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In a Distributed Database System (DDBS), transactions on objects can be read requests or write requests in a random manner The replication algorithm of objects critically affects the system performance. In this paper 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.