服务台可修的M/G/1/N排队系统分析(Ⅱ)

The analysis of M/G/1/N queuing system with repairable service station (Ⅱ)

本文在较弱的假定下进一步讨论了服务台可修的M/G/1/N排队系统模型,利用“补充变量法”建立了系统状态概率的微分-差分方程组,运用Laplace变换等工具还得到了系统状态概率的一个递推公式。当N较小时,由递推公式易得系统状态概率的Laplace变换的明显表达式,由此即可求出有关的排队论指标和可靠性指标。

This article discusses the M / G / 1 / N queuing system with a repairable service station under a weaker condition than in paper (5). Using the 'inclusion of supplementary variable technique' we have set up the differential-difference equations of system state probability, and also developed the recurrence formula of system state probability using Laplace transformation and other techniques. For a small N, we could obtain the Laplace transformation of system state probability in an explicit form directly from the recurrence formula, so that we could get the number quantities of system state probability for the quening theory and reliability.