Real-time search algorithms need to address the deadlines imposed by applications like process control and robot navigation. Possible deadline violations should be predicted ahead of time to allow remedial actions to prevent the undesirable consequences of missing deadlines. The algorithms should also demonstrate progressively optimizing behavior. That is, they should improve the quality of the solutions as time constraints are relaxed. To successfully address these issues, a real-time search algorithm must address the central problem of choosing the proper values for its parameters, which control the time allocated to planning. We proposed a new approach to determine the parameter values of a real-time search algorithm, in order to enable the algorithm to meet deadlines, exhibit progressively optimizing behavior, and to predict deadline violation prior to the deadline. The paper provides a theoretical and experimental characterization of the proposed algorithm.