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In this paper we present a recursive algorithm to compute some important performance metrics for wireless networks, such as throughput, channel occupancy, average number of packets in the queue and service time. Our model comprises packet queuing, channel access contention, backoff and hybrid automatic retransmission request (HARQ) error control. The analysis is carried out recursively to reduce the computational complexity and makes use of semi-Markov processes and renewal theory. We present results showing that the proposed model is able to accurately predict the aforementioned metrics even for networks with many nodes, where traditional analysis requires infeasible complexity to account for the overall network status.