Abstract. The design of an efficient Medium Access Control (MAC) is challenging in ad-hoc networks where users can enter, leave or move inside the network without any need for prior configuration. The existing topology-unaware TDMA-based schemes are capable of providing a minimum guaranteed throughput by considering a deterministic policy for the utilization of the assigned scheduling time slots. In an earlier work, a probabilistic policy that utilizes the non-assigned slots according to an access probability, common for all nodes in the network, was proposed. The achievable throughput for a specific transmission under this policy was analyzed. In this work, the system throughput is studied and the conditions under which the system throughput under the probabilistic policy is higher than that under the deterministic policy are established. In addition, the value for the access probability that maximizes the system throughput is determined analytically, as well as simplified lower and upper bounds that depend only on a topology density metric. Since the analysis of the system throughput is shown to be difficult or impossible in the general case an approximation is introduced whose accuracy is investigated. Simulation results show that the approximate analysis successfully determines the range of values for the access probability for which the system throughput under the probabilistic policy is not only higher than that under the deterministic, but it is also close to the maximum.