Showing papers on "Static routing published in 1985"

A warehouse location-routing problem

Abstract: The interdependence between distribution center location and vehicle routing has been recognized by both academics and practitioners. However, only few attempts have been made to incorporate routing in location analysis. This paper defines the Warehouse Location-Routing Problem (WLRP) as one of simultaneously solving the DC location and vehicle routing problems. We present a mixed integer programming formulation of the WLRP. Based on this formulation, it can be seen that the WLRP is a generalization of well-known and difficult location and routing problems, such as the Location-Allocation Problem and the Multi-depot Vehicle Dispatch Problem. It is therefore a large and complex problem which cannot be solved using existing mixed-integer programming techniques. We present a heuristic solution method for the WLRP, based on decomposing the problem into three subproblems. The proposed method solves the subproblems in a sequential manner while accounting for the dependence between them. We discuss a large-scale application of the proposed method to a national distribution company at a regional level.

A computational comparison of algorithms for the inventory routing problem

Abstract: The inventory routing problem is a distribution problem in which each customer maintains a local inventory of a product such as heating oil and consumes a certain amount of that product each day. Each day a fleet of trucks is dispatched over a set of routes to resupply a subset of the customers. In this paper, we describe and compare algorithms for this problem defined over a short planning period, e.g. one week. These algorithms define the set of customers to be serviced each day and produce routes for a fleet of vehicles to service those customers. Two algorithms are compared in detail, one which first allocates deliveries to days and then solves a vehicle routing problem and a second which treats the multi-day problem as a modified vehicle routing problem. The comparison is based on a set of real data obtained from a propane distribution firm in Pennsylvania. The solutions obtained by both procedures compare quite favorably with those in use by the firm.

Fault-Tolerant Routing in DeBruijn Comrnunication Networks

Abstract: A class of communication networks which is suitable for "multiple processor systems" was studied by Pradhan and Reddy. The underlying graph (to be called Shift and Replace graph or SRG) is based on DeBruijn digraphs and is a function of two parameters r and m. Pradhan and Reddy have shown that the node-connectivity of SRG is at least r. The same authors give a routing algorithm which generally requires 2m hops if the number of node failures is ≤(r -1). In this paper we show that the node-connectivity of SRG is (2r - 2). This would immediately imply that the system can tolerate up to (2r - 3) node failures. We then present routing methods for situations with a certain number of node failures. When this number is ≤(r - 2) our routing algorithm requires at most m + 3 + logr m hops if 3 + logr m ≤m. When the number of node failures is ≤(2r - 3) our routing algorithm requires at most m + 5 + logr m hops if 4 + logr m ≤ m. In all the other situations our routing algorithm requires no more than 2m hops. The routing algorithms are shown to be computationally efficient.

Randomized routing on fat-tress

Abstract: Fat-trees are a class of routing networks for hardwareefficient parallel computation. This paper presents a randomized algorithm for routing messages on a fat-tree. The quality of the algorithm is measured in terms of the load factor of a set of messages to be routed, which is a lower bound on the time required to deliver the messages. We show that if a set of messages has load factor λ = Ω(lg n lg lg n) on a fat-tree with n processors, the number of delivery cycles (routing attempts) that the algorithm requires is O(λ) with probability 1-O(1/n). The best previous bound was O(λ lg n) for the off-line problem where switch settings can be determined in advance. In a VLSI-like model where hardware cost is equated with physical volume, we use the routing algorithm to demonstrate that fat-trees are universal routing networks in the sense that any routing network can be efficiently simulated by a fat-tree of comparable hardware cost.

Integrated network controller for a dynamic nonhierarchical routing switching network

Abstract: A nonhierarchial switching system employing a modified unified algorithm for developing link sizes for paths that connect switches in the system and routing sequences for the switches in the system, and further employing means for updating the routing sequences to minimize potential blocking in the network. In one embodiment, the modified unified algorithm develops improved link size determinations by taking advantage of traffic sensitive dynamic routing on the alternate paths available in the nonhierarchial switching system for connecting any switch to any other switch in the system. Updating of the routing sequences is achieved in that embodiment by evaluating the least loaded path for each potential connection of two switches in the system and, when appropriate, by installing the least loaded path as the second choice path in the routing sequence for that potential connection.

