A real-time message stream is said to have an (m,k)-firm requirement if at least m out of any k consecutive messages from the stream must meet their deadline to ensure adequate quality of service (QoS). A scheduling policy is proposed recently called Distance-Based Priority (DBP) to better service multiple input queues single server (MIQSS) model, each stream with (m,k)-firm. But DBP cannot always provide good performance in MIQSS model. The raison is that DBP assignment is only based on the distance to failure state of each individual message stream with (m,k)-firm. Neither the message timing parameters (period, deadline, service time in server) nor its relationship with other streams sharing the same server is taken into account. Song et al proposed a modification of DBP called matrix-DBP to improve its performance. But this improved policy just only applies to periodic source. In this paper, we propose a new policy referred to equivalent matrix (E_Matrix) DBP for aperiodic streams by considering the above factor. The effectiveness of this proposal is evaluated through simulation under varying service rate in Poisson streams with same and different (m,k)-firm constraints. The evaluation shows that substantial reductions in the probability of dynamic failure for overall system are achieved when the proposed policy is used.