We introduce a new approximation procedure to improve the accuracy of matrix analytic methods when using truncated queueing models to analyse infinite buffer systems. This is accomplished through emulating the presence of unobserved waiting customers beyond the finite buffer that are able to immediately enter the system following an observed customer’s departure. We show that this procedure results in exact steady-state probabilities at queue lengths below the buffer for truncated versions of the classic M/M/1, \(M/M/1+M\), \(M/M/\infty \), and M/PH/1 queues. We also present two variants of the basic procedure for use within a \(M/PH/1+M\) queue and a N-queue polling system with exhaustive service, phase-type service and switch-in times, and exponential impatience timers. The accuracy of these two variants in the context of the polling model are compared through several numerical examples.

我们引入了一种新的近似程序，以在使用截断排队模型分析无限缓冲系统时提高矩阵分析方法的准确性。这是通过在有限缓冲区之外模拟未观察到的等待客户的存在来实现的，这些客户能够在观察到的客户离开后立即进入系统。我们表明，对于经典M / M /1、\(M/M/1+M\)、\(M/M/\infty \)和M / PH /1 队列。我们还介绍了在\(M/PH/1+M\)队列中使用的基本过程的两种变体和一个N队列轮询系统，具有详尽服务、阶段类型服务和切换时间以及指数急躁计时器。通过几个数值示例比较了这两种变体在轮询模型上下文中的准确性。