d型工作休假的多台M/M/c排队及在HCS中的应用
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摘要
在多服务台M/M/c排队系统中,引入半空竭服务的d型工作休假策略.当系统中有d个服务台空闲时,令d个空闲的服务台开始一次多重同步工作休假,休假期间的服务台继续慢速服务新到顾客,其余c-d个服务台正常工作.在工作休假期间,系统中顾客数小于等于c-d个时,一个顾客的离开是由正常工作速率服务台完成的.系统中顾客数多于c-d个时,一个服务的完成可能是接受了正常速率服务,也可能是接受了低速服务.利用拟生灭过程和矩阵几何解方法得到了稳态队长分布,给出模型在多层蜂窝系统(HCS)中的应用,并对影响系统性能指标的参数做出了数值分析.
Introducing the half exhaustive and the d setup time policy into an multi-server M/M/c queue.d servers take multiple synchronous working vacation when there are d servers become idle in a system with c servers,the servers on working vacation keep on serving new customers in a low rate,and the rest c-d servers work as usual.During the working vacation,a customer's departure is done by the normal working rate server when the customers is not more than c-d,while the number of customer is more than c-d,a customer's departure is done by the normal work rate or low rate.Using a quasi-birth and death process and matrix geometric method,we obtain the stationary distributions of queue length,giving an application in hierarchical cellular mobile communication system with the numerical analysis of parameters which influence the system performance index.
Introducing the half exhaustive and the d setup time policy into an multi-server M/M/c queue.d servers take multiple synchronous working vacation when there are d servers become idle in a system with c servers,the servers on working vacation keep on serving new customers in a low rate,and the rest c-d servers work as usual.During the working vacation,a customer's departure is done by the normal working rate server when the customers is not more than c-d,while the number of customer is more than c-d,a customer's departure is done by the normal work rate or low rate.Using a quasi-birth and death process and matrix geometric method,we obtain the stationary distributions of queue length,giving an application in hierarchical cellular mobile communication system with the numerical analysis of parameters which influence the system performance index.
引文
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[4]朱翼隽,徐鸿洋.N-策略带负顾客的M/M/c部分工作休假排队[J].江苏大学学报(自然科学版),2013,34(3):367-372.
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[8]Neuts M F.Matrix-geometric solutions in stochastic models[M].Johns Hopkins University Press,1981.
[2]田乃硕,徐秀丽,马振友,韦才敏.部分服务台同步多重休假的M/M/c排队[J].运筹学学报,2001,5(3):85-94.
[3]李继红,李文焘,田乃硕.带有部分工作休假和休假中断的M/M/c排队[J].数学的实践与认识,2009,39(8):129-134.
[4]朱翼隽,徐鸿洋.N-策略带负顾客的M/M/c部分工作休假排队[J].江苏大学学报(自然科学版),2013,34(3):367-372.
[5]Xu X L,Tian N S.The M/M/c queue with(e,d)setup time[J].Journal of Systems Science and Complexity,2008,21(3):446-455.
[6]Lo K R,Chang C J,Chang C,Shung C B.A QoS-guaranteed fuzzy channel allocation controller for hierarchical cellular systems[J].IEEE Transactions on Vehicular Technology,1999,49(5):1588-1598.
[7]Lo K R,Chang C J,Chang C,Shung C B.A combined channel assignment mechanism for hierarchical cellular systems 1[J].Computer Communications,1998,21(13):1143-1152.
[8]Neuts M F.Matrix-geometric solutions in stochastic models[M].Johns Hopkins University Press,1981.