Abstract
In this paper we consider a large deviations problem for a discrete-time
polling system consisting of two-parallel queues and a single server. The arrival process
of each queue is a superposition of traffic streams generated by a number of mutually
independent and identical Markovian on/off sources, and the single server serves the
two queues according to the so-called Bernoulli service schedule. Using the large deviations
techniques, we derive the upper and lower bounds of the probability that the
queue length of each queue exceeds a certain level (i.e., the buffer overflow probability).
These results have important implications for traffic management of high-speed
communication networks such as call admission control and bandwidth allocation.
