In ubiquitous environment the traffic is expected more diverse than ever – ranging from traditional file transfer to continuous media applications such as audio and video conferencing. In this paper, we present a traffic scheduling scheme and an admission control algorithm for servicing a mix of non-real-time and real-time traffic in ubiquitous environment. Proposed scheduling algorithm assigns a deadline to the non-real-time packet by calculating the slack time on-line and services the non-real-time packet along with the real-time packet using Earliest Deadline First algorithm. The time complexity for calculation of the slack time and deadline assignment to the non-real-time packet is O(1) and thus the scheduling of non-real-time traffic can be performed at a low cost. Since proposed scheme services the non-real-time traffic while the link bandwidth is not used by the real-time traffic, it can guarantee the schedulability of real-time flows. Moreover, by limiting the number of admitted real-time flows in admission control algorithm, proposed method can provide the non-real-time flows with fast response time.