A method for controlling access to a system of finite resources with excess demand employs a two stage admission process. Subscribers are first admitted based on an initial bid price and resource availability. The market price is determined by the highest bid price among the rejected arrivals in the current batch. Admitted subscribers are then given the option to secure continued access to the resource by accepting a fee-based reservation. The fee for the reservation is determined in a manner which is fair to the reserving subscriber, as well as all other subscribers, in that the reservation fee is priced to provide access at a cost which prevents arbitraging opportunities. If the current market price exceeds a non-reserved subscriber's bid price, that non-reserved subscriber is displaced. If the current market price exceeds a reserved subscriber's bid price, that reserved subscriber's reservation is activated and access to the resource continues. In the case of a communications system having a finite number of access lines, the reservation fee is based on the bid price from the subscriber and the duration of the requested reservation.