Asymptotic analysis of Schoute´s estimate for dynamic frame Aloha

This paper represents a further attempt to provide definite results about the asymptotic performance of protocols of the dynamic frame Aloha (DFA) family for radio frequency identification (RFID) systems. Here we deal with a simple and popular backlog estimate known as Schoute´s estimate, apt to the DFA version that do not make use of the Frame Restart capability. This estimate performs very well in multiple access systems, but presents some efficiency impairment in RFID. Recent studies have shown that, with a perfect backlog estimate, the asymptotic efficiency of DFA, with or without Frame Restart, equals e^-1. Here we prove that the asymptotic efficiency of Schoute´s backlog estimate is 0.311 for any finite initial frame length. The analysis shows that the impairment is due to the slow convergence of the estimate to the true value, and opens the path to future work.