In this paper, we apply the matrix-analytic approach to explore the conditional drop behavior of router with UDP and TCP traffic under RED scheme. We constructed a simple queuing model for RED mechanism with UDP and TCP traffic which follow a continuous-time Markovian arrival process (MAP). The queueing model of the router with RED scheme is modeled as MAP/M/1/K. With the numerical results, we find that as the traffic intensity of UDP traffic increases, the conditional drop probability of TCP traffic will also increase under RED scheme. In practice, this effect causes TCP congestion control protocol to reduce the transmission rate of TCP traffic. This is an unfair effect for providing multimedia applications on the Internet. Based on this observation, the router in the Internet must implement some mechanisms to suppress this effect.