延迟D-策略Geo/G/1排队系统的队长分布及容量的优化设计

Queue size distribution and capacity optimum design for Geo/G/1 queueing system with delayed D-policy

考虑延迟D-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-变换的递推表达式和稳态队长分布的递推表达式,并获得稳态队长的随机分解结果,同时得到了系统在三种任意时刻(n^-,n,n^+)处稳态队长分布的重要关系.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优化设计中的重要应用价值.

This paper considers the discrete-time Geo/G/1 queueing system with delayed D-policy. By using the total probability decomposition technique, we study the transient and equilibrium properties of the queue length from the beginning of the any initial state, obtain both the recursion expressions of the z-transformation of the transient queue length distribution at any time n＋ and the recursion expressions of the steady state queue length distribution, and then we give the stochastic decomposition of the queue length in equilibrium. The important relations between the steady state queue length distributions at different epochs （n , n, n＋） are discovered. 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 conveniently in the system capacity design.