Queuing analysis of polling system with mixed serve

In this paper, the mean cyclic period of polling systems with mixed serve, in which the gated serve and limited serve are adapted to different classes of messages respectively, is given. The mixed serve is introduced first, and then the mean queue length and mean cyclic period are obtained through the embedded Markov chain, generating function and Laplace-Stieltjes transform. Further, the station stability and system stability are distinguished, and the mean cyclic period of the polling system under part or all unstable queues, in which messages are adapted to the limit serve, is given. Lastly, the performance of the polling system under mixed serve is compared with that under gated serve based on the mean cyclic period.