ABSTRACT

In the present article, we deal with the multi-server finite capacity queueing system with Bernoulli’s scheduled modified vacation policy and the realistic retaining policy of reneged customers. After completion of the service of any customer, the server decides whether to go for the vacation of random duration or to continue facilitating the service to the waiting customer, if any, present in the queue. All servers, homogeneous in nature, provide the state-dependent service following the threshold policy to reduce the overload of the system. The impatience behavior of customers like balking and reneging is also considered in the stochastic modeling of the studied problem. The matrix analytic approach is employed to obtain the steady-state probabilities with which various system performance measures are also developed with practical justification. Finally, the expected cost minimization problem is formulated and dealt with the meta-heuristic approach: particle swarm optimization (PSO). All results of numerical simulation and optimal analysis are summarized in tables and graphs to provide quick insight. The concluding remarks and future scopes have also been discussed.

摘要

在本文中，我们使用Bernoulli的计划的修改后的休假策略和保留客户的实际保留策略来处理多服务器有限容量排队系统。在完成任何客户的服务后，服务器将决定是随机休假还是继续为队列中存在的等待客户（如果有）提供服务。本质上是同质的所有服务器都遵循阈值策略来提供状态相关的服务，以减少系统的过载。在所研究问题的随机建模中还考虑了客户的急躁行为，例如行和退潮。采用矩阵分析方法来获得稳态概率，并利用实际理由开发各种系统性能度量。最后，制定了预期成本最小化问题，并用元启发式方法进行了处理：粒子群优化（PSO）。表格和图表中汇总了数值模拟和最佳分析的所有结果，以提供快速的洞察力。结束语和将来的范围也进行了讨论。