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In wide area ubiquitous wireless networks, most wireless terminals (WTs) will transmit small amounts of data at comparatively long intervals. Therefore, each AP must be capable of accommodating a great many WTs. Moreover, this network is required to accommodate a variety of services; some services need to be prioritized. In this paper, we propose a novel prioritized control scheme that applies random access to wide area ubiquitous wireless networks. Two kinds of priority classes are considered; high priority (HP) class and low priority (LP) class. The transmission performance of HP class must be guaranteed regardless of LP class traffic situation. To meet this requirement, the proposed scheme isolates the random access (RA) periods of the two classes and controls the RA period for HP class according to the HP class traffic situation, which is predicted from the HP event notification history (event here means that a WT has HP traffic to send). This paper also clarifies the problems of the conventional scheme and reveals the transmission performance of the conventional and proposed scheme by computer simulation.