides on-demand computation and installation of specialized routes that are not shared by enough sources to justify computation by NR. The potentially large number of different specialized routes, combined with their sparse utilization, make them too costly to support with the NR mechanism. Together NR and SDR address the issue of scaling to global internet sizes without restricting the availability of a diverse set of routes. Routing will adapt naturally over time to changing traffic patterns and new services by shifting computation and installation of particular types of routes between the two components.To complement earlier discussions of SDR design choices [3], this paper evaluates the algorithmic design choices for the NR component in terms of scalability and functionality. In addition, we discuss mechanisms for improving the scaling properties of link-state SDR, and for integrating the two components of the architecture.

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.

Performance comparison of routing protocols using MaRS: distance-vector versus link-state

Abstract: There are two approaches to adaptive routing protocols for wide-area store-and-forward networks: distance-vector and link-state. Distance-vector algorithms use O(N x e) storage at each node, whereas link-state algorithms use O(N2), where N is the number of nodes in the network and e is the average degree of a node. The ARPANET started with a distance-vector algorithm (Distributed Bellman-Ford), but because of long-lived loops, changed to a link-state algorithm (SPF). We show, using a recently developed network simulator, MaRS, that a newly proposed distance-vector algorithm (ExBF) performs as well as SPF. This suggests that distance-vector algorithms are appropriate for very large wide-area networks.

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. >

A parallel algorithm for channel routing problems (VLSI)

Abstract: A parallel algorithm for channel routing problems is presented. The problem is to route the given interconnections between two rows of terminals on a multilayer channel where the channel area must be minimized. The current advancement of VLSI chip technology allows one to use four layers composed of two metal layers and two polysilicon layers for routing in a chip. The goal of the proposed parallel algorithm is to find the near-optimum routing solution for the given interconnections in a short time. The algorithm is applied to four-layer channel routing problems requiring n*m*2 processing elements for the n-net-m-track problem. The algorithm has three advantages over the conventional algorithms: (1) it can be easily modified for accommodating more than four-layer problems; (2) it runs both on a sequential machine and on a parallel machine with maximally n*m*2 processors; and (3) the program size is very small. The algorithm is verified by solving seven bench-mark problems. >

On channel segmentation design for row-based FPGAs

Abstract: The channel segmentation design problem for row-based FPGAs is to design a segmented channel to maximize the probability of successful routing. In this pa- per, we present an algorithm which takes an arbitrary net distribution and an integer K (specifying the maximum number of segments allowed in routing a net) as inputs, and automatically generates a segmented channel which is most suitable for K-segment channel routing. Our algo- rithm was tested extensively over various net distributions. We also present a new algorithm for segmented channel routing based on reducing the problem to the maximum independent set problem for undirected graphs.

Minimum-expected-delay alternate routing

Abstract: The authors consider the problem of finding a routing strategy that minimizes the expected delay from every source to a single destination in a network in which each link fails and recovers according to a Markov chain. It is assumed that each node knows the current state of its own outgoing links and the state-transition probabilities for every link of the network. It is shown that the general problem is #P-complete, and two special cases are considered: case 1 assumes the network is a directed acyclic graph oriented toward the destination, and case 2 assumes that the link states are independent from slot to slot. For each case, it is proved that the optimal routing strategy has a simple state-independent representation. An efficient algorithm is presented for finding the optimal strategy.

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. >

Information routing and reliability issues in distributed sensor networks

Abstract: Communication issues and problems in information routing in distributed sensor networks (DSNs) are considered. Two important communication constraints, viz., the delay constraint and the reliability constraint, are identified, and their impact on information routing is discussed. It is shown that the maximum end-to-end delay in a network depends on the diameter of the network, and efficient distributed algorithms are presented to determine the diameter of asynchronous networks. A distributed algorithm that determines the diameter of an asynchronous tree network when an arbitrary node in the network initiates the algorithm is introduced. An efficient algorithm for determining the diameter when multiple nodes initiate the algorithm is presented. An algorithm to determine the diameter of arbitrary networks is presented, and its message complexity is shown. Effects of link/node failures on network delay are studied, and important network structure design criterion are discussed. The distributed, dynamic routing algorithms are reviewed, and their adaptation to DSN environments is discussed. >

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. >

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. >

A routing algorithm for virtual circuit data networks with multiple sessions per O—D pair

Abstract: In virtual circuit networks, all the packets in a session are transmitted over exactly one path established between the origin and the destination. For each origin–destination pair, it is assumed that there are multiple sessions. We consider the problem of choosing a path for each session so as to minimize the average packet delay in the network. We formulate this problem as a nonlinear multicommodity flow problem with integer decision variables. An iterative scheme that is similar to local search is developed to solve this problem. In each iteration, we apply Lagrangean relaxation and a multiplier adjustment procedure to solve a restricted problem. We show that the Lagrangean dual problem can be solved exactly by solving a convex program. In computational experiments, our algorithm determines solutions that are within 1% of an optimal solution in minutes of CPU time for networks with 26–61 nodes. In addition, we show that our proposed algorithm is better both theoretically and computationally than K(0)-ordering, single-path routing, or round-off Frank–Wolfe heuristics.