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Dense passive radio frequency identification (RFID) systems are particularly susceptible to reader collision problems, categorized by reader-to-tag and reader-to-reader collisions. Both may degrade the system performance decreasing the number of identified tags per time unit. Although many proposals have been suggested to avoid or handle these collisions, most of them are not compatible with current standards and regulations, require extra hardware and do not make an efficient use of the network resources. This paper proposes the Geometric Distribution Reader Anti-collision (GDRA), a new centralized scheduler that exploits the Sift geometric probability distribution function to minimize reader collision problems. GDRA provides higher throughput than the state-of-the-art proposals for dense reader environments and, unlike the majority of previous works, GDRA is compliant with the EPCglobal standard and ETSI EN 302 208 regulation, and can be implemented in real RFID systems without extra hardware.