Showing papers on "Multipath routing published in 1993"

A survey of wormhole routing techniques in direct networks

Abstract: Several research contributions and commercial ventures related to wormhole routing, a switching technique used in direct networks, are discussed. The properties of direct networks are reviewed, and the operation and characteristics of wormhole routing are discussed in detail. By its nature, wormhole routing is particularly susceptible to deadlock situations, in which two or more packets may block one another indefinitely. Several approaches to deadlock-free. routing, along with a technique that allows multiple virtual channels to share the same physical channel, are described. In addition, several open issues related to wormhole routing are discussed. >

Packet Routing in Dynamically Changing Networks: A Reinforcement Learning Approach

Abstract: This paper describes the Q-routing algorithm for packet routing, in which a reinforcement learning module is embedded into each node of a switching network. Only local communication is used by each node to keep accurate statistics on which routing decisions lead to minimal delivery times. In simple experiments involving a 36-node, irregularly connected network, Q-routing proves superior to a nonadaptive algorithm based on precomputed shortest paths and is able to route efficiently even when critical aspects of the simulation, such as the network load, are allowed to vary dynamically. The paper concludes with a discussion of the tradeoff between discovering shortcuts and maintaining stable policies.

Cyclic transfer algorithms for multivehicle routing and scheduling problems

Abstract: This paper investigates the application of a new class of neighborhood search algorithms—cyclic transfers—to multivehicle routing and scheduling problems. These algorithms exploit the two-faceted decision structure inherent to this problem class: First, assigning demands to vehicles and, second, routing each vehicle through its assigned demand stops. We describe the application of cyclic transfers to vehicle routing and scheduling problems. Then we determine the worst-case performance of these algorithms for several classes of vehicle routing and scheduling problems. Next, we develop computationally efficient methods for finding negative cost cyclic transfers. Finally, we present computational results for three diverse vehicle routing and scheduling problems, which collectively incorporate a variety of constraint and objective function structures. Our results show that cyclic transfer methods are either comparable to or better than the best published heuristic algorithms for several complex and important ...

How bad is naive multicast routing

Abstract: In previous approaches to routing multicast connections in networks, the emphasis has been on the source transmitting to a fixed set of destinations (the multicast group). There are some applications where destinations will join and leave the multicast group. Under these conditions, computing an 'optimal' spanning tree after each modification may not be the best way to proceed. An alternative is to make modest alterations to an existing spanning tree to derive a new one. An extreme, though nonoptimal, variation of this is to use minimal cost source to destination routing for each destination, effectively ignoring the existing multicast tree. The authors examine just how nonoptimal these trees are in random general topology networks and conclude that they are worse by only a small factor. The factor is reduced still further if a hierarchy is imposed on the random network to give a more realistic model. >

Computing approximate blocking probabilities for large loss networks with state-dependent routing

Abstract: A reduced load approximation (also referred to as an Erlang fixed point approximation) for estimating point-to-point blocking probabilities in loss networks (e.g., circuit switched networks) with state-dependent routing is considered. In this approximation scheme, the idle capacity distribution for each link in the network is approximated, assuming that these distributions are independent from link to link. This leads to a set of nonlinear fixed-point equations which can be solved by repeated substitutions. The accuracy and the computational requirements of the approximation procedure for a particular routing scheme, namely least loaded routing, is examined. Numerical results for six-node and 36-node asymmetric networks are given. A novel reduced load approximation for multirate networks with state-dependent routing is also presented. >

A comparison of adaptive wormhole routing algorithms

Abstract: Improvement of message latency and network utilization in torus interconnection networks by increasing adaptivity in wormhole routing algorithms is studied. A recently proposed partially adaptive algorithm and four new fully-adaptive routing algorithms are compared with the well-known e-cube algorithm for uniform, hotspot, and local traffic patterns. Our simulations indicate that the partially adaptive north-last algorithm, which causes unbalanced traffic in the network, performs worse than the nonadaptive e-cube routing algorithm for all three traffic patterns. Another result of our study is that the performance does not necessarily improve with full-adaptivity. In particular, a commonly discussed fully-adaptive routing algorithm, which uses 2n virtual channels per physical channel of a k-ary n-cube, performs worse than e-cube for uniform and hotspot traffic patterns. The other three fully-adaptive algorithms, which give priority to messages based on distances traveled, perform much better than the e-cube and partially-adaptive algorithms for all three traffic patterns. One of the conclusions of this study is that adaptivity, full or partial, is not necessarily a benefit in wormhole routing.

