Medium Access Control (MAC) policies in which the scheduling time slots are allocated irrespectively of the underline topology are suitable for ad-hoc networks, where nodes can enter, leave or move inside the network at any time. Topology-unaware MAC policies, that allocate slots deterministically or probabilistically have been proposed in the past and evaluated under heavy traffic assumptions. In this paper, the heavy traffic assumption is relaxed and the system throughput achieved by these policies is derived as a function of the traffic load. The presented analysis establishes the conditions and determines the values of the access probability for which the system throughput under the probabilistic policy is not only higher than that under the deterministic policy but it is also close to the maximum achievable, provided that the traffic load and the topology density of the network are known. In case the traffic load and/or the topology density are not known (which is commonly the cas...