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<p>In this paper we analyse a multi-server <i>k</i>-out-of-<i>n</i>: F system with <i>N</i> policy of repair. There are <i>n</i> identical servers in this queuing system. Customers arrive to the system according to a Poisson process. Service time of each customer is exponentially distributed. Servers are subjected to breakdown, which happens at exponentially distributed time intervals. The repair process will be conducted in accordance with the <i>N</i> policy and the time for repairing each failed server is exponentially distributed. Even though all these <i>n</i> servers operate independently of one another, the system cannot function if any <i>k</i> of its servers fails. Throughout this paper we assume the system to be COLD. Using Matrix Analytic Method we perform the steady state analysis of the model. We compute several performance measures associated with the system and evaluate the impact of various system parameters on them using numerical examples. Also we discuss an optimization problem.</p>

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On a Multi-Server k-out-of-n: F System with Repair under N Policy

  • 期刊论文

  • 发表日期：

    2025年5月29日

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  • Greeshma Joseph,
  • Varghese Jacob,
  • Achyutha Krishnamoorthy,
  • Ambily P. Mathew

摘要

In this paper we analyse a multi-server k-out-of-n: F system with N policy of repair. There are n identical servers in this queuing system. Customers arrive to the system according to a Poisson process. Service time of each customer is exponentially distributed. Servers are subjected to breakdown, which happens at exponentially distributed time intervals. The repair process will be conducted in accordance with the N policy and the time for repairing each failed server is exponentially distributed. Even though all these n servers operate independently of one another, the system cannot function if any k of its servers fails. Throughout this paper we assume the system to be COLD. Using Matrix Analytic Method we perform the steady state analysis of the model. We compute several performance measures associated with the system and evaluate the impact of various system parameters on them using numerical examples. Also we discuss an optimization problem.