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This paper derives approximate formulas for a token ring system with nonexhaustive service, which is commonly used in local area networks. In order to obtain performance measures, the token ring system is regarded as a multiqueue model with cyclic service. The model under consideration is a generalization of the ones treated in the literature. The virtual load probability density function is derived via a diffusion approximation technique. The relation between the virtual load and the actual waiting time is presented. The approximate formula obtained here is evaluated by comparing it to simulation results as well as to other results presented in the literature.