Admission control is an important part of modern 
high-speed network control and has received 
extensive attention in the recent literature. 
In this paper we consider an admission control problem 
for a discrete-time polling system consisting of 
two queues and a single server. The arrival process 
in each queue is a superposition of mutually independent 
Markov-modulated processes and the server serves 
the two queues according to a Bernoulli service schedule. 
Basing on the theory of effective bandwidths and the 
buffer upper bound results on the overflow probability 
obtained by large deviation techniques, we derive an 
admission control criterion for the polling system 
under which  {\it Quality of Service} (QoS) requirement 
by each queue is guaranteed.