Optimum Storage Allocation for a File in Steady State

A file of fixed-length records in auxiliary storage using a key-to-address transformation to assign records to addresses is considered. The file is assumed to be in steady state, that is that the rates of additions to and of deletions from the file are equal. The loading factors that minimize file maintenance costs in terms of storage space and additional accesses are computed for different bucket sizes and different operational conditions. Introduction This paper describes a study of auxiliary storage allocation for a key-to-address transformation file organization [ 1 31. In this organization, there is a primary storage area divided into buckets. Each bucket can contain s records of the file. The transformation is applied to the key of a record to be loaded and it produces the address of the bucket into which that record will be stored. If more records are assigned to a bucket than it can hold, the excess records are stored in a separate overflow area. The overflow records belonging to a particular bucket are organized in a chain with address pointers. To retrieve a record with a given key, a single access to auxiliary storage is sufficient if that record is stored in the primary storage area. If it is in the overflow area, one or more additional accesses following the pointers from bucket to record and from record to record-are required. The number of accesses depends on the position of the record in the chain. The average length of the chains and, therefore, the average number of additional accesses depends on the bucket size and the storage capacity that is provided in the primary area relative to the number of records to be stored. Studies [3 -51 have been made of the optimal storage allocation for a file that does not change after initial loading. Lum, et al. [3], made performance studies using actual files and different key-to-address transformations. As performance indicators, the authors use the average number of accesses per record and the number of overflow records. Under certain assumptions, formulae can be derived for these quantities [4]. Using these formulae it is possible to compute, for each bucket size, the load factors (that is, the ratio between the number of records to be loaded and the capacity of primary storage) that makes file-handling costs minimal [ 5 ] . These costs consist of storage cost for primary and overflow area, plus the cost for additional accesses. In the study reported in this paper, a different situation is analyzed. A file is considered to which records are added and from which records are deleted. Olsen [6] points out the difference between this situation and the initial loading problem. He considers a steady-state situation in which the number of additions and deletions per time period are equal, and he derives a formula for the average overflow. In this paper, a method is developed to compute also the average number of additional accesses. With these results, the optimal loading for the steady-state situation can be computed in a similar fashion to that for the initial loading model [5]. Analytical approach The file contains II records. The primary storage area consists of b buckets, each of size s. The average loading -number of records assigned to a bucket-is thus: rn = nlb. The load factor is It is assumed that the overflow area has unlimited capacity. AI1 records have equal probability to be de27 STEADY STATE FILE STORAGE