Minimum crosstalk channel routing

Abstract: As technology advances, interconnection wires are placed in closer proximity and circuits operate at higher frequencies. Consequently, reduction of crosstalk between interconnection wires becomes an important consideration in VLSI design. In this paper, we study the gridded channel routing problem with the objective of satisfying crosstalk constraints for the nets. We proposed a new approach to the problem which utilizes existing channel routing algorithms and improves upon the routing results by permuting the routing tracks. The permutation problem is proven to be NP-complete. A novel mixed ILP formulation and effective procedures for reducing the number of variables and constraints in the mixed ILP formulation are then presented. The new algorithm is tested on three large benchmark circuits as well as many randomly generated circuits. The experimental results are very promising.

Fault-tolerant wormhole routing in meshes

Abstract: It is shown how to modify the routing algorithms produced by the turn model to encompass dynamic faults The authors describe how to modify the negative-first routing algorithm, which the turn model produces for n-dimensional meshes without virtual channels, to make it one-fault tolerant Simulations of the one-fault-tolerant routing algorithms in a two-dimensional mesh indicate that misrouting increases communication latencies significantly at high throughputs The conclusion is that misrouting should be used only for increasing the degree of fault tolerance, never for just increasing adaptiveness Finally, the authors describe how to modify the negative-first routing algorithm to make it (n-1)-fault tolerant for n-dimensional meshes

A Distributed Reinforcement Learning Scheme for Network Routing

Abstract: In this paper we describe a self-adjusting algorithm for packet routing, in which a reinforcement learning module is embedded into each node of a switching network. Only local communication is used to keep accurate statistics at each node on which routing policies lead to minimal delivery times. In simple experiments involving a 36-node, irregularly connected network, this learning approach proves superior to a nonadaptive algorithm based on precomputed shortest paths.

Economical payload stream routing in a multiple-ring network

Abstract: The present invention is directed to a system for routing data between rings. A routing symbol is provided, and as it crosses a bridge, the local target address of the bridge is dropped, and the local source address of the bridge node (in the far side ring) is added to the routing symbol. Fields are shifted in the routing symbol so that the value that was in a hop field becomes the local target address in the new ring. Because the routing symbol that arrives at the ultimate target has been transformed into a source node list, the return path is available to the target.

Dispersity routing in high-speed networks

Abstract: Dispersity routing distributes the data between a source and destination over several paths through the network, rather than concentrating it on a single path. Non-redundant and redundant dispersity routing techniques are described. By using dispersity routing on virtual circuits, that operate similar to the TASI circuits used in voice networks, long, bursty data sources can share channels without buffering in the network or resequencing packets. This sharing ability is demonstrated by an example that has characteristics and requirements similar to those in medical image transmission. Dispersity routing is better able to deal with unexpected network loads than conventional, single channel systems. This ability is demonstrated by allowing a rogue source to upset the expected statistical utilization of the network.

Choice of allocation granularity in multipath source routing schemes

Abstract: Multipath source routing schemes can be distinguished by their choice of allocation granularity. The schemes proposed in the literature advocate a per-connection allocation wherein all the packets of a connection are constrained to follow the same path. The authors believe that a smaller allocation granularity permits a finer control to be exerted and would result in improved performance, especially in the presence of bursty traffic sources. A simple two-node network is used to compare the performance of both allocation schemes. An analytical model is developed to compute the resequencing delay distribution for the per-packet allocation. It is observed that as the burstiness of the arrival process increases, the per-packet allocation is able to accommodate bursts in a more graceful fashion, resulting in better performance. The per-packet allocation also permits a more equitable distribution of network resources than the per-connection. >

Algorithms for the vehicle routing problems with time deadlines

Abstract: SYNOPTIC ABSTRACTThe vehicle routing problem with time deadlines (VRPTD) is an extension of the classical vehicle routing problem (VRP) with constraints on the latest allowable time (deadline) for servicing each customer. The objective is to minimize the number of vehicles and the distance travelled without exceeding the capacity of the vehicles or violating the customer deadlines. VRPTD belongs to the class of NP-complete problems. As the computational time taken to solve such problems using exact methods is prohibitive, heuristic methods are used instead to obtain near optimal solutions for large-size problems. We develop three heuristics to solve the VRPTD: deadline sweep, push-forward insertion and genetic sectoring. The solutions obtained by these heuristics are improved using a local post-optimization procedure. Computational analysis of the three heuristics are reported on 25 problems consisting of 200 customers each with different geographical and temporal characteristics.

