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    <copyright>Copyright © 2026. National Academy of Sciences. All rights reserved.</copyright>
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    <managingEditor>tris-trb@nas.edu (Bill McLeod)</managingEditor>
    <webMaster>tris-trb@nas.edu (Bill McLeod)</webMaster>
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      <title>Effects of Failure Correlation on Reliable Facility Location: A Continuum Approximation Approach</title>
      <link>https://trid.trb.org/View/909471</link>
      <description><![CDATA[This paper studies the reliable fixed charge location problem (RUFL) where facilities are subject to spatially correlated disruptions that occur with location-dependent probabilities (due to reasons such as natural or man-made disasters). If a facility fails, its customers are diverted to other facilities and incur excessive transportation cost. We develop a continuum approximation (CA) model to minimize the sum of initial facility construction costs and expected customer transportation costs under normal and failure scenarios. The paper presents ways to formulate the correlation among adjacent facility disruptions, and incorporates such correlations into the efficient CA optimization model. Numerical experiments are conducted to illustrate how the proposed model can be used to optimize facility location design, and how the correlations significantly influence the total system cost.]]></description>
      <pubDate>Tue, 27 Apr 2010 08:44:38 GMT</pubDate>
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      <title>Design of Vehicle Routing Zones for Large-Scale Distribution Systems</title>
      <link>https://trid.trb.org/View/840010</link>
      <description><![CDATA[This paper proposes algorithms to automatically discretize vehicle routing zones (VRZs) from continuum approximation guidelines. VRZs that satisfy these guidelines (i.e., shape and size requirements) are useful to the planning and operation of distribution systems in several practical contexts. In the literature, however, VRZ design normally requires human intervention, and this is inconvenient and time-consuming especially for large-scale and complex systems. This study fills this gap by utilizing a combination of spatial partitioning techniques to systematically obtain optimum zone designs. Numerical examples show that the proposed algorithm yields satisfying outcomes.]]></description>
      <pubDate>Thu, 15 Nov 2007 10:33:05 GMT</pubDate>
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      <title>Toward a Physical Damage Variable for Concrete</title>
      <link>https://trid.trb.org/View/787787</link>
      <description><![CDATA[Continuum damage mechanics models, while elegant and useful, suffer from what are typically highly idealized relationships between model and material. In this technical note, using 3-D measurements of internal cracking, direct, albeit simple relationships were made between the quantity of cracking and a corresponding scalar damage variable. Geometric properties of internal cracks were measured through 3-D image analysis of in situ microtomographic scans of small concrete specimens subject to compression. A scalar damage variable was determined from the changes in stiffness measured in successive loading cycles. Results showed a nearly linear relationship between the damage variable and the volume of new cracks formed. In contrast, results showed a nonlinear relationship between the damage variable and the crack surface area. Such relationships can potentially lead to a more physical basis for continuum damage formulations.]]></description>
      <pubDate>Wed, 23 Aug 2006 07:58:01 GMT</pubDate>
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      <title>GAS-KINETIC MODEL FOR MULTILANE HETEROGENEOUS TRAFFIC FLOW</title>
      <link>https://trid.trb.org/View/512003</link>
      <description><![CDATA[A gas-kinetic traffic flow model is presented that describes the traffic flow operations of heterogeneous traffic on specific lanes of a motorway.  To realistically portray the multilane dynamics of traffic flow, traffic is described as a collection of vehicle platoons that consist of an unconstrained vehicle followed by a nonnegative number of constrained followers.  It is shown that the gas-kinetic dynamics of this unconstrained and constrained traffic are governed by continuum and noncontinuum processes.  The continuum processes describe smooth changes in the mesoscopic traffic flow variables caused by motions in the phase space.  The noncontinuum processes reflect, among other things, deceleration of vehicles due to interactions between vehicles from the same and from different user classes, immediate lane changing, postponed lane changing by constrained drivers, and spontaneous lane changing by free-flowing drivers. Finally, it is shown how the multilane-multiclass model relates to traditional aggregate-lane and mixed-class gas-kinetic equations.  This is accomplished by aggregation across the motorway lanes and the user classes.  It is shown that the expression reflecting vehicle interactions in traditional models is only valid for dilute traffic.  A remedial expression is proposed.]]></description>
      <pubDate>Mon, 29 Nov 1999 00:00:00 GMT</pubDate>
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