Linear Routing Research Articles

Scheduling Production Tasks in a Two Stage FMS

The paper analyzes an existing flexible manufacturing system containing two dedicated machines with buffer space and a transportation system in the form of a robot with a linear routing. A mathematical model of the system has been developed. In general, there are batches of identical parts to be produced in the system for which the technological routes are defmed and which constitute a job-shop environment. Additionally, the set-up times for batches and particular operations are taken into account. For this model, a heuristic scheduling algorithm has been constructed. Computational exgeriments and simulation studies validate the model and the proposed algorithm.

Lower bounds for linear interval routing

Linear interval routing is a space-efficient routing method for point-to-point communication networks. It is a restricted variant of interval routing where the routing range associated with every link is represented by an interval with no wraparound. A common way to measure the efficiency of such routing methods is in terms of the maximal length of a path a message traverses. For interval routing, the upper bound and lower bound on this quantity are 2D and 2D − 3, respectively, where D is the diameter of the network. We prove a lower bound of Ω(D2) on the length of a path a message traverses under linear interval routing. We further extend the result by showing a connection between the efficiency of linear interval routing and the total2-diameter (defined in Section 4) of the network, and by presenting a family of graphs for which this lower bound is tight. © 1999 John Wiley & Sons, Inc. Networks 34: 37–46, 1999

Lower bounds for linear interval routing

Linear interval routing is a space-efficient routing method for point-to-point communication networks. It is a restricted variant of interval routing where the routing range associated with every link is represented by an interval with no wraparound. A common way to measure the efficiency of such routing methods is in terms of the maximal length of a path a message traverses. For interval routing, the upper bound and lower bound on this quantity are 2D and 2D - 3, respectively, where D is the diameter of the network. We prove a lower bound of Ω(D 2 ) on the length of a path a message traverses under linear interval routing. We further extend the result by showing a connection between the efficiency of linear interval routing and the total 2 -diameter (defined in Section 4) of the network, and by presenting a family of graphs for which this lower bound is tight.

グローバルな河川流路網情報(TRIP)を利用した世界の主要河川の流出量による地表面数値モデルの検証

As one effort to estimate the global soil moisture distribution, the Global Soil Wetness Project (GSWP) was conceived. Under the GSWP, the global soil moisture distribution on 1°×1° mesh for 1987 and 1988 was simulated in an offline mode by 11 land surface models (LSMs). Even though the forcing conditions are mostly based on observations, validation studies are necessary because LSMs may not simulate accurately the partitioning of water at the surface of the earth between runoff, evaporation, and changes in soil moisture. A gridded 1°×1° global river channel network, named Total Runoff Integrating Pathways (TRIP) is used to calculate mean runoff estimated by the LSMs for drainage areas upstream of 250 operational gauging stations. Runoff observations from these stations in 150 major river basins of the world have been collected for 1987 and 1988, and were compared with the LSM products. It was found that LSMs estimated annual runoff fairly well, with a relative root mean square error of 40% for drainage areas with a fairly high density of raingauge observations (≥30/106km2), which was used to prepare the forcing precipitation. The error corresponds to approximately 18% of annual evapotranspiration. LSMs are also found to have a tendency to underestimate the annual runoff. This may be caused by underestimation of raingauges under strong wind conditions, especially for snow, because all of the LSMs underestimated the runoff for most of the drainage areas located in higher latitudes. A linear river routing model was applied for the global runoff products from the LSMs and analyzed at 250 gauging stations. The correlations between observed and simulated monthly runoff were improved for most of the LSMs by introducing the routing. River runoff information was found to be effective for the validation of water cycles on the continental scale.

