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If we assume that during the RTAP a tag is allowed to transmit only once, the average trial count until the transmission succeeds is:
Since we can measure the empty slot count [E.sub.empty] from the result of previous RTAP, the number of transmitted tags can be estimated as:
After an RTAP with a certain slot count L, the number of transmitted tags during the RTAP can be obtained probabilistically as in (13).
where [N.sub.succ] is the number of successfully transmitted tags during the last RTAP.
Meanwhile, the increment of RTAP slot count increases the effort of finding the beacon signal as well, hence incurring increased power consumption.
where [P.sub.trans-prev] is the transmission probability used in the previous RTAP. Then the optimal transmission probability for the next RTAP can be obtained as follows:
where L is a fixed slot count in a single RTAP. Since the optimal throughput can be obtained regardless of L, we can determine the slot count merely in terms of energy efficiency.
Since our algorithm employs two different periods, STAP and RTAP, the channel utilization should be considered for each period, respectively.
Any device wishing to communicate during the CAP shall compete with other devices using a slotted CSMA-CA mechanism as in the RTAP of our proposed method.
6 depicts the simulation results regarding the channel utilization of RTAP. As derived in section 4.3, the best throughput is obtained when the slot count in RTAP is the same as the available tag count.
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