Modern high speed networks (and ATM networks in particular) use resource reservation as a basic means of establishing communications. One-way on-the-fly reservation is a method for allocating resources for short bursts of data when regular reservation is too costly. The first of such algorithms were recently suggested by Turner. We investigate two examples that are characteristic to the way traffic streams interact in virtual circuit networks: a three node subnetwork that also acts as a 4×2 switch and a ring. For both systems we compute system throughput under homogeneous load, and compare it with the throughput when fast reservation protocols (FRP) are used. For the three node subnetwork we give an explicit expression for an upper bound.