Performance Analysis of a Heterogeneous Traffic Scheduler using Large Deviation Principle

In this paper, we analyze a scheduling algorithm which is suitable for the heterogeneous traffic network. In the large deviation setting, we are interested to see, how the asymptotic decay rate of maximum queue overflow probability achieved by this algorithm.We first derive an upper bound on the decay rate of the queue overflow probability as the queue overflow threshold approaches infinity. Then, we study several structural properties of the minimum cost path of the maximum queue length. Given these properties, we prove that the maximum queue length follows a sample path with linear increment. For certain parameter values, the scheduling algorithm is asymptotically optimal in reducing the maximum queue length. Through numerical results, we have show the large deviation properties of the queue length typically used in practice. Index Terms Scheduling, Heterogeneous Traffic, Large Deviation Principle.