The primary task of radio-frequency identification (RFID) readers is to identify multiple objects as quickly and reliably as possible with minimal power consumption and computation. An optimisation problem related to the selection of appropriate frame sizes for the framed slotted ALOHA protocol, commonly used in passive RFID tag identification systems, is considered. The fundamental question concerning this issue is: what frame size is most suitable for identifying as many tags as possible in a given time? More formally, what is the optimal value for frame sizes in the sense that the probability of successful identification is maximised? Thus far, many research results related to this problem have been reported in the literature, but most are either suboptimal or empirical. Through asymptotic analysis, it is shown that the optimal frame size is approximately given by N/ln 2 for N tags.