Available bandwidth (ABW) estimation in wirelessnetworks is a critical issue for quality-of-service (QoS) provisioning. Nowadays, a network path often contains at least onewireless link e.g., mobile users having wireless connection to theInternet through laptop PCs or smartphones. Most of the existingtools for measuring ABW have been developed and evaluatedin wired networks. Since the characteristics of wired links andwireless links differ in many respects, such as fluctuations incapacity and stability due to the shared and unreliable natureof the wireless links, ABW estimation tools also need to beevaluated for network paths containing at least one wirelesslink. In this paper, we have extended our previous work, NewEnhanced Available Bandwidth Estimation Technique (NEXT) byintroducing a parameter-independent curve-fitting technique todetect the ABW from a one-way queuing delay signature andconducted a real test over a radio interface in a 4G/LTE mobilecommunication network. For the experiments, a commercial4G/LTE mobile network of a Japanese mobile operator was used. Extensive simulations over an IEEE 802.11 network were alsoperformed. Simulation results as well as real-world experimentalresults demonstrate that it is feasible to achieve reliable estimatesunder certain circumstances. Our extended approach, which wecall NEXT -- FIT, has very good ABW estimation results underconditions of different packet sizes, dynamic wireless link rates, and channel noises.