The scheduling scheme in packet switching networks is one of the most critical features that can affect the performance of the network. Hence, many scheduling algorithms have been suggested and some indices, such as fairness and latency, have been proposed for the comparison of their performances. While the nature of Internet traffic is bursty, traditional scheduling algorithms try to smooth the traffic and serve the users based on this smoothed traffic. As a result, the fairness index mainly considers this smoothed traffic and the service rate as the main parameter to differentiate among different sessions or flows. This work uses burstiness as a differentiating factor to evaluate scheduling algorithms proposed in the literature. To achieve this goal, a new index that evaluates the performance of a scheduler with bursty traffic is introduced. Additionally, this paper introduces a new scheduler that not only uses arrival rates but also considers burstiness parameters in its scheduling algorithms.