Well-posedness and asymptotic behavior of the time-dependent solution of an M/G/1 queueing model View Full Text


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Article Info

DATE

2019-03

AUTHORS

Nurehemaiti Yiming, Geni Gupur

ABSTRACT

By using the Hille–Yosida theorem, Phillips theorem and Fattorini theorem we prove that the M/G/1 queueing model with vacations and multiple phases of operation, which is described by infinitely many partial differential equations with integral boundary conditions, has a unique positive time-dependent solution that satisfies the probability condition. Next, by studying the spectrum of the operator, which corresponds to the model, on the imaginary axis we prove that the time-dependent solution of the model strongly converges to its steady-state solution. More... »

PAGES

1-44

References to SciGraph publications

  • 2014-02. On the Well-posedness and Asymptotic Behavior of a Nonlinear Dispersive System in Weighted Spaces in APPLIED MATHEMATICS & OPTIMIZATION
  • 2017-12. Dynamic Analysis of the M/G/1 Queueing Model with Single Working Vacation in INTERNATIONAL JOURNAL OF APPLIED AND COMPUTATIONAL MATHEMATICS
  • 2018-02. Analysis of an M/G/1 queue with vacations and multiple phases of operation in MATHEMATICAL METHODS OF OPERATIONS RESEARCH
  • 1990-12. Time-dependent analysis of M/G/1 vacation models with exhaustive service in QUEUEING SYSTEMS
  • 2011-12. On a dynamical system for a reliability model in JOURNAL OF PSEUDO-DIFFERENTIAL OPERATORS AND APPLICATIONS
  • 1986-06. Queueing systems with vacations — A survey in QUEUEING SYSTEMS
  • 2012-06. Well-posedness and asymptotic behavior a multidimensional model of morphogen transport in JOURNAL OF EVOLUTION EQUATIONS
  • 2016-09. Point spectrum of the operator corresponding to a reliability model and application in JOURNAL OF PSEUDO-DIFFERENTIAL OPERATORS AND APPLICATIONS
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    http://scigraph.springernature.com/pub.10.1007/s11868-018-0256-x

    DOI

    http://dx.doi.org/10.1007/s11868-018-0256-x

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