In most network security analysis, researchers mainly focus on qualitative studies on security schemes and possible attacks, and there are few papers on quantitative analysis in the current literature. In this paper, we propose one queueing model for the evaluation of the denial of service (DoS) attacks in computer networks. The network under DoS attacks is characterized by a two-dimensional embedded Markov chain model. With this model, we can develop a memory-efficient algorithm for finding the stationary probability distribution which can be used to find other interesting performance metrics such as the connection loss probability and buffer occupancy percentages of half-open connections for regular traffic and attack traffic. Different from previous works in the literature, this paper gives a more general analytical approach to the study of security measures of a computer network under DoS attacks. We hope that our approach opens a new avenue to the quantitative evaluation of m...