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An Long Term Evolution (LTE) network based mobile Internet of Things (IoT) is modeled and analyzed with the probabilistic delay distribution as the main interest. Stochastic network calculus is relied on to conduct the analysis. Two typical traffic models, i.e., Compound Poisson and Aggregated ON-OFF Source, are analyzed. The wireless fading channel is modeled as a Gilbert-Elliot channel. Numerical results are presented, where the probabilistic delay distribution and guaranteed capacity under certain delay constraint are shown and discussed.