In the Internet, data packets from a source node (e.g., a web server) to a destination (e.g., a client computer) may experience different delay, resulting in out-of-order packet arrivals at the destination. A common solution is to buffer out-of-order packets at the destination and re-order the packets into correct order before sending them to the application layer. This project is to investigate the benefit of using priority queueing in the intermediate routers to alleviate the packet re-ordering problem. In first phase of the project, we examine a state where data packets arrive in a FIFO queue which is represented by a basic M/G/1 queue. For the Second phase, we extend our project to model and analyze the case where two queues are involved: one is low priority queue and the other is high priority queue.