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The paper models and analyzes the end-to-end performance in a multi-hop wireless data network for a class of hop-level ARQ (automatic repeat request) protocols. The performance metric is the number of transmissions required for successful delivery of a packet over a multi-hop path. By using a discrete time Markov model, the distribution for the required number of transmissions is modeled as a phase type distribution. The paper investigates the effects of different network parameters, such as packet error rate in each hop, maximum number of allowable retransmissions at each hop and retransmission probability at each hop, on the required total number of transmissions. The novelty of this model is that the probability density function (pdf) for the number of transmissions required for successful end-to-end delivery of a packet can easily be obtained from this model. Using the pdf, different quality of service (QoS) performance metrics, such as end-to-end delay, transmission energy and percentage of data delivery, can be calculated. The numerical results obtained from this model are observed to be very close to those obtained from simulation for end-to-end TCP (transmission control protocol) and reliable UDP (user datagram protocol) flows, which demonstrates the usefulness of this model for analyzing end-to-end protocol performance across multi-hop wireless links.