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<p>By using functional analysis we study well-posedness, asymptotic behavior of the time-dependent solution and asymptotic behavior of some time-dependent performance measures of the M/G/1 retrial queueing model with general retrial times, negative customers, feedback and repairs. This queueing model is described by infinitely many partial differential equations with integral boundary conditions. Under some conditions, by using <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11868_2024_672_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="36" /> </InlineMediaObject> <EquationSource Format="TEX">\(C_0-\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>C</mi> <mn>0</mn> </msub> <mo>-</mo> </mrow> </math></EquationSource> </InlineEquation>semigroup theory and spectral theory of linear operators, we prove that this model has a unique positive time-dependent solution which satisfies the probability condition and its time-dependent solution converges strongly to its steady-state solution. Moreover, we give asymptotic behavior of some time-dependent indices of the queueing system. Finally, we conclude with some further research problems.</p>

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Application of functional analysis in research of an M/G/1 retrial queueing model

  • 期刊论文

  • 发表日期：

    2025年1月8日

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  • Zhuocheng Xu,
  • Geni Gupur

摘要

By using functional analysis we study well-posedness, asymptotic behavior of the time-dependent solution and asymptotic behavior of some time-dependent performance measures of the M/G/1 retrial queueing model with general retrial times, negative customers, feedback and repairs. This queueing model is described by infinitely many partial differential equations with integral boundary conditions. Under some conditions, by using \(C_0-\) C 0 - semigroup theory and spectral theory of linear operators, we prove that this model has a unique positive time-dependent solution which satisfies the probability condition and its time-dependent solution converges strongly to its steady-state solution. Moreover, we give asymptotic behavior of some time-dependent indices of the queueing system. Finally, we conclude with some further research problems.