Resource reservation and QoS negotiation is a common way to guarantee timely progress of programs in distributed multimedia systems. For this, determining the available resource capacity, resource budget, is important. The resource budget depends on resource characteristics (e.g., processor, memory, disk, and network bandwidth) and scheduling algorithms. The paper provides an improved processor budget for the fixed-priority scheduling algorithm, which is most common in commercial real-time operating systems. The improvement is possible by noting that, in multimedia systems, there is a prefixed set of task periods for the finite set of QoS options and parameters. Our approach explicitly takes these periods into account and calculates the tight bound of the processor budget using the linear programming technique. This bound significantly improves Liu and Layland bound (Liu and Layland, 1973) and also it is proved to be better than any other bounds in the literature. We also show how this bound is effectively used for resource reservation and QoS re-negotiation for adapting to dynamic workload.