In this paper we introduce the globally gated Markovian limited service discipline in the cyclic polling model. Under this policy at most K customers are served during the server visit to a station among the customers that are present at the start of the actual polling cycle. Here the random limit K is the actual value of a finite state Markov chain assigned to the actual station. At each station customers arrive with Poisson process and the customer service time is constant. Moreover the cycle time is a fixed integer multiple of the customer service time. The model enables asymmetric arrival flows and each station has an individual Markov chain. This model is analyzed and the numerical solution for the mean of the stationary waiting time is provided. This model is motivated by the problem of dynamic capacity allocation in Media Access Control of wireless communication networks with Time-Division Multiple Access mechanism. The "globally gated" character of the model is the consequence of the applied reservation mechanisms. In a fixed length frame after allocating the required capacity for the delay sensitive real-time traffic the random remaining capacity is shared among the subscriber stations for the non real-time traffic. The Markovian character of the random limits enables to model the inter frame dependencies of the required real-time capacity at each station individually. In the second part of the paper the application of this model to the uplink traffic in the IEEE 802.16 network is demonstrated.