We consider a polling system with adaptive dynamic polling order for modeling a broadband wireless network with a centralized control mechanism. A new algorithm has been developed for calculating the steady-state probability distribution of the number of packets in subscriber stations. The algorithm makes it possible to calculate the average waiting time and other network performance characteristics. We investigate a queuing system with several queues in which the server serves queues in a dynamic polling order. This order of queuing involves skipping queues that had been empty in the previous polling cycle. The queues that have been skipped in the current cycle can be polled by the server only in the next cycle. The specified queue servicing algorithm allows one to reduce the queue polling time and thus increase the system performance. A comparative numerical analysis of various options for constructing and evaluating the performance characteristics of broadband wireless IEEE 802.11 networks with a centralized control mechanism is presented. Numerical studies have been carried out using a software package for evaluating stochastic polling systems.