Control and synchronization in switched arrival systems

Rem, B Bart; Armbruster, H.D.

doi:10.1063/1.1500284

Cited by 23 publications

(15 citation statements)

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“…Chase et al [10] showed that this function, which describes the amount of work in the buffers, can be chaotic. Others have extended the model in various ways, as may be found in Ushio et al [22], Katzorke and Pikovsky [14], Rem and Armbruster [20], Armbruster [2], Peters et al [19], and citations therein. Of particular note, is Rem and Armbruster [20], which added complications such as setup times and maintenance to the switched arrival system to make the chaotic behavior have external effects.…”

Section: Chaosmentioning

confidence: 99%

Deterministic chaos in a model of discrete manufacturing

Bartholdi

Eisenstein

Lim

2009

Naval Research Logistics

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A natural extension of the bucket brigade model of manufacturing is capable of chaotic behavior in which the product intercompletion times are, in effect, random, even though the model is completely deterministic. This is, we believe, the first proven instance of chaos in discrete manufacturing. Chaotic behavior represents a new challenge to the traditional tools of engineering management to reduce variability in production lines. Fortunately, if configured correctly, a bucket brigade assembly line can avoid such pathologies. ChaosSome simple deterministic systems can generate surprisingly complicated behavior that has been termed "chaotic". A system that is chaotic has long-term behavior that can be hard to describe, hard to predict, and hard even to simulate. Indeed, long-term behavior of chaotic systems seems to be deeply connected to randomness. discrete-event models of discrete production systems that show chaotic behavior, as defined in the theory of chaos in dynamic systems, were not found in this study".To our knowledge, only one model of a production system has heretofore been formally shown to exhibit chaotic dynamics and that is the switched arrival system studied in Chase et al. [10]. This model treats manufacturing as a process and the product as a fluid. In this model there are no discrete or intermediate products and therefore it did not satisfy the criteria of Schmitz et al. [21]. Armbruster [2] agrees, saying "One major drawback of the switched arrival system is the fact that the chaotic dynamics are strictly internal to the production-the total throughput through the set of machines is always constant and does not reflect the chaotic dynamics". In short, it is not the strong example one would prefer to display if chaos can indeed be found in manufacturing systems.In the model of Chase et al.[10] a single switching server distributes work over n parallel machines. The amount of work in the buffer in front of each machine is assumed to be a continuous variable and the processing rate of each machine is assumed to be constant. The server continues to fill the current buffer until some other buffer empties. The rate at which the server fills a buffer is equal to the sum of the processing rates of all machines. When the system is sampled at the instants when any buffer empties, the dynamics of the system can be represented by a function that, for n = 3, maps the unit interval into itself. Chase et al.[10] showed that this function, which describes the amount of work in the buffers, can be chaotic. Others have extended the model in various ways, as may be found in Ushio et al. We offer a model of bucket brigade assembly lines that meets the criteria of Schmitz et al.[21]. The model is realistic: Indeed, bucket brigades are currently used in a variety of manufacturing environments, examples of which are documented at Bartholdi and Eisenstein [4]. Furthermore, the model explicitly represents each product as a discrete entity with start and completion times. As we show, the product intercompletion times...

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Section: Chaosmentioning

confidence: 99%

Deterministic chaos in a model of discrete manufacturing

Bartholdi

Eisenstein

Lim

2009

Naval Research Logistics

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“…For the majority of all material flow systems, a parallel service of several intersecting flows or conflicting tasks is impossible, unsafe or inefficient. Alternating exclusion of competing tasks is frequently observed at crossroads in road traffic [1,2,3,4,5,6,7], in the organisation of production processes [8,9,10,11] or in communication networks [12,13]. Instead of parallel processing of different flows, a sequential processing must be organised in an optimal manner.…”

Section: Introductionmentioning

confidence: 99%

Decentralised control of material or traffic flows in networks using phase-synchronisation