Partial characterizations of networks supporting shortest path interval labeling schemes

In this paper, we consider the problem of shortest path interval routing, a space-efficient strategy for routing in distributed networks. In this scheme, an ordering of the vertices is chosen so that the edges of the network can be labeled with one or more subintervals of the vertex ordering: The resulting routing tables must be deterministic and route along shortest paths between all pairs of vertices. We first show constructively that any interval graph can be labeled with one circular subinterval on each edge; this extends a known result for proper interval graphs. We also provide a partial characterization for networks that admit linear interval routing when edges are labeled with exactly one interval, in terms of the biconnected components of any such network. This is the first such characterization when the paths are required to be shortest paths under the distance metric. Finally, we show that the class of networks that can be labeled with k ≥ 1 subintervals per edge is closed under composition with a certain class of graphs.

Interval Routing Schemes

Interval routing was introduced to reduce the size of routing tables: a router finds the direction where to forward a message by determining which interval contains the destination address of the message, each interval being associated to one particular direction. This way of implementing a routing function is quite attractive but very little is known about the topological properties that must satisfy a network to support an interval routing function with particular constraints (shortest paths, limited number of intervals associated to each direction, etc.). In this paper we investigate the study of the interval routing functions. In particular, we characterize the set of networks which support a linear or a linear strict interval routing function with only one interval per direction. We also derive practical tools to measure the efficiency of an interval routing function (number of intervals, length of the paths, etc.), and we describe large classes of networks which support optimal (linear) interval routing functions. Finally, we derive the main properties satisfied by the popular networks used to interconnect processors in a distributed memory parallel computer.

Annotated Bibliographies in Combinatorial Optimization.

Part I: General methodologies complexity and approximability polyhedral combinatorics branch-and-cut algorithms matroids and submodular functions advances in linear programming decomposition and column generation stochastic integer programming randomized algorithms local search graphs and matrices. Part II: Specific topics and applications sequencing and scheduling Travelling Salesman Problem max cut location problems network design flows and paths quadratic and 3-dimensional assignments linear assignment vehicle routing cutting and packing combinatorial topics in VLSI design applications in computational biology.

Regional scale hydrology: I. Formulation of the VIC-2L model coupled to a routing model

A grid network version of the two-layer Variable Infiltration Capacity (VIC-2L) macroscale hydrological model is described. The VIC-2L model is a hydrologically-based SVAT (Soil Vegetation Atmospheric Transfer) scheme designed to represent the land surface in numerical weather prediction and climate models. It is coupled to a linear routing scheme which is optimized with measured precipitation and streamflow data and is derived independently from the VIC-2L model. In this way it is possible to utilize streamflow measurements for the validation of coupled atmospheric-hydrological models. A baseflow separation routine is used to derive an equivalent description between the VIC-2L model and the routing model.

Flood routing based on diffusion wave equation using mixing cell method

A one-dimensional non-linear diffusion wave equation is derived from the Saint Venant equations with neglect of the inertia terms. This non-linear equation has no general analytical solution. Numerical schemes are therefore employed to discretize the space and time axes and convert the differential equation to difference form. In this study, the mixing cell method is used to convert the diffusion wave equation to difference form, in which the difference term can be eliminated by selecting an optimal space step size Δx when time step size Δt is given. When the time step size Δt → 0, the space step size Δx = Q/(2S 0 BC k ) where Q is discharge, S 0 is bed slope, B is channel width and C k is kinematic wave celerity, which is the same as the characteristic length proposed by Kalinin and Milyukov. The results of application to two cases show that the mixing cell and linear channel flow routing methods produce hydrographs that are in agreement with the observed flood hydrographs.

Streamflow recession in basins with multiple water storages

A streamflow recession formula for natural basins is derived by linear hydrologic routing of the sum of inflows from discrete, independent water storages through a channel storage. Water storages include depression, detention, snow and ice, channel bank, aquifer and cavern. Evapotranspiration is incorporated in the recession formula, but seasonal effects and basin wetness and storage conditions before storms are not considered. Data from seven basins involving 156 precipitation-free recessions are used to test the performance of two- and three-parameter approximations to the theoretical recession formula. Recessions are defined to last at least 2 weeks and to begin 2 days after the peak of a basin outflow hydrograph, or at a point on the falling limb 2 days after any precipitation occurs. Recessions end when precipitation recommences, or when daily flow data stop decreasing. An inverse square formula explains most variance in the two-parameter case, in contrast to the simple exponential formula usually recommended for recession modelling. With three parameters, equally good performance is shown by formulae involving a constant plus an inverse square, or inverse cubic, or simple exponential term. These theoretically based formulae should be useful at basin scale for interpolating or extrapolating recession data, particularly in basins where little is known about water storage behaviour.

