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.