In this research, we deviate from the conventional traffic models and approaches. We use a traffic model recently proposed by Cruz. In Cruz’s model, the rate functions of traffic sources are assumed to satisfy some linear "burstiness constraints." Such traffic models can be used to describe a class of rate-based flow-controlled sources. A state vector is defined to describe the queueing system. We divide the operation of the studied queueing system into multiple phases. For each phase, we write a system equation to describe completely the behavior of this studied queueing system. We then propose the iterative feasible set method to identify the feasible region of the state vector using some linear programming techniques and other existing theorems regarding the projection of convex sets into a space with a lower dimension. Using the above technique, we studied the performance of three routing schemes in a simple dynamic routing problem, namely the route to shortest rule, the fixed routing rule and the bounded linear rule. We first identified the feasible regions of a defined state vector for each routing scheme using the proposed method. From the identified feasible regions, we then analyzed the extremal performance of these routing schemes and compared their performances.