We analyze a multi-processor two-stage tandem call center retrial queueing network in which the processors are subject to active breakdowns and repairs at stage-I. A level-dependent quasi-birth-and-death (LDQBD) process is formulated and a sufficient condition for ergodicity of the system is discussed. Under the stability condition, the stationary distribution of the number of calls in the system, the mean number of calls in the orbit, the mean waiting time of calls in the orbit and the mean busy period of the system along with other descriptors of the system are determined by using the matrix-analytic techniques. Besides, the availability analysis of the processors is also studied. Further, we have also discussed the characteristics of the first-passage time to reach the orbit critical level, the number of calls served in the call center during this period and their corresponding moments. Finally, extensive numerical results are presented to highlight the impact of the system parameters on the performance measures of the two-stage tandem call center retrial queueing system under investigation.

我们分析了一个多处理器两阶段串联呼叫中心重试排队网络，其中处理器在第一阶段受到主动故障和维修。提出了一个与水平有关的准生死（LDQBD）过程，并讨论了系统遍历的充分条件。在稳定状态下，系统中呼叫数量的固定分布，轨道中的平均呼叫数量，轨道中的平均呼叫等待时间，系统的平均繁忙时间以及系统的其他描述符通过使用矩阵分析技术确定。此外，还研究了处理器的可用性分析。此外，我们还讨论了到达轨道临界水平的首次通过时间的特征，在此期间在呼叫中心服务的呼叫数量及其相应的时刻。最后，给出了广泛的数值结果，以突出说明系统参数对所研究的两阶段串联呼叫中心重试排队系统的性能指标的影响。