Active queue management schemes are used to reduce the number of dropped packets at the routers. Random early detection uses dropping probability which is calculated based on the average queue size. Further it is modified according to the value of the count indicating the number of unmarked packets that have arrived after a marked packet. The impact of random variable i.e. number of packets arrived after a marked packet over the dropping pattern is investigated. The proposed model achieves smooth dropping pattern which results in improvement of quality of service parameters. A new model for dropping probability is proposed with different dropping function. The effect of new dropping probability results in the increase of the throughput and reduction of the expected end-to-end delay. An important finding is that the choice of modified dropping function significantly affects the performance measures of the networks.