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In this paper, we present a mathematical analysis to evaluate the contention phase of a wireless system in which each contending station transmits multiple copies of the bandwidth reservation/request packet to increase the probability of successful transmissions using multiple slots randomly selected from the pool of available slots at the given moment. Here, we define this type of systems as a multi-token reservation scheme with uniform random backoff (MT-UNI). The proposed MT-UNI mechanism can be used in various broadband wireless access systems including IEEE 802.16, PRMA, C-TDMA and others. The simulation results show that the proposed performance formulae are very accurate, and the MT-UNI mechanism can improve the performance of the system at low load conditions. In addition, when each station uses 2 reservation tokens, the MT- UNI scheme seems to produce the near-optimal performance.