Voice over Internet protocol service (VoIP) is growing fast during the last few years. Unlike the usual best effort traffic, the voice traffic is delay and delay jitter sensitive. The current scheduling schemes meet the voice traffic delay constraint by assigning its packets with the highest priority. This behavior is acceptable as long as the volume of voice traffic is relatively very small in comparison with other competitor traffic. With the notable increase of voice traffic volume, the current scheduling will not be able to handle the voice packets with the same behavior otherwise a forceful unfair resource sharing, to other traffic, will rise up. In this paper, we introduce a new flexible scheduling architecture which is capable of satisfying the voice traffic delay constraint while providing a fair resource sharing to the rest of the traffic, as verified by both analytical analysis and an extensive experimental simulation study under various traffic workloads.