The Message Flow Model for Routing in Wormhole-Routed Networks

Abstract: In this paper, we introduce a new approach to deadlock-free routing in wormhole-routed networks called the message flow model. We first establish the necessary and sufficient condition for deadlock-free routing based on the analysis of the message flow on each channel. We then show how to use the model to prove that a given adaptive routing algorithm is deadlock-free. Finally, we use the method to de? velop new, efficient adaptive routing algorithms for 2D meshes and hypercubes.

A direct combination of the Prim and Dijkstra constructions for improved performance-driven global routing

Abstract: Motivated by analysis of distributed RC delay in routing trees, a new tree construction is proposed for performance-driven global routing which directly trades off between Prim's minimum spanning tree algorithm and Dijkstra's shortest path tree algorithm. This direct combination of two objective functions and their corresponding optimal algorithms contrasts with the more indirect 'shallow-light' methods. The authors' method achieves routing trees which satisfy a given routing tree radius bound while using less wire than previous methods. Detailed simulations show that these wirelength savings translate into significantly improved delay over standard MST routing in both IC and multichip module (MCM) interconnect technologies. >

Adaptive Deadlock-Free Routing in Multicomputers Using Only One Extra Virtual Channel

Abstract: We present three protocols defin ing the relationship between messages and the chan nel resources requested: request-then-hold, requestthen wait, and request-then-relinquish. Based on the three protocols, we develop an adaptive deadlockfree routing algorithm called the SP routing. The SP routing uses shortest paths and is fully-adaptive, so messages can be routed via any of the shortest paths from the source to the destination. Since it is a minimal or shortest routing, the SP routing guar antees the freedom of livelocks. The SP routing is not limited to a specific network topology. The main requirement for an applicable network topology is that there exists a deterministic, minimal, deadlock-free routing algorithm. Most ex isting network topologies are equipped with such an algorithm. In this paper, we present an adaptive deadlock-free routing agorithm for n-dimensional meshes by using the SP routing. The hardware re quired by the SP routing uses only one extra virtual channel as compared to the deterministic routing.

Fast deflection routing for packets and worms

Abstract: We consider deflection routing on the n x n mesh and torus. In deflection routing a message cannot be buffered, and is therefore always moving until it reaches its destination. In addition, routing choices have to be made locally. We give a nearly optimal deterministic algorithm for the permutation routing problem for packets, the first such result for deflection routing. We extend the deterministic algorithm to the case when the messages are worms; a contiguous physical stream of bits that must follow the head of the message uninterrupted through the network. We then give an optimal randomized algorithm for permutation routing for worms of any length up to n.

Routing multipoint connections using virtual paths in an ATM network

Abstract: The point-to-multipoint routing problem is studied for an asynchronous transfer mode (ATM) network that uses virtual paths (VPs). ATM networks with asymmetric and symmetric VPs are considered, and the performance factors studied are bandwidth and establishment and switching costs. A VP with intermediate exit, where a node that performs VP switching can copy the switched packets for the local destination, is proposed and studied. Mathematical formulations of multicast routing problems are presented, and heuristics for finding a low cost multicast routing tree, based on the transshipment simplex algorithm, are developed. >

An Efficient Timing-Driven Global Routing Algorithm

Abstract: In this paper, we propose an efficient timing-driven global routing algorithm. Unlike other conventional global routing techniques, interconnection delays are modeled and included during routing and rerouting process in order to minimize the routing area as well as to satisfy timing constraint. The timing-driven global routing problem is formulated as a multiterminal, multicommodity flow problem with integer flows and additional timing constraint. Two efficient timing-driven Steiner tree approach and one Steiner tree improving approach have been used to create initial routing results and reroute trees respectively. The algorithm has been implemented and the experimental results are quite promising.

Deadlock-Free Adaptive Routing Algorithms for the 3D-Torus: Limitations and Solutions

Abstract: In this paper, a deadlock-free adaptive routing algorithm, obtained from the application of the theory proposed in [4] to the 3D-torus, is evaluated under different load conditions and compared with other algorithms. The results show that this algorithm is very fast, also increasing the network throughput considerably. Nevertheless, this adaptive algorithm has cycles in its channel dependency graph. As a consequence, when the network is heavily loaded messages may temporarily block cyclically, drastically reducing the performance of the algorithm. Two mechanisms are proposed to avoid this problem.

