| ANALYSIS AND COMPUTATIONAL ALGORITHM FOR QUEUES WITH STATE-DEPENDENT VACATIONS I： G/M（n）/1/K |
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| 引用本文： | Xiuli CHAO Ayyar RAHMAN. ANALYSIS AND COMPUTATIONAL ALGORITHM FOR QUEUES WITH STATE-DEPENDENT VACATIONS I： G/M（n）/1/K[J]. 系统科学与复杂性, 2006, 19(1): 36-53. DOI: 10.1007/s11424-006-0036-1 |
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| 作者姓名： | Xiuli CHAO Ayyar RAHMAN |
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| 作者单位： | Industrial Engineering and Operations Research, North Carolina State University, Raleigh, NC 27695, USA |
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| 基金项目： | The research is partially supported by National Science Foundation under DMI-0200306. |
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| 摘 要： | In this paper we study a queueing system with state-dependent services and state-dependent vacations, or simply G/M（n）/1/K. Since the service rate is state-dependent, this system includes G/M/c and G/M/c/K queues with various types of station vacations as special cases. We provide a recursive algorithm using the supplementary variable technique to numerically compute the stationary queue length distribution of the system. The only input requirement is the Laplace-Stieltjes transform of the interarrival distribution as well as the state-dependent service rate and state-dependent vacation rate. In a subsequent companion paper, we study its dual system M（n）/G/1/K queue with statedependent vacations.
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| 关 键 词： | G/M（n）/1/K行列 递归算法 队列长度分布 可移动服务器 补充变量 |
| 收稿时间： | 2005-10-09 |
| 修稿时间： | 2005-10-09 |
Analysis and Computational Algorithm for Queues with State-Dependent Vacations I: G/M(n)/1/K |
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| Xiuli Chao,Ayyar Rahman. Analysis and Computational Algorithm for Queues with State-Dependent Vacations I: G/M(n)/1/K[J]. Journal of Systems Science and Complexity, 2006, 19(1): 36-53. DOI: 10.1007/s11424-006-0036-1 |
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| Authors: | Xiuli Chao Ayyar Rahman |
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| Affiliation: | (1) Industrial Engineering and Operations Research, North Carolina State University, Raleigh, NC 27695, USA |
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| Abstract: | In this paper we study a queueing system with state-dependent services and state-dependent vacations,or simply G/M(n)/I/K:Since the service rate is state-dependent,this system includes G/M/c and G/M/c/K queues with various types of station vacations as special cases.We provide a recursive algorithm using the supplementary variable technique to numerically compute the stationary queue length distribution of the system.The only input requirement is the Laplace-Stieltjes transform of the interarrival distribution as well as the state-dependent service rate and state-dependent vacation rate.In a subsequent companion paper,we study its dnal system M(n)/G/1/K queue with state- dependent vacations. |
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| Keywords: | G/M(n)/1/K queue recursive algorithm queue length distribution removable server supplementary variable state-dependent service and vacations |
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