带有止步和状态相依的M/H_k/1排队系统——矩阵几何解法

M/H_k/1 Queuing System with Balking and State-dependent Service——the Matrix-geometric Solution

本文研究了带有止步和状态相依的M/Hk/1排队系统,建立了排队模型的拟生灭过程并获得了系统的平衡条件。利用拟生灭过程理论得到系统稳态概率的矩阵几何解。通过求解分块矩阵方程组,给出了系统边界状态概率的迭代计算公式。在此基础上,得到了系统的平均队长,平均等待队长和平均止步率等一些性能指标。

A M/Hk/1 queuing system with balking and state-dependent service was studied in this paper. The queuing model was formulated as a quasi-birth and death （QBD） process. Then, the equilibrium condition of the system was obtained. Using the QBD theory, the matrix-geometric form solution for the steady-state probability was also obtained. By solving blocked matrix equations, the iterative computation formula for the steady-state probability in boundary state was derived. Based on these analyses, some performance measures such as the expected number of the customers in the system, in the queue and the mean balking rate of the system were obtained.