Routing Region Definition and Ordering Scheme for Building-Block Layout

Abstract: We present a new routing region definition and ordering (RRDO) scheme for building block layout. Given an arbitrary placement of rectangular blocks (including the case with cycles in the channel precedence constraints), without modifying the placement, our scheme defines and orders channels so that when a new channel is being routed, its width can be expanded or contracted without destroying the previously routed channels. The cycles in the channel precedence constraints are broken by introducing a new kind of channel--the L-shaped channels. Unlike switchboxes, L-shaped channels can be expanded or contracted to permit the completion of routing without rerouting other existing channels. An efficient greedy RRDO algorithm has been implemented, which tries to generate as few L-shaped channels as possible since L-shaped channels are harder to route than straight channels. Our algorithm represents routing regions by a floor plan graph, for which we provide a precise definition and a construction algorithm. The experimental results of the RRDO algorithm are promising.

Routing method in computer aided customization of a two level automated universal array

Abstract: A routing method implemented in the stored programs of a digital computer ich is programmably operated to generate the wire interconnect masks for a two level metallization automated universal array having undefined roadbeds between rows of cells comprised of identical semiconductor device basic units which are further interconnected to provide a particular integrated circuit structure. Conductor routing is provided by a computer aided design system that, among other things, carries out a route analysis process which determines in which roadbed each wire should be tentatively routed in conjunction with generating a routing density profile for minimizing congestion for a particular circuit design and when the roadbed density is exceeded, certain wires are removed under a set of criteria for routing by a pathfinder routing process. Following route analysis, detailed routing and rerouting is performed sequentially by a direct routing process, a greedy channel routing process, and a pathfinder routing process with rerouting being performed after each channel router and pathfinding process. Furthermore, the greedy channel routing process makes a single pass from left to right in all wires which cross successive points simultaneously and, if necessary, deleting a wire or wires which are then rerouted by the pathfinding process.

WEAVER: A Knowledge-Based Routing Expert

Abstract: In this paper we describe WEAVER, a channel/switch-box knowledge-based routing program. WEAVER considers all the important routing metrics such as 100% routability, minimum routing area, minimum wire length, and minimum number of vias simultaneously. It allows pre-routed nets, and user interaction throughout the entire routing process. It also relaxes unnecessary constraint of assigning different layers to different directions, the constraint imposed by all of the current channel and switch-box routers. WEAVER is a grid-based router that utilizes two interconnection layers and can be easily expanded to route any shape routing area such as 'T' or '+'. Implemented in OPS5, a production system language, WEAVER routinely produces routings requiring less area than routers that focus on a single routing metric.

Two-Dimensional Router for Double Layer Layout

Abstract: A heuristic algorithm for two dimensional routing utilizing two distinct layers is presented. It is assumed that all terminals are on the boundary of a rectilinear routing region with or without initial routes present. The router produces a Manhattan-style routing collapsed into one layer. Another program decides the layering, however, it is not described here. By default, when the layering program is not used, vertical segments of routes are placed on one layer, horizontal on the other.

Fault location techniques for distributed control interconnection networks

Abstract: One class of networks suitable for use in parallel processing systems is the multistage cube network. The authors focus on fault location procedures suitable for use in networks that use distributed routing control through the use of routing tags and message transmission protocols. Faults occurring in the data lines can corrupt message routing tags transmitted over them and thereby cause misrouting of messages. Protocol lines (used in handshaking between network sources and destinations), if faulty, can prevent a message path from being established or can cause the path to `lock up' once transmission of data has begun. These faults have more pronounced effects on the network performance than faults previously considered for centralized routing control systems. The single-fault location procedures presented form a logical superset to those of the centralized control systems (where message routing is dictated by the actions of a global control unit) and can be adapted for use in both circuit and packet switching networks.

Network routing arrangement

Abstract: Circular paths in a multinode connection are avoided by passing an adaptive routing state, from node to node, which specifies the path options that the current node may use in its selection of a next step in the connection. The routing state, which is characterized by, for example, a single digit, is updated by the current node and is a function of the recent path history of the connection. The single-digit routing state controls the advancement of the connection by specifying whether the next selected step can be either a forward step, a null step or a backward step, or any combination thereof. A forward step advances the connection toward its destination, a null step does not advance the connection and a backward step causes the connection to step backward to a node not yet in the connected path. When a node selects a next step, it adapts the routing state digit to reflect its selection and passes the new routing state digit to the next node.

