In this paper, we consider a cyclic polling system in which arrivals are governed by the Markovian arrival process. Each queue is visited according to the exhaustive time-limited service discipline to coincide with IEEE 802.5 and 802.4 standards. Using the decomposition approach, each queue is analyzed as a single server queue with vacation. By exploiting the properties of the discrete time phase distribution we construct the vacation period from the visit period of the other queues in the polling system. Using an iterative procedure we were able to compute the queue length distribution and the average waiting time for polling systems with finite capacity (or infinite capacity) in all queues. Comparison of the mean waiting time with simulation results shows that the proposed models give reasonable results.