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<p>In this paper, we consider a single server queueing system with working breakdown. The arrival and service processes evolve through transitions on the product space of two Markov chains and they are assumed to be interdependent. The transitions in the product space are governed by a semi-Markov rule, with sojourn times in states governed by the exponential distribution. The server failure occurs according to a Poisson process with rate <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12597_2025_938_Article_IEq1.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(\gamma\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>γ</mi> </math></EquationSource> </InlineEquation>. The repair time of the server follows exponential distribution with parameter <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12597_2025_938_Article_IEq2.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">\(\beta\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>β</mi> </math></EquationSource> </InlineEquation>. During the working breakdown, the server continues serving the customers, at a low rate. Simultaneously repair of the server is done. When the repair is completed, the server resumes normal service. We analyse this model using the matrix geometric method. Numerical illustrations are provided. </p>

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On queues with working breakdown and interdependence between arrival and service processes

  • 期刊论文

  • 发表日期：

    2025年4月2日

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  • S. Sindhu,
  • Achyutha Krishnamoorthy

摘要

In this paper, we consider a single server queueing system with working breakdown. The arrival and service processes evolve through transitions on the product space of two Markov chains and they are assumed to be interdependent. The transitions in the product space are governed by a semi-Markov rule, with sojourn times in states governed by the exponential distribution. The server failure occurs according to a Poisson process with rate \(\gamma\) γ . The repair time of the server follows exponential distribution with parameter \(\beta\) β . During the working breakdown, the server continues serving the customers, at a low rate. Simultaneously repair of the server is done. When the repair is completed, the server resumes normal service. We analyse this model using the matrix geometric method. Numerical illustrations are provided.