  In this paper we investigate backlog estimation procedures for Dynamic Frame
Aloha (DFA) in Radio Frequency Identification (RFID) environment. In
particular, we address the tag identification efficiency with any tag number
$N$, including $N\rightarrow\infty$. Although in the latter case efficiency
$e^{-1}$ is possible, none of the solution proposed in the literature has been
shown to reach such value. We analyze Schoute's backlog estimate, which is very
attractive for its simplicity, and formally show that its asymptotic efficiency
is 0.311. Leveraging the analysis, we propose the Asymptotic Efficient backlog
Estimate (AE$^2$) an improvement of the Schoute's backlog estimate, whose
efficiency reaches $e^{-1}$ asymptotically. We further show that AE$^2$ can be
optimized in order to present an efficiency very close to $e^{-1}$ for
practically any value of the population size. We also evaluate the loss of
efficiency when the frame size is constrained to be a power of two, as required
by RFID standards for DFA, and theoretically show that the asymptotic
efficiency becomes 0.356.
