Geo/G/1重试排队队长的尾渐近

Tail Asymptotics for the Queue Length in a Geo/G/1 Retrial Queue

利用随机分解法研究离散时间Geo/G/1重试排队队长的尾行为.通过对服务时间具有有限指数阶矩的离散时间Geo/G/1重试排队进行分析,利用稳态队长的几何尾渐近结果,得到该排队系统稳态队长尾分布与其相应的标准排队系统稳态队长尾分布的关系;再基于离散时间排队与连续时间排队的近似关系,进一步将结果应用到连续时间M/G/1重试排队.

The tail behavior of the stationary queue length of a discrete time Geo/G/1 retrial queue was studied by using stochastic decomposition.With the service time featuring a finite exponential moment,the correlation between the stationary queue length tail distribution of a Geo/G/1 retrial queue and the stationary queue length tail distribution in the corresponding standard Geo/G/1 queue was obtained by using the geometry tail asymptotic solution of the steady-state queue.Based on the approximate relation of the stationary queue length between discrete-time and continuous-time,the results can also be applied to continuous-time counterpart.