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The theoretical analysis on quality-of-service (QoS) performances is required to provide the guides for the developments of the next-generation wireless networks. As a good analysis tool, the probabilistic network calculus with moment generating functions (MGFs) recently can be used for delay and backlog performance measures in wireless networks. Different from the existed studies which mostly focused on the single-hop networks with single-user under a two state Markov channel model, this study develops an analytical framework for wireless multi-hop relaying networks under the finite-state Markov channel by using probabilistic network calculus with MGFs. By using the concatenation character of network calculus, the authors regard a two-hop wireless relaying channel as a single server equivalently, which consisting of two dynamic servers in series. When the single-user model is straightforwardly extended and applied in multi-user scenarios, the state space of service process is increased exponentially with the number of users, which is only applicable in case of very small user number. Then, in order to avoid the limitation of user number, the authors propose to reflect the multi-user effects by using the equivalent data rate of the modified service process, whose transition and stationary probabilities are kept unchanged with those in single-user scenarios. Next, delay and backlog bounds of multi-hop wireless relaying networks are derived with the proposed analytical framework. Simulation results show that analytical bounds match simulation results, whose accuracy depends on the required violation probability. The effectiveness of the relaying techniques in improving the performances is also demonstrated.