Parallel scheduling algorithms are used extensively in the high-speed switches today. In order to benchmark the performance of various scheduling algorithms, it is of paramount importance to evaluate the performance under a traffic model that is more realistic. It makes more sense to study the performance of various scheduling algorithms under the correlated traffic, in the special context to the discovery of the highly correlated or self-similar nature or Long Range Dependence (LRD) of the Ethernet traffic. In this paper, a simple, linear discrete time model for the arrival of packets at the input of the high-speed switch is assumed. In sequel, a comparative study of the performance of various parallel-scheduling algorithms is undertaken.