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Finding the available network capacity for a TCP connection is an important research problem as it allows the connection to improve its throughput and fairness in addition to reducing packet losses. As flows arrive and depart randomly in the network, the state of a TCP connection at any instant is very dynamic and a good estimate of the available capacity can enable TCP to quickly adapt to the actual available capacity in the network. This is especially relevant to heterogeneous access network environments where the end-to-end path characteristics of a TCP connection may abruptly change due to the changes in the access link characteristics after a vertical handoff. In this paper, we present an approach that combines available network capacity estimation with cross-layer notifications to TCP about the access link bandwidth and delay to quickly determine a rough estimate of the available capacity for a TCP connection. Using simulation experiments we evaluate our algorithms in the different phases of a TCP connection where the available capacity is unknown such as in the beginning of a TCP connection and after a vertical handoff. Our results show that the proposed algorithms improve TCP throughput and reduce the transfer time after a vertical handoff in heterogeneous access networks.