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  • 1
    Electronic Resource
    Electronic Resource
    Illuminating high-dimensional convex sets (1995)
    Springer
    Geometriae dedicata 56 (1995), S. 115-120 
    Details
    ISSN: 1572-9168
    Keywords: 52-XX
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A setL of points in thed-spaceE d is said toilluminate a familyF={S 1, ...,S n } ofn disjoint compact sets inE d if for every setS i inF and every pointx in the boundary ofS i there is a pointv inL such thatv illuminatesx, i.e. the line segment joiningv tox intersects the union of the elements ofF in exactly {x}. The problem we treat is the size of a setS needed to illuminate a familyF={S 1, ...,S n } ofn disjoint compact sets inE d . We also treat the problem of putting these convex sets in mutually disjoint convex polytopes, each one having at most a certain number of facets.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01267636
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Optimal Open-Loop Control of Vacations, Polling and Service Assignment (2000)
    Springer
    Queueing systems 36 (2000), S. 303-325 
    Details
    ISSN: 1572-9443
    Keywords: multimodular functions ; balanced sequences ; control of vacations ; polling ; service assignment
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract We consider in this paper the optimal open-loop control of vacations in queueing systems. The controller has to take actions without state information. We first consider the case of a single queue, in which the question is when should vacations be taken so as to minimize, in some general sense, workloads and waiting times. We then consider the case of several queues, in which service of one queue constitutes a vacation for others. This is the optimal polling problem. We solve both problems using new techniques from [2,4] based on multimodularity.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1011085302786
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Optimal Allocation Sequences of Two Processes Sharing a Resource (1997)
    Springer
    Discrete event dynamic systems 7 (1997), S. 327-354 
    Details
    ISSN: 1573-7594
    Keywords: Optimal Scheduling ; Petri Nets ; Sturmian Word
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, we show that the “most regular” word in the language formed by all the words containing a fixed number of each letter of an alphabet gives the optimal resource allocation policy of the generic system composed by two processes sharing a resource. This system will be modeled as a Petri net to derive the proof of this result which is partially generalized to non periodic allocation sequences and non rational frequencies. For N processes sharing a resource, we show that a strongly optimal sequence may not exist. In this case, we give an heuristic to find a good allocation sequence which relates to regular words in higher dimensions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008256825451
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    Paper (German National Licenses)
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  • 4
    Book
    Book
    Discrete-event control of stochastic networks : multimodularity and regularity; 1829 (2003)
    Berlin [u.a.] :Springer,
    Details
    Title: Discrete-event control of stochastic networks : multimodularity and regularity; 1829
    Author: Altman, Eitan
    Contributer: Gaujal, Bruno , Hordijk, A.
    Publisher: Berlin [u.a.] :Springer,
    Year of publication: 2003
    Pages: XIV, 313 S.
    Series Statement: Lecture notes in mathematics 1829
    ISBN: 3-540-20358-3
    Type of Medium: Book
    Language: English
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