A real-time distributed database system (RTDDBS) must maintain the consistency constraints of objects and must also guarantee the time constraints imposed by each request arriving at the system. Such a time constraint of a request is usually defined as a deadline period, which means that the request must be serviced on or before its time constraint. Servicing these requests may incur I/O costs, control-message transferring costs or data-message transferring costs. As a result, in our work, we first present a mathematical model that considers all these costs. Using this cost model, our objective is to service all the requests on or before their respective deadline periods and minimize the total servicing cost. To this end, from theoretical standpoint, we design a dynamic object replication algorithm, referred to as Real-time distributed dynamic Window Mechanism (RDDWM), that adapts to the random patterns of read-write requests. Using competitive analysis, from practical perspective, we study the performance of RDDWM algorithm under two different extreme conditions, i.e., when the deadline period of each request is sufficiently long and when the deadline period of each request is very short. Several illustrative examples are provided for the ease of understanding.