The advanced waiting time priority scheduler (AWTP), modified from the waiting time priority scheduler (WTP), was proposed to achieve proportional delay differentiation. AWTP not only achieves more accurate delay proportion than the WTP scheduler no matter in short or long timescales, but also greatly reduces the overall queuing delay when the traffic load is moderate. In this paper, we find that AWTP can not steadily keep the delay ratio under different traffic load distributions because its scheduling sometimes ignores considering packet waiting time. Thus, three remedied algorithms, named Minus-WTP (MWTP), Existing-WTP (EWTP), and Counting-WTP (CWTP), are proposed to resolve this problem. All remedies simultaneously consider the packet waiting time and packet transmission time. Simulation results reveal that these modifications inherit the merit of AWTP and actually alleviate this side effect.