具有两个备用服务台的异步限制休假排队

Asynchronous Restricted Vacation Queue with Two Standby Servers

考虑休假期间仍会有顾客到达,将备用服务台引入多服务台异步限制休假排队中.模型设有5个标准服务台和2个备用服务台,标准服务台工作时备用服务台备用,标准服务台若因某种原因休假,备用服务台立刻工作,备用服务台不休假,标准服务台采用异步限制休假.采用拟生灭过程和矩阵几何解的方法求解出系统稳态队长分布,证明了服务台全忙条件下队长和等待时间的条件随机分解,给出了附加队长的母函数和附加延迟的LST(拉普拉斯变换),并分析了备用服务台的服务率对平均附加队长和平均附加延迟的影响.

Considering the arrival of customers during the vacation,the standby servers is introduced into the multi-service asynchronous restricted vacation queue.The model has five standard servers and two standby servers.When standard servers work,standby servers are standby.If standard servers are on vacation for some reasons,the standby ones replace them immediately.Standby servers don't have vacations.Standard servers have asynchronous restricted vacations.Using QBD(quasi-birth-and death)process and matrix-geometric solution method,we obtain the steady state distribution for queue length.We prove the conditional stochastic decomposition of queue length and waiting time under the condition that all the servers are busy.We give the probability generating function of additional queue length and LST(Laplace Transform)of additional delay.The change of the average additional queue length and average additional delay with the service rate of spare service is analyzed.