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With the advent of stored program control and common channel signaling, more network state information is available in a real-time fashion, and dynamically choosing route with real-time network state information becomes a popular topic. We focus on dynamic routing of Virtual Path (VP)-based ATM networks. First, effective bandwidth is used to simplify call admission control (CAC) of VP-based ATM networks, while maintaining a certain level of multiplexing gain. We propose a novel dynamic routing random early blocking routing (REBR) as CAC for virtual connections. Further, we derive approximation methods to calculate call-level related performance measures, e.g., call blocking probability and expected revenue loss. It is shown that approximation results are close to simulation results for most cases considered. It is shown via approximation and/or simulation that REBR performs better than least loaded routing (LLR) under light and moderate traffic loads, while performs similar to LLR under heavy traffic loads. We also compare REBR and other routing schemes, and similar conclusions can be drawn. We consider 2-rate heterogeneous traffic cases. Last but not least, various dynamic routing schemes are compared under non-stationary traffic.