Abstract

We present analytic expressions (in terms of roots of the underlying characteristic equation) for the steady-state distributions of the number of customers for the finite-state queueing model $Ge{o}^X/G/1/N+1$ with partial-batch rejection policy. We obtain the system-length distributions at a service-completion epoch by applying the imbedded Markov chain technique. Using the roots of the related characteristic equation, the method leads to giving a unified approach for solving both finite- and infinite-buffer systems. We find relationships between system-length distributions at departure, random, and arrival epochs using discrete renewal theory and conditioning on the system states. Based on these relationships, we obtain various performance measures and provide numerical results for the same. We also perform computational analysis and compare our results with respect to the solution obtained by solving a linear system of equations in terms of running times.

摘要

我们提出了有限状态排队模型的客户数量的稳态分布的解析表达式（根据基本特征方程的根）$Ge{○}^X/G/1/ñ+1$部分批次拒绝政策。我们通过应用嵌入式马尔可夫链技术获得了服务完成时期的系统长度分布。使用相关特征方程的根，该方法导致为求解有限和无限缓冲系统提供统一的方法。我们使用离散更新理论和对系统状态的调节，发现了出发、随机和到达时期的系统长度分布之间的关系。基于这些关系，我们获得了各种性能指标并提供了相同的数值结果。我们还执行计算分析，并将我们的结果与通过求解线性方程组在运行时间方面获得的解进行比较。