Tail Asymptotically For The Queue Length Of The M/G/1 Retrial Queue

Retrial queue model is a widely applied queueing model. In recent years, retrial queue system applied to telephone switching system, communication network,computer systems and follow CSMA/CD LAN. Moreover the classical M/G/1 type of queuing theory has been studied quite perfect. Therefore M/G/1 type retrial queue model has studied in this paper based on practical and theoretical significance. The continuous and discrete retrial queue model is analyzed in this paper,then compared with standard queue of stationary queue length tail distribution,some good results are obtained.First,the basic knowledge of retrial queue system is introduced. The queuing system composition,symbol presentation method,and the main index are mainly introduced;then we show the characteristics and applications with retrial queue system;at last, we provide several related important distributions and random process.Second,we research two single arrival of retrial queues,and give some analysis of station-ary queue length tail distribution. On one hand,based on the M/G/1 retrial queue model,we obtain the correlation between the stationary queue length tail distribution of an M/G/1 retrial queue and the stationary queue length tail distribution in the corresponding standard M/G/1 queue when the service time has subexponential and regularly varying;on the other hand.based on the Geo/G/1 retrial queue model,we obtain the correlation between the sta-tionary queue length tail distribution of an Geo/G/1 retrial queue and the stationary queue length tail distribution in the corresponding standard Geo/G/1 queue when the service time has a finite exponential moment;finally,during the relation of the stationary queue length be-tween discrete-time and continuous-time,our results also can be applied to continuous-time counterpart.Third,we give out two batch arrival of retrial queues,and provide some analysis of sta-tionary queue length tail distribution. On one hand,based on the Mξ/G/1 retrial queue model.we obtain the correlation between the stationary queue length tail distribution of an M/G/1 retrial queue with batch arrival and the stationary queue length tail distribution in the corresponding standard M/G/1 queue with batch arrival,when the service time has subexponential; on the other hand,based on the Geoξ/G/1 retrial queue model.we obtain the correlation between the stationary queue length tail distribution of an Geoξ/G/1 retrial queue and the stationary queue length tail distribution in the corresponding standard.Geoξ/G/1 queue when the service time has a finite exponential moment;finally.we also obtain the equaling relation of stationary queue length between discrete-time and continuous-time in batch arrival.