Lämmer

Kori

Peters

et al. 2006

Physica A: Statistical Mechanics and its Applications

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We present a self-organising, decentralised control method for material flows in networks. The concept applies to networks where time sharing mechanisms between conflicting flows in nodes are required and where a coordination of these local switches on a system-wide level can improve the performance. We show that, under certain assumptions, the control of nodes can be mapped to a network of phase-oscillators.By synchronising these oscillators, the desired global coordination is achieved. We illustrate the method in the example of traffic signal control for road networks. The proposed concept is flexible, adaptive, robust and decentralised. It can be transferred to other queuing networks such as production systems. Our control approach makes use of simple synchronisation principles found in various biological systems in order to obtain collective behaviour from local interactions.

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“…In contrast to the stationary behavior assumed by most production engineers, this flow may display a complex dynamics in time, including oscillatory patterns and chaos [7,8]. A particular focus has been on the empirically observed and well-known "bull-whip effect" [3,5,8,9,10], which describes the amplification of the oscillation amplitudes of delivery rates in supply chains compared to the variations in the consumption rate of goods.A promising approach to the non-linear interactions and dynamics of supply chains is based on "fluid-dynamic models" [5,9], which are related to macroscopic traffic models [3,4,5]. In contrast to classical approaches like queueing theory and event-driven simulations, they are better suited for an on-line control under dynamically changing conditions.…”

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Physics, stability, and dynamics of supply networks

et al. 2004

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We show how to treat supply networks as physical transport problems governed by balance equations and equations for the adaptation of production speeds. Although the non-linear behaviour is different, the linearized set of coupled differential equations is formally related to those of mechanical or electrical oscillator networks. Supply networks possess interesting new features due to their complex topology and directed links. We derive analytical conditions for absolute and convective instabilities. The empirically observed "bull-whip effect" in supply chains is explained as a form of convective instability based on resonance effects. Moreover, it is generalized to arbitrary supply networks. Their related eigenvalues are usually complex, depending on the network structure (even without loops). Therefore, their generic behavior is characterized by oscillations. We also show that regular distribution networks possess two negative eigenvalues only, but perturbations generate a spectrum of complex eigenvalues.PACS numbers: 89.65. Gh,89.75.Hc,84.30.Bv Econophysics has stimulated a lot of interesting research on problems in finance and economic systems [1], applying methods from statistical physics and the theory of complex systems. Recently, the dynamics of supply networks [2, 3, 4], i.e. the flow of materials through networks, has been identified as an interesting physical transport problem [3,4,5], which is also reflected by the notion of "factory physics" [6]. Potential applications reach from production networks to business cycles, from metabolic networks to food webs, up to logistic problems in disaster management. Empirical and theoretical studies have shown that the flow of goods between different producers or suppliers can be described analogously to driven many-particle flows between sources and sinks (depots), where the particles represent materials, goods, or other resources. In contrast to the stationary behavior assumed by most production engineers, this flow may display a complex dynamics in time, including oscillatory patterns and chaos [7,8]. A particular focus has been on the empirically observed and well-known "bull-whip effect" [3,5,8,9,10], which describes the amplification of the oscillation amplitudes of delivery rates in supply chains compared to the variations in the consumption rate of goods.A promising approach to the non-linear interactions and dynamics of supply chains is based on "fluid-dynamic models" [5,9], which are related to macroscopic traffic models [3,4,5]. In contrast to classical approaches like queueing theory and event-driven simulations, they are better suited for an on-line control under dynamically changing conditions. These fluid-dynamic models have recently been generalized to cope with discrete spaces (production steps) [3,5]. However, the impact of the topology of supply networks, connecting the subject to the statistical physics of networks [11] has not yet been thoroughly investigated. Its relevance for the stability and dynamics of supply networks will, therefore...

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Control and synchronization in switched arrival systems

Cited by 23 publications

References 5 publications

Deterministic chaos in a model of discrete manufacturing

Deterministic chaos in a model of discrete manufacturing

Decentralised control of material or traffic flows in networks using phase-synchronisation

Physics, stability, and dynamics of supply networks

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