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In this paper, we examine the performance of uniform backoff (UB) and binary exponential backoff (BEB) algorithms with retry limit, which can be used in the random-access channels of Universal Mobile Telecommunication System (UMTS)-Long Term Evolution (LTE) and IEEE 802.16 systems under the assumption of finite population under unsaturated traffic conditions. Additionally, we consider access prioritization schemes to provide differential performance by controlling various system parameters. We show that controlling the persistence value as specified in UMTS is effective in both backoff algorithms. The performances with and without access prioritization schemes are presented in terms of throughput, mean, and variance of packet retransmission delay, packet-dropping probability, and system stability. Finally, we consider a dynamic window assignment algorithm that is based on Bayesian broadcasting, in which the base station adaptively controls the window size of the UB algorithm under unsaturated traffic conditions. Results show that the proposed window assignment algorithm outperforms fixed window assignment in static and dynamic traffic conditions under the assumption of perfect orthogonality between random-access codes.