COMMON UNITGRAPHS FOR SETS OF RUNOFF EVENTS. PART 2: COMPARISONS AND INFERENCES FOR RAINFALL LOSS MODELS

Common unitgraphs obtained from streamflow data for a set of runoff events have higher peaks, shorter times to peak and generally shorter total durations than average unitgraphs obtained by conventional techniques from rainfall and streamflow data for single events. The calculated inputs to these unitgraphs lag behind the corresponding peaks in the catchment rainfall and continue after the end of rainfall. It eventuates that these inputs are best modelled by including a strongly non-linear storage in the rainfall loss model. For common loss and storage parameters, runoff hydrographs from the overall model fit the observed hydrographs over a wider range of flows than predictions from application of conventional unitgraph methods. The new approach can be interpreted physically as a non-linear process of rainfall loss and routing to stream channels, followed by linear routing of stream flow; or functionally as a separation of the common linear elements in the overall rainfall-runoff process from the loss and non-linear elements. It has the potential to lead to improved predictions of storm runoff hydrographs.

A dynamic hillslope response model in a geomorphology based rainfall-runoff model

This paper presents a technique for the determination of a dynamic hillslope instantaneous unit hydrograph (IUH) in concert with a variable saturation excess runoff production model using a grid-based digital elevation model (DEM). The total channel network responsible for routing the runoff produced on the catchment is divided into two parts: the main channel network and the hillslope channel network. The hillslope IUH, which routes water from the hillslopes to the main channel network, is essentially the solution of the linear advection-dispersion routing model weighted by the hillslope travel distance distribution of saturated pixels to the main channel network. The shape of the hillslope travel distance is found to consist of an initial spike, representing saturated pixels on the main channel network, and an exponential decay function for those pixels on the hillslope. However, the proportion of saturated pixels on the main channel network varies with total saturated pixels, causing an inverse change of scale of the spike and the exponential decay part. As the number of saturated pixels changes during a storm event, the hillslope IUH is dynamic. The main channel network IUH is also modelled by the linear advection-dispersion model weighted by the normalized width function of the main channel network. Convolution of the hillslope and main channel network IUHs gives the catchment IUH, which is also dynamically changing with the degree of saturation. It is demonstrated that the direct runoff hydrograph is sensitive to the variation of the degree of saturation within and between storm events.

Numerical stability of implicit four-point scheme applied to inverse linear flow routing

In this paper an analysis of stability and accuracy for numerical solution of the inverse problem for the Saint Venant equations is presented. For inverse flow routing a four-point implicit difference scheme with two weighting parameters θ and ψ is used. This is the same scheme which with ψ = 1 2 and θ ⩾ 1 2 is used as the Preissmann scheme for the conventional solution of the Saint Venant equations. The numerical experiments presented by Szymkiewicz ( J. Hydrol., 147: 105–120, 1993) showed that the numerical stability of an inverse flow routing requires different values of parameters ψ and θ than for a conventional solution. This problem can be explained by Fourier analysis carried out for a linear hyperbolic system. From this analysis it is found that the four-point implicit scheme applied to inverse flow routing is unconditionally stable if ψ ⩾ 1 2 and θ ⩽ 1 2 . These conditions of stability are the inverse of the conventional solution.

On Multi-Label Linear Interval Routing Schemes

We consider linear interval routing schemes studied by [3,5] from a graph-theoretic perspective. We examine how the number of linear intervals needed to obtain shortest path routings in networks is affected by the product, join and composition operations on graphs. This approach allows us to generalize some of the results of [3,5] concerning the minimum number of intervals needed to achieve shortest path routings in certain special classes of networks. We also establish an Ω(n 1/3 ) lower bound on the minimum number of intervals needed to achieve shortest path routings in the network considered.

