GI/G/1 queue with vacations;
fluid approximation;
exponential rate of convergence;
NETWORKS;
D O I:
10.1007/s10255-011-0038-1
中图分类号:
O29 [应用数学];
学科分类号:
070104 ;
摘要:
A GI/G/1 queue with vacations is considered in this paper. We develop an approximating technique on max function of independent and identically distributed (i.i.d.) random variables, that is max{eta (i) , 1 a parts per thousand currency sign i a parts per thousand currency sign n}. The approximating technique is used to obtain the fluid approximation for the queue length, workload and busy time processes. Furthermore, under uniform topology, if the scaled arrival process and the scaled service process converge to the corresponding fluid processes with an exponential rate, we prove by the approximating technique that the scaled processes characterizing the queue converge to the corresponding fluid limits with the exponential rate only for large N. Here the scaled processes include the queue length process, workload process and busy time process.
机构:Western Washington Univ, Coll Business & Econ, Dept Finance Mkt & Decis Sci, Bellingham, WA 98225 USA
Tian, NS
Zhang, ZG
论文数: 0引用数: 0
h-index: 0
机构:
Western Washington Univ, Coll Business & Econ, Dept Finance Mkt & Decis Sci, Bellingham, WA 98225 USAWestern Washington Univ, Coll Business & Econ, Dept Finance Mkt & Decis Sci, Bellingham, WA 98225 USA
机构:
Beijing Jiaotong Univ, Dept Math, Beijing 100044, Peoples R China
Fuyang Normal Coll, Dept Math, Fuyang 236037, Peoples R ChinaBeijing Jiaotong Univ, Dept Math, Beijing 100044, Peoples R China
Gao, Shan
Yao, Yunfei
论文数: 0引用数: 0
h-index: 0
机构:
Fuyang Normal Coll, Dept Math, Fuyang 236037, Peoples R ChinaBeijing Jiaotong Univ, Dept Math, Beijing 100044, Peoples R China