系统工程理论与实践
繫統工程理論與實踐
계통공정이론여실천
Systems Engineering—Theory & Practice
2011年
1期
131~137
,共null页
N-策略排队 启动时间 队长分布 随机分解 全概率分解技术
N-策略排隊 啟動時間 隊長分佈 隨機分解 全概率分解技術
N-책략배대 계동시간 대장분포 수궤분해 전개솔분해기술
N-policy queue; set-up; queue length distribution; stochastic decomposition; total probability decomposition technique
考虑带启动时间的N-策略M/G/1排队系统,从任意初始状态出发,直接研究了系统队长的瞬态分布和稳态分布.通过引进的＂服务员忙期＂,使用全概率分解技术和拉普拉斯变换,导出了在任意时刻t队长的瞬态分布的拉普拉斯变换的表达式,进一步获得了有重要应用价值的稳态分布的具体的递推式子,以及稳态队长的随机分解结果.特别地,还直接获得了一些特殊排队系统的更实用的稳态队长分布的递推表达式.
攷慮帶啟動時間的N-策略M/G/1排隊繫統,從任意初始狀態齣髮,直接研究瞭繫統隊長的瞬態分佈和穩態分佈.通過引進的＂服務員忙期＂,使用全概率分解技術和拉普拉斯變換,導齣瞭在任意時刻t隊長的瞬態分佈的拉普拉斯變換的錶達式,進一步穫得瞭有重要應用價值的穩態分佈的具體的遞推式子,以及穩態隊長的隨機分解結果.特彆地,還直接穫得瞭一些特殊排隊繫統的更實用的穩態隊長分佈的遞推錶達式.
고필대계동시간적N-책략M/G/1배대계통,종임의초시상태출발,직접연구료계통대장적순태분포화은태분포.통과인진적＂복무원망기＂,사용전개솔분해기술화랍보랍사변환,도출료재임의시각t대장적순태분포적랍보랍사변환적표체식,진일보획득료유중요응용개치적은태분포적구체적체추식자,이급은태대장적수궤분해결과.특별지,환직접획득료일사특수배대계통적경실용적은태대장분포적체추표체식.
This paper considered the M/G/1 queue with N-policy and set-up times,and directly studied both the transient distribution and equilibrium distribution of the queue length.By introducing the server busy period,and using the total probability decomposition technique and Laplace transform,the recursion expressions of the Laplace transform of the transient queue length distribution at any time t are obtained. Furthermore,the recursion expressions of the distribution and stochastic decomposition of the queue length at a random point in equilibrium are also obtained,which have important value on application.Especially, some corresponding results which have more really value in some special queueing models are obtained directly.
