In a real-time constrained network, some of the applications coexisting in the network require bounds on their worst case end-to-end response times and jitters to have a behavior compliant with their specifications (e.g. voice over IP, control-command applications, multimedia applications, distributed interactive games). To provide deterministic guarantees on these times, we developed an approach, called ``trajectory approach'', based on flow scheduling. More precisely, assuming that flows are scheduled in each node according to fixed and/or dynamic priorities, our worst case analysis allow establishing upper bounds on the real-time constraints. These results address many applications. They enable to derive, for example, a simple admission control in charge of deciding whether a new flow can be accepted or not, by verifying that the new flow will not experiment a worst case response time greater than its end-to-end deadline and that the acceptance of this new flow will not compromise real-time guarantees given to the already accepted flows.