DARPA ULTRALOG Final Report - Industrial and Manufacturing ...

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non-linear and non-stationarity. New tools and techniques are required for their analysis such that the structure, function and growth of networks can be considered simultaneously. In this regard we discuss “Network Dynamics” in Section 9, which deals with such issues and can be used to study the structure of supply chain and its implication for its functionality. Understanding the behavior of large complex networks is the next logical step for the field of nonlinear dynamics, because they are so pervasive in the real world. We begin with a brief introduction to dynamical systems theory, in particular nonlinear dynamics in next section. 5 Dynamical Systems Theory Many physical systems that produce continuous-time response can be modeled by a set of differential equations of the form: dy = f ( y, a) , (I) dt where, y = y ( t), y ( t),...... y ( )) represents the state of the system and may be thought of as a ( 1 2 n t point in a suitably defined space S-which is known as phase space and a = a ( t), a ( t) L, a ( )) is a parameter vector. The dimensionality of S is the number of ( 1 2 m t apriori degrees of freedom in the system. The vector field f(y,a) is in general a non-linear operator acting on points in S. If f(y,a) is locally Lipschtiz, above equation defines an initial value problem in the sense that a unique solution curve passes through each point y in the phase space. Formally we may write the solution at time t given an initial value y0 as y( t) = ϕ t y0 . ϕ t represents a oneparameter family of maps of the phase space into itself. We can perceive the solutions to all possible initial value problems for the system by writing them collectively as ϕ . This may be thought of as a flow of points in the phase space. Initially the dimension of the set ϕ t S will be that of S itself. As the system evolves, however, it is generally the case for the so-called dissipative system that the flow contracts onto a set of lower dimension known as attractor. The attractors can vary from simple stationary, limit cycle, quasi-periodic to complicated chaotic ones (Strogatz 1994, Ott 1996). The nature of attractor changes as parameters (a) are varied, a phenomena studied in bifurcation analysis. Typically a nonlinear system is always chaotic for some range of parameters. Chaotic attractors have a structure that is not simple; they are often not smooth manifolds, and frequently have a highly fractured structure, which is popularly referred to as Fractals (self–similar geometrical objects having structure at every scale). On this attractor, stretching and folding characterize the dynamics; the former phenomenon causes the divergence of nearby trajectories and latter constraints the dynamics to finite region of the state space. This accounts for fractal structure of attractors and the extreme sensitivity to changes in initial conditions, which is hallmark of chaotic behavior. System under chaos is unstable everywhere never settling down, producing irregular and aperiodic behavior which leads to a continuous broadband spectrum. While this feature can be used to distinguish chaotic behavior from stationary, limit cycle, quasi-periodic motions using standard Fourier Analysis it makes it difficult to separate it from noise which also has a broadband spectrum. It is this “deterministic randomness” of chaotic behavior, which makes standard linear modeling and prediction techniques unsuitable for analysis. 5.1 Nonlinear Models for Supply Chain Understanding the complex interdependencies, effects of priority, nonlinearities, delays, uncertainties and competition/cooperation for resource sharing is fundamental for prediction and control of supply chains. System dynamics approach often leads to models of supply chains, which can be described in the form of equation (I). Dynamical systems theory provides a powerful framework for rigorous analysis of such models and thus can be used to supplement the S t
system dynamics approach. We next describe some nonlinear models and their detailed analysis. These models can be either used to represent entities in a supply chain or as macroscopic models, which capture collective behavior. The models reiterate the fact that simple rules can lead to complex behavior, which in general are difficult to predict and control. 5.1.1 Preemptive Queuing Model with delays Priority and heterogeneity are fundamental to any logistic planning and scheduling. Tasks have to be prioritized in order to do the most important things first. This comes naturally as we try to optimize an objective and assign the tasks their “importance.” Priorities may also arise due to the non-homogeneity of the system where “knowledge” level of one agent is different from the other. In addition in all logistics systems, resources are limited, both in time and space. Temporal dependence plays an important role in logistic planning (interdependency). Sometime they can also arise from the physical facts when different stages of processing have certain temporal constraint. The considerations regarding the generality of assumptions and the clear one-to-one correspondence between the physical logistics tasks and the model parameters described in (Erramilli, and Forys 1991) made us apply the queuing model in context of supply chains (Kumara et al. 2003). The Queuing system considered here has two queues (A and B) and a single server with following characteristics: • Once served, the class A customer returns as a class B customer after a constant interval of time • Class B has non-preemptive priority over class A, i.e., the class A queue does not get served until the class B queue is emptied. • The schedules are organized every T units of time, i.e., if the low priority queue is emptied within time T, the server remains idle for the reminder of the interval. • Finally, the higher priority class B has a lower service rate than the low priority class A. Figure 2. Preemptive Queuing Model Suppose the system is sampled at the end of every schedule cycle, and the following quantities are observed at the beginning of the kth interval: A k : Queue length of low priority queue B : Queue length of high priority queue k C : Outflow from low priority queue in the kth interval k
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Ultra*Log PSU/IAI Final Report for
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Contents Contents .................
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Executive Summary Ultra*Log is a De
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2.3 Gnanasambandam, N., Lee, S., Ku
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6 Characterization and analysis of
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timizing simultaneously the link de
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where ∆ 1 (j) ≥ 0 and ∆ 2 (i,
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Table 2. GA Results Agent N A D max
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connected component, in which a pat
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Random Small-world Scale-free with
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Growth mechanisms Start with a smal
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Table 2. The proposed network’s c
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tems. Proceedings of the Second Joi
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Proceedings of the 1st Open Cougaar
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1 SITUATION IDENTIFICATION USING DY
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3 3.2 Behavior In SSC society an ag
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5 All the behavior parameters may n
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Estimating Global Stress Environmen
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chaotic deterministic time series.
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100% 1 95% 2 14 15 64% TAO 4 64% 62
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interactions as a dynamical system
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ehavior states under varying system
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Extensive testing and validation of
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5 Conclusions and Future Research T
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2 to function critically even under
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4 points into a corresponding inner
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6 stresses well. The Warehouse 1 ag
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Table 1: Notation Symbol Descriptio
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4 Conclusions and Future Work 4.1 C
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O, U Stresses Physical/Infrastructu
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Manuscript for IEEE Transactions on
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2 discuss problem domain and in Sec
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4 t Si t ∫ + ( ) i ) t When RA i
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6 S UB i ∑ = P LI / LI . (16) i p
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8 policies while underutilizing in
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architecture based on both the Grid
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to machines (network topology) and
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component is a member of one of the
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denotes the immediate predecessors
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limit of large number of tasks. If
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Min-min heuristic algorithm Step 1:
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We set up eight different experimen
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0. 4 8057 8237 0.5 6439 6635 0.6 53
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pp. 191-200. [3] I. Foster, C. Kess
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Technology, Cambridge, MA, 1995. [2
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Manuscript for IEEE TRANSACTIONS ON
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Page 156 and 157: Coordinating Control Decisions of S
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Page 160 and 161: Understanding Agent Societies Using
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Page 168 and 169: Figure 1. Agent Hierarchy in CPE So
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Page 176 and 177: Acknowledgements The work described
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Page 196 and 197: focusing on the computational compl
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Page 200 and 201: ealizable. But the inherent complex
Page 202 and 203: Min, H. and Zhou, G., 2002, Supply
Page 204 and 205: In the rest of this paper we report
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