Optimal and Near-Optimal Scheduling Algorithms for Batched Processing in Linear Storage

In this paper, we consider the accessing of batched requests in a linear storage medium. The batch size is assumed fixed and the access probabilities of individual records known. For a given arrangement of records in the storage, we consider the problem of read/write head scheduling to minimize the expected access time for a batch measured in terms of the distance traveled by the head. In the first part of the paper, several simple algorithms are proposed, analyzed and compared. The effect of different record arrangements is also discussed. In the second part of the paper, a family of algorithms called B-optimal rules are described. When B is $\infty $, an $\infty $-optimal rule is indeed optimal in the sense of minimizing expected distance traveled by the head per batch when accessing an arbitrarily large number of batches. A procedure to calculate an $\infty $-optimal rule for any given record arrangement is described, which is based on the idea of “discrete dynamic programming”.