Modern high speed networks and ATM networks in particular use resource reservation as a basic means of establishing communications. One-way on-the- y reservation is a method for allocating resources for short bursts of data when regular reservation is too costly. The rst such algorithmswere recently suggested by Turner. We investigate two examples that are characteristic to the way tra c streams interact in virtual circuit networks: a three node subnetwork that also acts as a 4X2 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. This work was supported in part by the Technion V.P.R. fund and the Fund for the Promotion of Research at the Technion. Journal of High Speed Networks, 5(4):347--363, 1996