Abstract This paper deals with a discrete-time batch arrival retrial queue with the server subject to starting failures.Diferent from standard batch arrival retrial queues with starting failures,we assume that each cu...Abstract This paper deals with a discrete-time batch arrival retrial queue with the server subject to starting failures.Diferent from standard batch arrival retrial queues with starting failures,we assume that each customer after service either immediately returns to the orbit for another service with probabilityθor leaves the system forever with probability 1θ（0≤θ〈1）.On the other hand,if the server is started unsuccessfully by a customer（external or repeated）,the server is sent to repair immediately and the customer either joins the orbit with probability q or leaves the system forever with probability 1 q（0≤q〈1）.Firstly,we introduce an embedded Markov chain and obtain the necessary and sufcient condition for ergodicity of this embedded Markov chain.Secondly,we derive the steady-state joint distribution of the server state and the number of customers in the system/orbit at arbitrary time.We also derive a stochastic decomposition law.In the special case of individual arrivals,we develop recursive formulae for calculating the steady-state distribution of the orbit size.Besides,we investigate the relation between our discrete-time system and its continuous counterpart.Finally,some numerical examples show the influence of the parameters on the mean orbit size.展开更多
Chinese volleyball icon(偶像)Zhu Ting spearheaded(做……的先锋)Tianjin to a win over Henan in the opening game of the Chinese Volleyball Super League in Tianjin on Tuesday.Even though she only scored five points and r...Chinese volleyball icon(偶像)Zhu Ting spearheaded(做……的先锋)Tianjin to a win over Henan in the opening game of the Chinese Volleyball Super League in Tianjin on Tuesday.Even though she only scored five points and rested in the third set,her homecoming debut has been carefully prepared by the team and enthusiastically welcomed by the local fans.Though she was in the starting lineup,Team Tianjin gave Zhu fewer offensive tasks out of concern for her physical state.展开更多
以1,10-菲咯啉-5,6-二酮为原料,合成了标题化合物。通过质谱、1H N M R对其进行了表征。X-射线单晶衍射测试进一步确定了化合物的结构,结果表明：化合物为单斜晶系,空间群P 21/n,晶胞参数：a=1.1492（5）nm,b=1.2622（6）nm,c=1.2506（5...以1,10-菲咯啉-5,6-二酮为原料,合成了标题化合物。通过质谱、1H N M R对其进行了表征。X-射线单晶衍射测试进一步确定了化合物的结构,结果表明：化合物为单斜晶系,空间群P 21/n,晶胞参数：a=1.1492（5）nm,b=1.2622（6）nm,c=1.2506（5）nm,α=90.00°,β=100.354（12）°,γ=90.00°,V=1.784nm 3,Z=4,D c=1.274m-3,μ=0.082m m-1,最终偏离因子：R=0.0467,w R=0.1386。展开更多
基金Supported by the National Natural Science Foundation of China(Nos.11171019,11171179,and 11271373)Program for New Century Excellent Talents in University(No.NCET-11-0568)+2 种基金the Fundamental Research Funds for the Central Universities(No.2011JBZ012)Tianyuan Fund for Mathematics(Nos.11226200 and 11226251)Program for Science Research of Fuyang Normal College(2013FSKJ01ZD)
文摘Abstract This paper deals with a discrete-time batch arrival retrial queue with the server subject to starting failures.Diferent from standard batch arrival retrial queues with starting failures,we assume that each customer after service either immediately returns to the orbit for another service with probabilityθor leaves the system forever with probability 1θ（0≤θ〈1）.On the other hand,if the server is started unsuccessfully by a customer（external or repeated）,the server is sent to repair immediately and the customer either joins the orbit with probability q or leaves the system forever with probability 1 q（0≤q〈1）.Firstly,we introduce an embedded Markov chain and obtain the necessary and sufcient condition for ergodicity of this embedded Markov chain.Secondly,we derive the steady-state joint distribution of the server state and the number of customers in the system/orbit at arbitrary time.We also derive a stochastic decomposition law.In the special case of individual arrivals,we develop recursive formulae for calculating the steady-state distribution of the orbit size.Besides,we investigate the relation between our discrete-time system and its continuous counterpart.Finally,some numerical examples show the influence of the parameters on the mean orbit size.
文摘Chinese volleyball icon(偶像)Zhu Ting spearheaded(做……的先锋)Tianjin to a win over Henan in the opening game of the Chinese Volleyball Super League in Tianjin on Tuesday.Even though she only scored five points and rested in the third set,her homecoming debut has been carefully prepared by the team and enthusiastically welcomed by the local fans.Though she was in the starting lineup,Team Tianjin gave Zhu fewer offensive tasks out of concern for her physical state.
文摘以1,10-菲咯啉-5,6-二酮为原料,合成了标题化合物。通过质谱、1H N M R对其进行了表征。X-射线单晶衍射测试进一步确定了化合物的结构,结果表明：化合物为单斜晶系,空间群P 21/n,晶胞参数：a=1.1492（5）nm,b=1.2622（6）nm,c=1.2506（5）nm,α=90.00°,β=100.354（12）°,γ=90.00°,V=1.784nm 3,Z=4,D c=1.274m-3,μ=0.082m m-1,最终偏离因子：R=0.0467,w R=0.1386。
