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Wide area ubiquitous wireless networks, which consist of access points (APs) connected to the fixed network and a great many wireless terminals (WTs), can offer a wide range of applications everywhere. In order to enhance network performance, we need to collect different kinds of data from as many WTs as possible; each AP must be capable of accommodating more than 103 WTs. To satisfy this requirement, we proposed DSA-I; it adds request-polling to random access. We showed that DSA-I increases throughput. However, in DSA-I, a request and its acknowledgement must be exchanged before sending data by request-polling even if the data size is known or can be predicted accurately, which increases the overhead. This paper proposes DSA-II; it adds data-polling to DSA-I to reduce the overhead. In DSA-II, the AP decides the polled data size according to the latest distribution of data size and polls the WT for the data directly. If the data-polling size cannot be determined with confidence, the AP uses request-polling instead of data-polling. Simulations verify that DSA-II offers better transmission performance than DSA-I and existing schemes.