Optimal garbage collection policies for a database in a computer system

It has recently become necessary to maintain a database periodically and economically for the requirements of continuous operation of a computer system. To use memory areas effectively and to improve the processing efficiency, garbage collections for a database are made at suitable times according to the number of updates and the amount of garbages. This paper considers that additive garbages arise according to Cdf G(x) when a database is updated, and that a database is useless if total garbages exceed a total threshold level K. To prevent this, the authors make a garbage collection at periodic time T or at N-th update, whichever occurs first. Using the theory of cumulative processes, the expected cost is obtained, and the optimal T* and N* which minimize it are discussed. Finally, numerical examples are given when G(x) is exponential.