A large number of terminals transmitting data packets over a common radio channel to a central base station is studied. In inhibit sense multiple access (ISMA), the base station broadcasts a busy signal when an incoming packet is being received, to inhibit other terminals from colliding transmissions. This busy signal arrives at each terminal with a propagation delay, proportional to the distance between the base station and the terminal. This leads to unfairness in the probability of successfully transmitting a data packet, since nearby terminals have more up-to-date information on the actual channel status than remote terminals. This unfairness is additional to the advantage that nearby terminals have because of the capture effect, which is also considered here. The paper applies non- stationary Poisson processes to describe the random arrivals of data packets at the central receiver. It is shown that the probability of a successful attempt to transmit a packet decreases, approximately linearly with the distance between the transmitter and the central receiver. The total throughput is also assessed, and is found that the assumption of a fixed propagation delay adopted in CSMA studies by others gives too optimistic results for ISMA. Moreover, our analysis suggests a subtle change of the fixed delay approximation that enhances its accuracy, without adding complexity. The effect of propagation delays in random access radio networks are of increasing importance, since newly developed systems are designed to transmit with increasingly high bit rates.