In this work we propose a verification methodology consisting of selective quantitative analysis and interval model checking. Our methods can aid not only in determining if a system works correctly, but also in understanding how well the system works.The selective quantitative algorithms compute minimum and maximum delays over a selected subset of system executions. We use a formula of the linear-time temporal logic LTL in order to select either infinite paths or finite intervals over which the computation is performed. We therefore define two semantics for LTL -over infinite paths and over finite intervals. We show how tableaux for LTL formulas can be used for selecting either paths or intervals and can also be used for model checking formulas interpreted over paths or intervals.We have implemented a tool based on our techniques. To demonstrate the usefulness of our methods we verified a complex distributed real-time system. Several features of this example make it an interesting target for our techniques. It is a system of realistic complexity, its components are existing systems and protocols executing a mixture of multimedia, traditional real-time and non-real time tasks. Also, the distributed nature of the system makes the interaction among its various components much richer. This also makes its analysis more difficult.Out tool were able to analyze the system and verify that the deadlines are met by the design. Moreover, we have been able to identify inefficiencies that caused the response time to increase significantly (about 50%). After changing the design we not only verified that the response time was lower, but were also able to determine the causes for the poor performance of the original model using interval model checking.