Malcolm C. Easton

Key-sequence data sets on indelible storage

Methods for creating and maintaining key-sequence data sets without overwriting the storage medium are described. These methods may be applied to erasable or to write-once storage devices, and they are compatible with conventional device error-management techniques. All past values of data records are preserved in a data structure called a Write-Once B-Tree. Rapid random access is available to records by key value; rapid sequential access is available to records in key-sequence order. