Scholarlink

<p>In certain queueing circumstances, a bi-level vacation policy according to which the server can switch over from the working vacation (WV) to the complete vacation (CV) has been noticed. In the WV (CV) mode, customers may exhibit reneging behavior due to the slow (absence&#xa0;of) service. This study examines the queueing metrics of a Markovian queueing system incorporating the concepts of the bi-level hybrid vacation strategy, state-dependent rates, discouraged customers, and waiting servers. The continued fraction, the probability generating function (PGF), and the confluent hypergeometric function are used to derive the transient queue size distributions. As a special case of the transient results, we derive the steady-state results. The analytical results for the average system size, variance, average reneging rate, system throughput, etc. are established. Furthermore, the cost function framed is optimized to provide the optimal decision parameters and respective minimum cost. Numerical simulation and parameter sensitivity have been performed by taking illustrations.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Analytical and Computational Study of Bi-level Vacation Policy for Transient Markovian Queue with State-Dependent Rates, Waiting Server, and Discouragement

  • 期刊论文

  • 发表日期：

    2025年1月2日

查看全文
  • Mayank Singh,
  • Madhu Jain,
  • Vijay Pratap Singh

摘要

In certain queueing circumstances, a bi-level vacation policy according to which the server can switch over from the working vacation (WV) to the complete vacation (CV) has been noticed. In the WV (CV) mode, customers may exhibit reneging behavior due to the slow (absence of) service. This study examines the queueing metrics of a Markovian queueing system incorporating the concepts of the bi-level hybrid vacation strategy, state-dependent rates, discouraged customers, and waiting servers. The continued fraction, the probability generating function (PGF), and the confluent hypergeometric function are used to derive the transient queue size distributions. As a special case of the transient results, we derive the steady-state results. The analytical results for the average system size, variance, average reneging rate, system throughput, etc. are established. Furthermore, the cost function framed is optimized to provide the optimal decision parameters and respective minimum cost. Numerical simulation and parameter sensitivity have been performed by taking illustrations.