In the IEEE 802.16 Wireless MAN standard specifies the air interface of fixed point-to-multipoint broadband wireless access systems providing multiple services. Among the service classes supported between the base station and subscriber stations in the wireless MAN, the best effort service class is ranked on the lowest position in priority and is assisted by a MAC scheme based on reservation ALOHA. The wireless MAN standard, however, does not reveal every detail of the MAC scheme but only describes the skeleton of the MAC scheme. Focusing on the amount of resource that a subscriber demands by a request and the amount of resource that the base grants to a request we thus present a number of resource demand rules and resource grant rules. Also, we construct a candidate MAC scheme by implanting a pair of resource demand and grant rules into the skeleton of the MAC scheme. Meanwhile a difficult situation for the best effort service is expected wherein only scarce resource is available after most of the resource is already preempted by other services. Perceiving such a situation, we evaluate the throughput and delay performance of each candidate MAC scheme. Especially we develop an analytical method to approximately calculate the throughput in the saturated environment. From the numerical results, we observe that the candidate MAC scheme which adopts the non-gated exhaustive demand rule paired with the full grant rule attains superior performance at the expense of the fairness.