An analytical model for wormhole routing in multicomputer interconnection networks

Abstract: The communication performance of the interconnection network is critical in a multicomputer system. Wormhole routing has been known to be more efficient than the traditional circuit switching and packet switching. To evaluate wormhole routing, a queueing-theoretic analysis is used. This paper presents a general analytical model for wormhole routing based on very basic assumptions. The model is used to evaluate the routing delays in hypercubes and meshes. Delays calculated are compared against those obtained from simulations, and these comparisons show that the model is within a reasonable accuracy. >

Optimal fully adaptive wormhole routing for meshes

Abstract: A deadlock-free fully adaptive routing algorithm for 2D meshes which is optimal in the number of virtual channels required and in the number of restrictions placed on the use of these virtual channels is presented. The routing algorithm imposes less than half as many routing restrictions as any previous fully adaptive routing algorithms. It is also proved that, ignoring symmetry, this routing algorithm is the only fully adaptive routing algorithm that achieves both of these goals. The implementation of the routing algorithm requires relatively simple router control logic. The new algorithm is extended, in a straightforward manner, to arbitrary dimension meshes. It needs only 4n-2 virtual channels, the minimum number of an n-dimensional mesh. All previous algorithms require an exponential number of virtual channels in the dimension of the mesh.

An Efficient Multilayer MCM Router Based on Four-Via Routing

Abstract: In this paper, we present an efficient multilayer general area router, named V4R, for MCM and dense PCB designs. It uses no more than four vias to route every net and yet produces high quality routing solutions. It combines global routing and detailed routing in one step and produces high quality detailed routing solutions directly from the given netlist and module placement. As a result, V4R is independent of net ordering, runs much faster, and uses far less memory compared to other multilayer general area routers. Experimental results show that V4R outperforms both the 3D maze router and the SLICE router significantly.

A new theory of deadlock-free adaptive multicast routing in wormhole networks

Abstract: A theory for the design of deadlock-free adaptive routing algorithms for wormhole networks has been proposed previously. This theory supplies the sufficient conditions for an adaptive routing algorithm to be deadlock-free, even when there are cyclic dependencies between channels. Also, two design methodologies have been proposed. Multicast communication refers to the delivery of the same message from one source node to an arbitrary number of destination nodes. Two multicast wormhole routing methods have been presented previously for multicomputers with 2D-mesh and hypercube topologies. This paper develops the theoretical background for the design of deadlock-free adaptive multicast routing algorithms for wormhole networks. Some basic definitions and two theorems are proposed, developing conditions to verify that an adaptive multicast routing algorithm is deadlock-free, even when there are cyclic dependencies between channels. As an example, the multicast routing algorithms presented previously are extended, so that they can take advantage of the alternative paths offered by the network. >

Prefix routing schemes in dynamic networks

Abstract: We study a routing scheme on dynamic networks called the Prefix Routing scheme. The scheme is an abstraction of source routing. It assigns fixed addresses to the nodes of the network and one label per link. A message is routed by sending it out via the link with the maximum length (i.e., the “longest”) label that is a prefix of the address of the destination node. Arbitrary insertions of links and nodes are feasible with constant adaptation cost. It is shown that any dynamic growing network can be assigned a valid Prefix Routing scheme. We characterize completely the types of fixed networks with dynamic links (i.e., networks in which only the cost of the links can vary over time) and of dynamic networks with arbitrary insertions and deletions of nodes and links (without disconnecting the network) that allow optimum routing in this scheme. A hierarchy of so-called multi-label Prefix Routing schemes is presented. The connections between Prefix Routing and static Interval Routing are presented.

Mesh Connected Computers with Fixed and Reconfigurable Buses: Packet Routing, Sorting, and Selection

Abstract: Mesh connected computers have become attractive models of computing because of their varied special features. In this paper we consider two variations of the mesh model: 1) a mesh with fixed buses, and 2) a mesh with reconfigurable buses. Both these models have been the subject matter of extensive previous research. We solve numerous important problems related to packet routing, sorting, and selection on these models. In particular, we provide lower bounds and very nearly matching upper bounds for the following problems on both these models: 1) Routing on a linear array; and 2) k-k routing, k-k sorting, and cut through routing on a 2D mesh for any k≥12. In addition we present greedy algorithms for 1-1 routing, k-k routing, cut through routing, and k-k sorting that are better on average and supply matching lower bounds. We also show that sorting can be performed in logarithmic time on a mesh with fixed buses. As a consequence we present an optimal randomized selection algorithm. Further, we provide a selection algorithm for the mesh with reconfigurable buses whose time bound is significantly better than the existing ones. Most of our algorithms have considerably better time bounds than known algorithms for the same problems.