The development of efficient media access control protocols for new generation networks, such as IEEE 802.16 metropolitan wireless system, is a challenging task nowadays. The problem of designing an efficient random multiple access algorithm for centralized data network, where subscriber stations transmit bandwidth requests to the base station in an uplink channel, is a focus of the paper. For this purpose special model for a centralized network is considered and new random multiple access algorithm is developed and analyzed. This algorithm, further referred to as distributed queue algorithm (multi-FS-ALOHA), is shown to provide higher tenacity and lower mean delay for the request transmission in comparison to binary exponential backoff, standardized in IEEE 802.16, as well as FS-ALOHA it is based on. Optimization of parameters for the developed algorithm is fulfilled; impact of the noise on its performance is investigated. The analysis is conducted by means of both analytical techniques and simulations