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  • 1
    ISSN: 1432-5217
    Keywords: Key words: Conservation laws ; Gittins index ; LP relaxation ; multi-armed bandit ; performance space ; undiscounted tax problem
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract. A radically new approach to indexable systems pioneered by Bertsimas and Niño-Mora is utilised to provide novel analyses of classes of complex multi-armed bandits in which the individual bandits have their own decision structure. A new index result for an undiscounted model is established. Parallel server versions of the models are studied via (the dual of) an LP relaxation. This analysis yields a natural heuristic policy which is evaluated numerically.
    Type of Medium: Electronic Resource
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  • 2
    ISSN: 0044-2313
    Keywords: Phosphoraneiminato complex of antimony ; Synthesis ; IR-spectra ; 121Sb-Mössbauer spectra ; Crystal Structure ; Chemistry ; Inorganic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Description / Table of Contents: [Sb(NPPh3)4]+SbF6-: Synthesis, Crystal Structure, and 121Sb Mössbauer SpectrumThe title compound as well as the hexachloro antimonate [Sb(NPPh3)4]+SbCl6- have been prepared by the reaction of Me3SiNPPh3 with SbF5 and SbCl5, respectively, in acetonitrile solutions. The compounds form colourless, moisture sensitive crystals, which were characterized by IR spectroscopy, by 121Sb Mössbauer spectroscopy, and by crystal structure analyses. A complete crystal structure analysis, however, could be carried out with [Sb(NPPh3)4]+SbF6- only. The compound crystallizes orthorhombically in the space group Pccn with four formula units per unit cell. The structure determination was done with 3 972 observed unique reflections, R = 0.053. Lattice dimensions at 19°C: a = 1 658,6; b = 1 698.9, c = 2 361.9 pm. In the cation [Sb(NPPh3)4]+ the antimony atom is tetrahedrally coordinated by the four nitrogen atoms of the phosphoraneiminato ligands with extremely short Sb—N bond lengths of 193 pm.
    Notes: Die Titelverbindung entsteht ebenso wie das Hexachloroantimonat [Sb(NPPh3)4]+SbCl6- durch Reaktion von Me3SiNPPh3 auf SbF5 bzw. SbCl5 in Acetonitrillösung. Die Verbindungen bilden farblose, feuchtigkeitsempfindliche Kristalle, die wir durch ihre IR-Spektren, durch 121Sb-Mößbauer-Spektren und durch Kristallstrukturanalysen charakterisiert haben. Eine vollständige Strukturanalyse gelang jedoch nur an [Sb(NPPh3)4]+SbF6-. Die Verbindung kristallisiert orthorhombisch in der Raumgruppe Pccn mit vier Formeleinheiten pro Elementarzelle. Strukturlösung mit 3 972 beobachteten unabhängigen Reflexen, R = 0,053. Die Gitterkonstanten sind bei 19°C: a = 1 658,6; b = 1 698,9; c = 2 361,9 pm. In dem Kation [Sb(NPPh3)4]+ ist das Antimonatom tetraedrisch von den vier Stickstoffatomen der Triphenylphosphaniminatoliganden umgeben. Die Sb—N-Bindungslängen sind mit 193 pm extrem kurz.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Computing 56 (1996), S. 95-104 
    ISSN: 1436-5057
    Keywords: 68M20 ; Probabilistic algorithm ; online scheduling ; interval ; busy time
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Wir betrachten das Problem der Zuteilung von Aufgaben bestimmter Rechenzeit auf einem Rechner, um so seine Auslastung zu maximieren. Die Aufgabe besteht darin, einen probabilistischen Online-Algorithmus mit vernünftigem worst-case Performance-Verhältnis zu finden. Wir geben die Antwort auf ein offenes Problem von Lipton und Tompkins, das das bestmögliche Verhältnis betrifft. Weiter verallgemeinern wir ihre Ergebnisse auf einm-Maschinen-Analogon. Schließlich wird eine Variante des Problems analysiert, in dem der Rechner mit einem Zwischenspeicher für einen Job versehen ist.
    Notes: Abstract We consider the problem of scheduling tasks requiring certain processing times on one machine so that the busy time of the machine is maximized. The problem is to find a probabilistic online algorithm with reasonable worst case performance ratio. We answer an open problem of Lipton and Tompkins concerning the best possible ratio that can be achieved. Furthermore, we extend their results to anm-machine analogue. Finally, a variant of the problem is analyzed, in which the machine is provided with a buffer to store one job.
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  • 4
    ISSN: 1572-9338
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract When controlled stochastic systems have performances which satisfy generalisedconservation laws (GCL), an objective which is linear in the performance is optimised by aGittins index policy. We develop measures of the extent to which a system fails to satisfyGCL and derive suboptimality bounds for suitable index policies in terms of such measures.These bounds are used, inter alia, to explore the robustness in performance of cm‐typerules for a multiclass G/G/1 queueing system to departures from an assumption of exponentialservice times. We also study Gittins index policies for parallel processor versions of theclassical undiscounted and discounted multi‐armed bandit problems. In the undiscountedcase, the cost of an index policy comes within a constant of the optimal cost ‐ thisconstant being independent of the number of projects submitted for scheduling. In thediscounted case, under fairly mild conditions, Gittins index policies come within an O(1) quantity ofoptimality and are hence average reward optimal when the discount rate is small enough.
    Type of Medium: Electronic Resource
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