Large Deviations Bounds for a Polling System with Markovian On/off Sources and Bernoulli Service Schedule

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.