The increasing popularity of high-volume performance-critical Internet applications is a challenge for servers to provide individual response-time guarantees. Considering the fact that most Internet applications can tolerate a small percentage of deadline misses, we define delay constraint as a statistical guarantee to relax server resource requirements. A recent decay function model characterizes the relationship between the request delay constraint, deadline misses, and server capacity in a transfer function based filter system. A time-invariant scheduler was proposed to minimize system load variances in support of requests with the same delay constraints. This paper extends the model to support requests with different deadlines and describes an optimal time-variant scheduling policy that minimizes load variances and capacity requirement. The resultant capacity bound is further tightened by utilizing the information of request arrival distribution. Simulation results validate the extended decay function model and show the superiority of the scheduler in comparison with other scheduling algorithms.