We propose a hybrid assignment protocol called the probabilistic reservation protocol in a fibre optic unidirectional bus system. Under this protocol, the channel is divided into frames and a frame is divided into a fixed number of slots, where the size of a slot is equal to a packet transmission time. A station with a packet to send transmits its packet with probability 1 if the currently passing slot is empty. If the slot is not available because an upstream station has used it or a station has reserved it to use at the last frame, the station attempts to reserve a slot of the next frame with the probability of r(i). We analyse this protocol with a finite population model. Each station has a single buffer that only one packet can be stored. We analyse the performance using an exact analytical model. We also introduce a computationally simpler approximate model and analyse the proposed protocol. This behaves as a random assignment protocol at low loads and as a demand assignment protocol at high loads. Since the transmission of a packet is achieved within two frames. the maximum delay is bounded.