This paper focuses on adaptive bandwidth allocation (ABA) to transport pre-stored VBR compressed video across networks in support of Video on Demand (VoD) service. Two key issues are addressed. First, using dynamic programming method, a relatively simple method based on playback tunnel is proposed to determine a feasible range of bandwidth, which can be dynamically allocated for transporting video segment to guarantee that the playback buffer neither underflows nor overflows. Second, several ABA schemes for various optimal criteria including Lower-Edge ABA (LoE-ABA), Middle-Tunnel ABA (MT-ABA) and Reduced-Bandwidth-Variability ABA (RBV-ABA), are investigated extensively. The proposed schemes are evaluated by a set of real-life MPEG video traces. The obtained results show that the RBV-ABA scheme outperforms other schemes in reducing peak rate, traffic burstiness and bandwidth variability. On the other hand, the MT-ABA scheme can effectively avoid overflow and underflow caused by delay jitter.