This paper studies the polling of two infinite queues by a synchronous server. The inputs to these queues are correlated and restricted to occur only at equally spaced time intervals. For simplicity, the walktime for the server to move from one queue to the other is assumed to be zero in this study. In essence, the problem studied in this paper is equivalent to a fixed service time queueing system which accepts two types of synchronized correlated inputs and adopts an alternating priority discipline. This paper contains a complete analysis of both the busy period and the waiting time. The validity of the analysis has been verified by computer simulations.