The emergence of edge computing has led to some data and tasks being decentralized to eligible edge servers. Obviously, the capacity of edge servers is limited. As tasks and data grow, the load on edge servers will increase. A reasonable allocation of resources to edge servers makes them better able to serve users, so the issue of resource allocation strategies needs to be studied. In this paper, we build a task arrival process as an M/M/1 queuing theory model, which is based on the Dominant Resource Fairness (DRF) allocation algorithm. In this model, the corresponding weight is calculated for each task. Moreover, the subsequent resource allocation process is carried out according to the weighted DRF allocation algorithm. So the efficiency of resource allocation, as well as the quality of service (QoS) is improved. In this paper, the effectiveness of the algorithm is verified experimentally. The experimental results show that the algorithm has improved the resource allocation process.