【摘要】 考虑带启动时间的N-策略离散时间Geo/G/1排队系统,使用全概率分解技术,从任意初始状态出发,研究了队长的瞬态和稳态性质,推导出了在任意时刻n瞬态队长分布的z-变换的递推表达式、稳态队长分布的递推表达式和附加队长分布的表达式,并获得稳态队长的随机分解结果.最后,通过数值实例,讨论了稳态队长分布对系统参数的敏感性,并阐述了获得便于计算的稳态队长分布的表达式在系统容量的优化设计中的重要应用价值.更多还原

【Abstract】 This paper considers the discrete-time Geo/G/1 queue withN-policy and setup time.By usingthe total probability decompositiontechnique,we studythe transient and equilibriumproperties of the queue length fromthe beginning of the any initial state,obtain boththe recursion expressions of thez-transformation of the transient queuelength distribution at any timenandthe recursion expressions of the steady state queue length distribution,and the stochastic decomposition of the queue length at a randompoint in equilibrium.Finally,by numerical examples,we discuss the sensitivity of the steady state queue length distribution towards system parameters,and illustrate the important value of the expressions of the steady state queue length distribution for calculating convenientlyin the systemcapacity design.更多还原