(m, k)-firm means at least m deadlines should be met among any k consecutive task invocations or message transmissions. Providing (m, k)-firm guarantee is becoming attractive as it proposes an alternative between hard real-time guarantee (case of m = k) and soft (or probabilistic) real-time guarantee with p = m/k (when m, k → ∞) and allows more effective utilization of server resources (processor for task processing or bandwidth for message transmission). A dynamic priority assignment scheme called DBP (Distance Based Priority) has been proposed to handle the (m, k)-firm constraint. This paper shows that DBP combined with EDF (EDF for making choice among tasks/messages of the same priority assigned by DBP) cannot always provide good performance in a MIQSS (Multiple input queues single server) non-preemptive model. The reason is that DBP assignment is only based on the distance to failure state of each individual stream under its own (m, k)-firm constraint. It does not take into account neither the stream timing parameters (period, deadline, service time in server) nor its relationship with other streams sharing the same server. Taking into account these additional parameters, two necessary schedulability conditions are derived and an enhancement of DBP called matrix-DBP is proposed. The performance improvement has been shown by simulations.