Double Loop Network Architectures--A Performance Study

Abstract: Single loop networks tend to become unreliable and suffer from poor performance when the number of nodes in the network becomes large. One approach to increasing reliability and improving performance is to use a double loop. In this paper, the performance (using analytical and simulation models) of a class of highly reliable double loop network architectures is presented. The richer topology of double loop networks allows more sophisticated routing algorithms to be used. Several routing algorithms are studied, including: fixed, adaptive to failure, and fully adaptive to failure and traffic load conditions.

Distributed Multi-Destination Routing: The Constraints of Local Information

Abstract: In computer networks, message routing is often accomplished by network nodes using local information. The unavailability of global information intuitively makes hard routing problems virtually impossible. This paper formalizes this intuition by examining a hard (NP-complete) routing problem, the problem of multi-destination routing. It is shown that with only limited information it is impossible to optimize network utilization for the multi-destination routing problem. Moreover, it is impossible to even approximate optimality to within a specific tolerance. Several versions of this result are proved; the versions differ in terms of the amount of information available at a node, and the extent to which the problem cannot be approximated. An improved local information algorithm is presented which is best possible amongst local information algorithms.

A routing algorithm for interconnected local area networks

Abstract: An algorithm to be used for distributing routing information between interconnected Local Area Networks (LANs) is presented and its dynamic behaviour is described. The operation of the routing algorithm is completely distributed and automatically adapts to topology changes. Routing information is propagated in the form of Routing Vectors broadcast by gateways. Routes are chosen based on mimimum distance (in hops) to a destination subnet. The paper presents the results of simulation studies of the performance of the algorithm. Both simulation and analysis of the algorithm show that routing tables stabilise to give a minimum distance route to each destination subnet after a change in network topology. Formulae are derived for the upper bound of the number of routing vectors transmitted during initialisation or as a result of a topology change. This upper bound is shown to be independent of any network topology. The routes are loop free when the tables in all gateways have stabilised, but the tables may temporarily give looped routes for a period after a component failure. This can lead to a “bouncing” effect of routing vectors exchanged between gateways. Several modifications of the basic routing mechanism are given which minimise the number of routing vectors exchanged and hence the time to reach stability.

Bifurcated routing in computer networks

Abstract: This paper presents a characterization and a survey of multiple path routing in computer networks. It also develops a routing protocol that achieves load sharing and combines the strengths of both virtual circuit and datagram networks.

New Routing and Preemption Algorithms for Circuit-Switched Mixed-Media Networks

Abstract: New routing and preemption algorithms were developed for circuit-switched networks such as the Defense Switched Network that include both broadcast satellite and point-to-point transmission media. Three classes of routing procedures were evaluated: (1) mixed-media routing with fixed routing tables and call processing rules that included crankback and remote earth-station querying, (2) adaptive mixed-media routing which adapted routing tables after network damage, and (3) precedence flooding which routed high-precedence calls using flooding techniques. A new preemption technique called guided preemption was also evaluated. When guided preemption is used, lower precedence calls to preempt are selected after examining the paths of all calls previously routed through a switch. Call paths are added to the call-setup-success common-channel-signalling (CCS) packet at the call destination and then read in and stored within each switch in the call path as this message travels back to the call source. Tools developed to evaluate algorithms included a steady-state network analysis program, a call-by-call simulator, and the EISN testbed network described in a companion paper by H.M. Heggestad. Analytic results with the simulator and the steady-state analysis program indicated that the new routing algorithms provided reduced point-to-point blocking probabilities after damage without adding extra trunking. Best performance was obtained with adaptive mixed-media routing and precedence flooding techniques. Guided preemption preempted fewer low-precedence calls than blind preemption as used in AUTOVON to complete the same number of high-precedence calls.

Customer routing to parallel servers with different rates

Abstract: We consider the problem of routing customers to parallel servers having different rates. There are no buffers in the system. Each customer must be rooted to a server immediately upon its arrival and if the server to which it is routed is occupied, then the customer is aborted. The aim is to maximize throughput (the proportion of customers which are successfully routed to a free server), when the routing must be done without knowing which servers are occupied and which are free. An upper bound on the throughput is found for a general renewal arrival process and geometric service times. Furthermore, a new routing policy, the golden ratio policy, is suggested and shown to approach a limit which is within at least 98.4 percent of the upper bound. The golden ratio policy is a generalization of the round robin policy, when the service rates of the servers are different.

