The ranging algorithm allows active stations to measure their distances to the headend for synchronization purpose in Hybrid Fiber Coax (HFC) networks. A practicable mechanism to resolve contention among numerous stations is to randomly delay the transmission of their control messages. Since shorter contention cycle time increases slot throughput, this study develops three mechanisms, fixed random delay, variable random delay, and optimal random delay, to minimize the contention cycle time. Simulation demonstrates that the optimal random delay effectively minimizes the contention cycle time and approaches the theoretical optimum throughput of 0.18 from pure ALOHA. Furthermore, over-estimation reduces the impact on contention cycle time more than under-estimation through sensitivity analysis, and both phenomenon damage slot throughput. Two estimation schemes, maximum likelihood and average likelihood, are thereby presented to estimate the number of active stations for each contention resolution round. Simulation proofs that the proposed estimation schemes are effective even when the estimated number of active stations in initial contention round is inaccurate.