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In this paper, we discuss the real-time issue related to QoS requirements in a communication system, which consists of several sensors and one central control unit. In order to guarantee real-time requirement and fairness among sensors, a polling mechanism with queuing priority is applied in it. By means of the imbedded Markov chain theory and generating function method, mean queue length and mean circle time of asymmetric system are studied quantitatively, and corresponding exact expressions are obtained. These results are critical for system device and system performance analysis. Finally, computer simulations demonstrate effectiveness of this analysis.