This paper solves the challenge of offline response time analysis of independent periodic tasks with constrained deadlines early in the software development cycle, under generalized rate-monotonic scheduling. CPU budgets are allocated to different applications and each application is composed of multiple periodic tasks that must share the same budget. Physical application requirements impose specifications on task periods and deadlines from the very beginning, but unlike the common assumption in traditional response time analysis, task execution times are not known. This is because task execution times depend on the exact system implementation, which is not finalized until later in the development cycle. Questions facing designers become: will my task meet its deadline given lack of knowledge of other tasks' execution times? What is the smallest deadline that my task can meet? These questions are traditionally addressed by using a two level scheduler: CPU is partitioned and assigned to application, and task priorities are determined within the scope of an application, and when server becomes active it schedules the tasks locally. Such two level scheduling approach introduces priority inversion across applications. In our approach, different applications' tasks are globally scheduled and yet the CPU resource is still partitioned and assigned to applications as a CPU budget. We schedule all the tasks globally while enforcing application budgets. The proposed new form of response time analysis is called budgeted generalized rate-monotonic analysis to compute the maximum response time for each task given only application budgets and task periods, but without knowledge of task execution times. We formulate this schedulability problem as a mixed integer linear programming problem and demonstrate a solution that computes the exact worst-case response times. Evaluation shows that our solution outperforms, in terms of schedulability, both global utilization bounds and mechanisms that attain temporal modularity via resource partitioning.