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<p>The efficiency of a machine repair system (MRS) is critical in industrial environments to sustain uninterrupted operations and reduce productivity losses. This study examines the queueing dynamics of an M/M/1/K/WV MRS incorporating a working vacation (WV), retrial queue (RQ), server (repairman) breakdown, and dual-phase repair mechanisms. When failed machines (FMs) arrive, and the repairman is busy, they are sent to a waiting area called the retrial orbit. After a random interval, these FMs reattempt to access repair services. Additionally, dissatisfied FMs from the phase-1 repair can proceed to a phase-2 repair process, ensuring adequate and satisfactory repairs. Furthermore, the working vacation concept is incorporated, allowing repairs to continue during the repairman’s vacation period, albeit at a slower rate than usual. A Markovian-based machine repair system is designed to derive transient probabilities using the Laplace transform (LT) and the matrix analytical method. From these probabilities, various queueing indices and reliability indices are derived. Furthermore, a non-linear cost function is formulated to optimize decision variables, such as repair rates during the phase-1 and phase-2 repair processes in WVP and NBP. Particle swarm optimization (PSO) and genetic algorithm (GA) methods are applied to address the cost optimization problem, with a comparative analysis of their performance. The findings suggest that the proposed model is versatile and applicable to real-world scenarios like transportation industries, manufacturing systems, and other operational environments.</p>

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Transient analysis and cost optimization of a machine repair system with dual-phase repair, working vacation, and retrial

  • 期刊论文

  • 发表日期：

    2026年3月16日

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  • Khushbu S. Antala,
  • Vijaykumar Panchal,
  • Sudeep Singh Sanga

摘要

The efficiency of a machine repair system (MRS) is critical in industrial environments to sustain uninterrupted operations and reduce productivity losses. This study examines the queueing dynamics of an M/M/1/K/WV MRS incorporating a working vacation (WV), retrial queue (RQ), server (repairman) breakdown, and dual-phase repair mechanisms. When failed machines (FMs) arrive, and the repairman is busy, they are sent to a waiting area called the retrial orbit. After a random interval, these FMs reattempt to access repair services. Additionally, dissatisfied FMs from the phase-1 repair can proceed to a phase-2 repair process, ensuring adequate and satisfactory repairs. Furthermore, the working vacation concept is incorporated, allowing repairs to continue during the repairman’s vacation period, albeit at a slower rate than usual. A Markovian-based machine repair system is designed to derive transient probabilities using the Laplace transform (LT) and the matrix analytical method. From these probabilities, various queueing indices and reliability indices are derived. Furthermore, a non-linear cost function is formulated to optimize decision variables, such as repair rates during the phase-1 and phase-2 repair processes in WVP and NBP. Particle swarm optimization (PSO) and genetic algorithm (GA) methods are applied to address the cost optimization problem, with a comparative analysis of their performance. The findings suggest that the proposed model is versatile and applicable to real-world scenarios like transportation industries, manufacturing systems, and other operational environments.