(m, k)-firm real-time or weakly hard real-time (WHRT) guarantee is becoming attractive as it closes the gap between hard and soft (or probabilistic) real-time guarantee, and enables finer granularity of real-time QoS through adjusting m and k. For multiple streams with (m, k)-firm constraint sharing a single server, an on-line priority assignment policy based on the most recent k-length history of each stream called distance based priority (DBP) has been proposed to assign priority. In case of priority equality among these head-of-queue instances, Earliest Deadline First (EDF) is used. Under the context of WHRT schedule theory, DBP is the most popular, gets much attention and has many applications due to its straightforward priority assignment policy and easy implementation. However, DBP combined with EDF cannot always provide good performance, mainly because the initial DBP does not underline the rich information on deadline met/missed distribution, specially streams in various failure states which will travel different distances to restore success states. Considering how to effectively restore the success state of each individual stream from a failure state, an integrated DBP utilizing deadline met/missed distribution is proposed in this paper. Simulation results validated the performance improvement of this proposal.