摘要
考虑了一个带有部分工作休假和休假中断的多服务台M/M/c排队.在休假期,d(d<c)个服务员以慢速继续服务新到顾客,其余c-d个服务员进行正常休假.同时,引入另一种休假策略:休假中断,即当休假期服务员服务完一个顾客,系统中至少有d个顾客,则所有服务员中断休假返回正常工作期;否则继续休假.利用拟生灭过程和矩阵几何解方法,得到了系统稳态下的队长分布;同时,表明了稳态队长和等待时间在服务员全忙条件下的条件随机分解结构.
Consider a multi-server M/M/c queue with partial working vacations and vacation interruption. In such system, d servers keep on taking service at a lower rate in the vacation period,and the other c- d servers go to the normal vacation. Meanwhile, we introduce another vacation policy., vacation interruption, i. e., when a service is completed in the vacation period, if there are at least d customers in the system, all servers will come back to the normal working level rather than keeping on the vacation; otherwise, they continue the vacation. Using quasi birth and death process and matrix-geometric solution method, we obtain the steady-state distribution for queue length. Furthermore, we indicate conditional stochastic decomposition structures for queue length and waiting time under the condition that all the servers are busy.
出处
《数学的实践与认识》
CSCD
北大核心
2009年第8期129-134,共6页
Mathematics in Practice and Theory
基金
国家自然科学基金(10671170)
燕山大学优秀博士生资助
关键词
多服务台
部分工作休假
休假中断
矩阵几何解
条件随机分解
multi-server
partial working vacations
vacation interruption
matrix-geometric solution
conditional stochastic decomposition
