带关闭期和启动期及负顾客的工作休假排队

在M/M/1工作休假排队模型中,引入负顾客和关闭期及启动期.启动时间相当于依照信号协议建立一个虚拟连接所延误的时间,工作休假期则可以认为是具有较低服务率的延误期,负顾客可视为外来干扰信号,并带RCE抵消策略.利用拟生灭过程和矩阵几何解法得到了系统稳态队长和稳态等待时间的分布.证明了稳态条件下的队长和等待时间的随机分解结果,得到了附加队长和附加延迟的分布.得到的结论将为ATM网络排队的优化设计提供依据.

Working vacation queue with closed-down set-up period and negative customers

In M/M/1 working vacation queue,the strategy of negative customers,closed-down and set-up period was introduced.The set-up period is the time needed for setting up a virtual connection accor-ding to signaling protocol.The working vacation period can be considered as a delayed period with a lo-wer service rate than that of busy period.With a strategy of removing customers in the end(RCE),negative customers are regarded as external noise.By quasi birth-and-death(QBD) process and matrix-geometric solution method,the distributions of the stationary queue length and stationary waiting time were obtained.The stochastic decomposition structures of queue length and waiting time in stationary state were proved to achieve the distributions of additional queue length and additional delay.The results can provide basis for optimal design of asynchronous transfer mode(ATM) networks queues.