Recent technological advances have lead to the deployment of high-speed networks which are capable of supporting a large number of applications in an integrated fashion. In this environment, the time required for the transmission of a fixed size information block (slot) has been constantly decreasing. A direct consequence of a shrinking slot is that time intervals (in seconds) increase in size, when measured in network time units (slots). As a result, time intervals which were considered to be too small in the past seem larger and -- for that matter -- their interpretation and associated functionalities may need to be reconsidered. In the shrinking slot environment time is becoming a commodity which may be used more effectively in the design of high-speed networks. The proposed research will be focused on the development of traffic management schemes which incorporate rather explicitly the significant time-constants (in slots) associated with the traffic generation process and QoS descriptors of the diversified applications in a high speed networking environment. Both, traditional computer-data-type and real time applications will be considered. In the first part of the proposed research, a Time-Constant-Based Call Admission and Traffic Control (TC-based CATC) framework is presented, for controllable (or, ABR/UBR in ATM Forum's classification) applications. This proposal is based on the positive impact of a large time-constant associated with a controllable application, on the effectiveness of a feedback-based traffic control scheme; this impact has been observed in preliminary results. The proposed class of TC-based traffic control policies can be viewed as a class of ``generalized'' adaptive, rate-based traffic control policies, since classical adaptive, rate-based policies are included in this large class. As a result, there is great potential to substantially improve on the performance achieved by the past schemes. The TC-based CATC scheme is expected to provide for a faster response to bandwidth availability fluctuations at different time-scales, by employing distinct mechanisms for the different time-scales. It is easy to argue that the proposed TC-based policies are scalable. In the second part of the proposed research, multiplexing schemes for real-time applications are considered. These schemes attempt to preserve time-constants of importance associated with these applications and/or take advantage of time-constant-based Quality of Service requirement, to maximize resource utilization. Specific proposals include the integration of the regulation and scheduling functions to improve performance by coordinating their functionality, as well as ``reinvent'' statistical multiplexing for real-time applications by taking advantage od the increased room for traffic manipulation in time, as the network speed increases and QoS-defining time-constants increase. Finally, a major part of the proposed research will be dedicated to the study of a number of interesting problems arising from the above proposals, which are becoming increasingly relevant to the broad high speed networking environment as the network time unit decreases.