51 research outputs found

    Stochastic Models for Order Picking Systems

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    Stochastic Models for Order Picking Systems

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    Queueing Networks With Blocking.

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    The area of classical (product form) queueing networks is briefly discussed. The principal results for classical queueing networks are summarized. The transfer, service and rejection blocking policies are defined, and their use in queueing network models are presented. An overview of the literature in the area of queueing networks with blocking is given, and the relations between the three blocking policies is discussed in general. Duality theorems for open and closed queueing networks with rejection blocking and a single job class are proved. Using a duality theorem, an exact solution is found for closed blocking networks which contain so many jobs that if one station is empty all other stations are full. Algorithms to compute performance measures, in particular throughputs, follow from the way the solution is obtained. It is then proved that for open, mixed and closed networks with rejection blocking, multiple job classes, general service time distributions and reversible routing the equilibrium state probabilities have product form. The reversed process for these networks is examined, and it is proved that it represents a network of the same type. Formulas for throughputs are derived, and algorithms to compute performance measures are outlined. Finally, closed central server models with state-dependent routing, multiple job classes and rejection blocking are investigated. The equilibrium state probabilities have a modified product form, and the reversed process is a network of the same type. Formulas for performance measures are derived for this model and algorithms to compute them are outlined

    Integrated performance evaluation of extended queueing network models with line

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    Despite the large literature on queueing theory and its applications, tool support to analyze these models ismostly focused on discrete-event simulation and mean-value analysis (MVA). This circumstance diminishesthe applicability of other types of advanced queueing analysis methods to practical engineering problems,for example analytical methods to extract probability measures useful in learning and inference. In this toolpaper, we present LINE 2.0, an integrated software package to specify and analyze extended queueingnetwork models. This new version of the tool is underpinned by an object-oriented language to declarea fairly broad class of extended queueing networks. These abstractions have been used to integrate in acoherent setting over 40 different simulation-based and analytical solution methods, facilitating their use inapplications

    Stochastic Models for Order Picking Systems

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    Approximate analysis of queueing network models

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    Message-driven dynamics

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    Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1997.Includes bibliographical references (p. 251-260).by Richard Anton Lethin.Ph.D
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