Optimal Linear Broadcast

We investigate the problem of linear broadcast, which is performed in a network in which messages follow linear routes. This is a characteristic of many high-speed networks, in which a special hardware is used for switching. Following, extending, and improving the recent work of Chou and Gopal ( J. Algorithms 10 (1989), 490-517), we study cases when the switching hardware has various limitations. We present algorithms that compute an optimal broadcast routing for any given number of linear routes. Our main result in an O( N) algorithm for the general problem of linear broadcast routing, for a tree network of size N for which an O( N 2) algorithm was given by Chou and Gopal.

Rapid Flow Model with Lateral Inflow

The rapid flow model (equivalent to the distributed delayed Muskingum model) is an attractive linear flood routing model meeting the conflicting demands of physical significance and simplicity. After having relaxed the assumption of negligible lateral inflow, made in former studies, the impulse response of the above model with lateral inflow is derived in the analytical (series) form. The cumulants of the impulse response of the model are developed. Although the results presented were obtained for the spatially uniform distribution of lateral inflow, it is possible to solve it also for non-uniform lateral inflows, at the cost of additional algebra.

River flow forecasting. Part 5. Applications of a conceptual model

A rainfall-runoff model of the conceptual type, known as the Soil Moisture Accounting and Routing (SMAR) Model, is described and applied to five of the 14 catchments described in Part 3. The model comprises a water balance component in which the rainfall and evaporation interact to produce runoff and a linear routing component which transforms the generated runoff into discharge. The structure of the model emphasizes the distinct roles of the non-linear water balance component and the linear routing component. A calibration procedure is suggested which maintains this distinction. Good results seem to be obtained particularly on semiarid catchments on which models of the systems analysis type do not perform well.

Linear flood routing model for rapid flow

The linear flood routing model presented has been derived from the linearized St. Venant equation for the case of a uniform open channel with arbitrary cross-sectional shape and friction law. In order to filter out the downstream boundary condition the kinematic wave solution is used to approximate the diffusion term in the St. Venant equation. The hydrodynamic model obtained is called the rapid flow model (RFM). It provides the exact solution for a Froude number equal to one. Such characteristics of the RFM impulse response as cumulants, amplitude and phase spectra are analysed, and then compared with those of the complete linearized St. Venant equations for different reach lengths, values of Froude number and frequencies of flood waves. The RFM can be applied for mountainous rivers that have large Froude numbers and both quick and slow rising waves.

Linear broadcast routing

In this paper we examine the problem of performing broadcasts in networks where the messages are constrained to follow linear paths. Many high speed networks, where routing is done in specialized hardware, have this characteristic. We show that the general problem is NP-complete but find a polynomial time approximation algorithm which is guaranteed to provide a solution which is within twice the optimal. We also suggest some generalizations of this work and propose several open problems.

The rational method in stormwater management modelling of peak flow flood control systems, I: Theoretical development

The well-known rational method, where the subject criterion variable of peak flow rate is evaluated by using a synthetic storm pattern composed of identical return frequencies of storm pattern input, is shown to be an effective approximation to a considerably more complex probabilistic model. The rational method is shown to be of equivalence to a model of a highly discretized catchment with linear routing for channel flow approximation, and effective rainfalls in subareas which are linear with respect to a selected “loss” function's effective rainfall output. The use of a simple “loss” function which directly equates to the distribution of rainfall depth-duration statistics (such as a constant fraction of rainfall) is shown to provide a higher level of statistical significance in estimating T-year outputs for a hydrologic criterion variable than use of an arbitrary “loss” function. When peak flow rates are the criterion variable of interest, the unit hydrograph method can be simplified to the well-known rational method. This simpler procedure is used to develop computerized master plans of drainage for urbanized regions.