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.