A result of Ward and Glynn (2005) asserts that the sequence of scaled offered waiting time processes of the GI/GI/1+GI queue converges weakly to a reflected Ornstein-Uhlenbeck process (ROU) in the positive real line, as the traffic intensity approaches one. We prove the convergence of the scaled stationary distributions of the offered waiting time process and their moments as the traffic intensity approaches one; thus the stationary distribution of ROU provides a valid approximation for the steady-state of the original offered waiting time process. {Our study extends Kingman's classical result to incorporate customer abandonments, irrespective of whether the system loading factor approaches 1 from above or below.

中文翻译：

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为 $$GI/GI/1+GI$$GI/GI/1+GI 队列在大流量中提供的等待进程的平稳分布收敛

Ward 和 Glynn (2005) 的结果断言 GI/GI/1+GI 队列的缩放提供等待时间过程的序列弱收敛到正实线中的反射 Ornstein-Uhlenbeck 过程 (ROU)，因为流量强度接近一。我们证明了当交通强度接近 1 时，所提供的等待时间过程及其时刻的缩放平稳分布的收敛性；因此，ROU 的平稳分布为原始提供的等待时间过程的稳态提供了有效的近似值。{我们的研究扩展了 Kingman 的经典结果以纳入客户放弃率，无论系统负载因子是从上方还是下方接近 1。