An available bandwidth at a link is an unused capacity. Its measuring and/or estimation is not simple in practice. On the other hand, we know that its continuous knowledge is crucial for the operation of almost all networks. Therefore, there is a continuous effort in improving the existing and developing new methods of available bandwidth measurement and/or estimation. This paper deals with these problems. Network calculus terminology allows to express an available bandwidth in terms of a service curve. The service curve is a function representing a service available for a traffic flow which can be measured/estimated in a node as well as at an endto- end connection of a network. An Internet traffic is highly unpredictable what hinders to a large extent an execution of the tasks mentioned above. This paper draws attention to pitfalls and difficulties with application of the existing network calculus methods of an available bandwidth estimation in a real Internet Service Provider (ISP) network. The results achieved in measurements have been also confirmed in simulations performed as well as by mathematical considerations presented here. They give a new perspective on the outcomes obtained by other authors and on their interpretations.