A Method of Improving the Terminal Assignment in the Channel Routing for Gate Arrays

Abstract: The channel router, which routes a rectangular channel with two rows of terminals along its top and bottom sides, is extensively used for the automatic routing of gate arrays. It is well known that in this routing method the routing can not be performed when the vertical constraint graph contains cycles. This paper deals with the problem of eliminating cycles in the vertical constraint graph by interchanging the nets assigned to logically equivalent terminals before channel routing. A heuristic algorithm is proposed for this problem. This algorithm yields a locally optimum assignment of nets to terminals, in the sense that the number of independent cycles in the vertical constraint graph of a resultant assignment can not be reduced by interchanging any pair of the nets assigned to logically equivalent terminals. Furthermore, in order to speed up the operation of this algorithm, it is shown that the checking as to whether or not the number of independent cycles in the vertical constraint graph is reduced can be done by noting only its subgraph, when a pair of nets assigned to logically equivalent terminals are interchanged. Experimental results have indicated that this proposed algorithm is efficient.

Rectilinear area routing: a channel router approach

Abstract: A final router has been developed which operates upon the rectilinear channel routing areas created by rectilinear macrocells. The router supports input and output pins on all sides of the rectilinear area. After the channel density estimation for the entire assembly is provided by a global router, the rectilinear area is partitioned into smaller rectangular regions which can be routed by applying traditional channel router methods. The regions are ordered, and a global routing of the nets within the rectilinear area is performed. The regions are routed individually while providing a smooth area routing. Algorithms for each phase of the final routing are described. Special rectilinear topological considerations are presented. The algorithms are implemented in Pascal on a DEC-SYSTEM 20 as a part of SLS - Sandia layout system, a hierarchical layout system.

An Algorithm for One and Half Layer Channel Routing

Abstract: Channel routing is one of the key problems in the automatic layout design of LSI chips This paper presents an efficient routing algorithm for one-and-half layer channel model which is based on single layer metal mask and fixed polysilicon crossunders in CMOS gate array The algorithm makes parallel horizontal routing in each zone by means of ordering and prediction The nets contend for crossunders in a greedy approach This results in higher probability of routing success and less crossunders occupied (equally less via holes) Furthermore, by inserting interactive information at the same time of execution if necessary, the router provides more chances of 100% routing success

Dynamic material handling for a class of flexible manufacturing systems

Abstract: A real-time hierarchical routing control scheme for a large class of material handling systems is presented. The higher level (coordinator) performs resource allocation tasks and supplies parameter values to the lower (local control) level. The lower level operates in an autonomous (without continuous supervision) and distributed fashion. If state information is made available to the coordinator, the routing strategy can furthermore be adaptively adjusted.

An algorithm for two-layer channel routing

Abstract: In this paper we show that any two-terminal channel routing problem of density d can be solved in a two-layer grid of width ω=(3/2)d+O(1) by using a model in which two wires are permitted to overlap for not more than a constant distance. This is an asymptotical improvement over the best known result ω=2d−1. The algorithm presented here has the following additional properties: (i) there are at most 6 pairs of over-lapping edges for any two wires produced by it, (ii)it uses 6n contacts, where n is the number of nets to be connected, (iii)it can be implemented to run in time O(n). An extension of the algorithm to the multi-terminal problem is also discussed.

Sensitivity analysis of a simple routing strategy

Abstract: For several classes of queueing networks, on-line perturbation techniques have been used to determine parametric sensitivity of performance. These techniques typically assume "small" perturbations affecting only the occurrence time of events in the system. In networks with dynamic routing, however, queue length perturbations are also inevitably created. In order to investigate the phenomena involved in this case, a simple routing strategy is considered, based on comparing queue length to a given threshold parameter. A process is presented for evaluating throughput sensitivity with respect to this parameter along an observed sample path. Compared to earlier results, some additional information is now needed for tracking state perturbations. It is shown, however, that sensitivity analysis can still be performed on-line and provide accurate results.