This paper investigates the near-memoryless behavior of the service time for IEEE 802.11 saturated single-hop ad hoc networks. We show that the number of packets successfully transmitted by any node over a time interval follows a general distribution, which is close to a Poisson distribution with an upper bounded distribution distance. The bound on the distribution distance is almost constant and is mainly affected by some system parameters and very slightly by the number of active nodes in the network. We also show that the service time distribution can be approximated by a geometric distribution. We illustrate that the usage of discrete-time queuing analysis (M/Geo/1) near network saturation greatly simplifies the queuing analysis and leads to sufficiently accurate results for both the first order statistics and the probability distribution of the number of packets in the queuing system. Computer simulation results demonstrate that the M/Geo/1 queuing model is very accurate.