Kinetic models and intrinsic timescales: Simulation comparison for a 2nd order queueing model

Hans Armbruster, Matthew Wienke

    Research output: Contribution to journalArticle

    Abstract

    Kinetic models of stochastic production ows can be expanded into deterministic moment equations and thus approximated with appropriate closures. A second order model for the product density and the product speed has previously been proposed. A systematic analysis comparing simulations of the partial differential equations (PDE) with discrete event simulations (DES) is performed. Specifically, factory production is modeled as an M/M/1 queue where the arrival process is a non-homogeneous Poisson process. Three fundamental scenarios for such a time dependent in ux are studied: An instant step up/step down of the arrival rate, an exponential step up/step down and periodic variation of the average arrival rate. It is shown that the second order model in general yields significant improvements over the first order model. Adding diffusion into the PDE further improves the agreement in particular for queues with low utilization. The analysis also points to fundamental open issues regarding kinetic models of time dependent agent based simulations. Memory effects and the possibility of resonance in deterministic models are caused by intrinsic timescales of the PDE that are not present in the original stochastic processes.

    Original languageEnglish (US)
    Pages (from-to)177-193
    Number of pages17
    JournalKinetic and Related Models
    Volume12
    Issue number1
    DOIs
    StatePublished - Feb 1 2019

    Fingerprint

    Queueing Model
    Kinetic Model
    Second-order Model
    Time Scales
    Partial differential equation
    Kinetics
    M/M/1 Queue
    Partial differential equations
    Non-homogeneous Poisson Process
    Moment Equations
    Simulation
    Memory Effect
    Agent-based Simulation
    Deterministic Model
    Simulation Analysis
    Discrete Event Simulation
    Instant
    Queue
    Stochastic Processes
    Closure

    Keywords

    • 2nd order models
    • Kinetic models
    • Production systems
    • Simulations
    • Transients

    ASJC Scopus subject areas

    • Numerical Analysis
    • Modeling and Simulation

    Cite this

    Kinetic models and intrinsic timescales : Simulation comparison for a 2nd order queueing model. / Armbruster, Hans; Wienke, Matthew.

    In: Kinetic and Related Models, Vol. 12, No. 1, 01.02.2019, p. 177-193.

    Research output: Contribution to journalArticle

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