In many current packet switching networks, packets are transmitted sequentially by means of so-called virtual circuits. In this paper, a queueing network model for a virtual circuit with local buffer size constraints and blocking at the intermediate nodes is derived and analysed. The analysis is based on the decomposition of the fixed virtual route into its individual links. Each hop is modelled as a closed BCMP queueing network. The introduction of the steady-state blocking probability p as the characterizing parameter of the interface between two consecutive links permits the recursive computation of important design parameters, such as throughput, utilization, and mean transmission time. A modified rejection probability, introduced to describe the behaviour at the interface more accurately, supports the previous results.