In this article, the investigation on a randomized arrival control policy for the prospective customers in the finite capacity queueing system with working vacation and vacation interruption is done. The impatience behavior of the customers is also considered in modeling and assumptions to the studied problem to make it more realistic. In the investigated queueing model, at the epoch when the number of customers in the system reaches system’s capacity, newly arriving customers are not allowed to join the system for service and referred as lost customers. As the length of the queue decreases to a pre-specified threshold value F, the server commences a start-up for allowing to join the customers according to an exponential distribution and starts allowing newly arriving customers to join the system for service. The steady-state probability distribution and vector representation of various system performance measures are derived using matrix-analytic approach. The cost optimization problem is also formulated, and the particle swarm optimization algorithm is implemented to determine the optimal decision parameters to achieve the minimal expected cost. Finally, some numerical results in tables and graphs are provided for the illustrative and comparative purpose which help the system analyst in decision making from the performance and economic perspective.

本文研究了带休假和休假的有限容量排队系统中潜在客户的随机到达控制策略。在建模和对研究问题的假设中还考虑了客户的不耐烦行为，以使其更加现实。在调查的排队模型中，当系统中的客户数量达到系统容量的时期，新到来的客户不允许加入系统进行服务，并称为丢失客户。随着队列的长度减小到预定阈值F，服务器开始启动以允许根据指数分布加入客户，并开始允许新到来的客户加入系统进行服务。利用矩阵分析方法推导了各种系统性能指标的稳态概率分布和矢量表示。还提出了成本优化问题，并实施了粒子群优化算法来确定最优决策参数，以实现最小的预期成本。最后，在表格和图表中提供了一些数值结果，用于说明和比较目的，有助于系统分析师从性能和经济角度进行决策。