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In this paper, a general teletraffic analysis to evaluate the performance of cognitive radio networks with arbitrary order Coxian distributed channel holding time in the primary network is developed. The relevance of the considered Coxian model relies on its universality property, mathematical tractability, reduced dimensionality, and the fact that it generalizes a large class of useful previous employed distributions in the literature to characterize the channel holding time (i.e., exponential, Erlang, hyper-exponential, and hypo-exponential). Additionally, recently, there have been major advances in fitting Coxian distributions. Our numerical results for 2nd order Coxian model show negligible differences compared with those obtained when the log-normal distribution is considered. (Empirical evidence supports the log-normal assumption for the primary channel holding time.) Thus, the analytical model presented in this paper represents a step towards a general and mathematically tractable framework for the performance evaluation of cognitive radio networks under more realistic assumptions.