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In this paper, we address the problem of servicing requests that arrive at a distributed database system(DDBS) in a mobile computing environment(MCE). In a MCE, mobile users may interact with a database system in retrieving objects. Transactions on objects can read or write requests from mobile users in a random manner. In this paper, from theoretical standpoint, we design and evaluate a practically realizable object allocation and replication algorithm, referred to as adaptive distributed request window (ADRW) algorithm, that adapts to the changing patterns of on-line requests. Our objective is to dynamically adjust the allocation schemes of objects so as to minimize the total servicing cost of all the requests that arrive at a DDBS. Finally, we use competitive analysis to quantify the performance of our ADRW algorithm.