The information of available bandwidth on an end-to-end path is important for various network applications, and several probing methods have been proposed to estimate it in recent years. However, previous methods are either based on fluid model or are only partially suitable for bursty real internet cross traffic; and the accuracy of their estimation degrades at different extents in multi-hop situations. Moreover, all previous PGM (Probing Gap Model) based methods require the knowledge of bottleneck link capacity, which may not be available in practice. In this paper, we extend the analysis of queuing behavior of probing packets from single-hop scenarios to multi-hop scenarios and propose a novel hybrid probing technique, called PATHCOS++, which integrates the advantages of both PRM (Probing Rate Model) and PGM based methods, to estimate the end-to-end available bandwidth. Unlike previous works, PATHCOS++ does not make fluid cross traffic assumption and does not require the information about bottleneck link capacity. Simulation results show that PATHCOS++ is quite efficient and provides end-to-end available bandwidth estimation that is significantly more accurate than current state-of-the-art techniques do. The accuracy of PATHCOS++ is nearly unaffected when there are multiple congestible links.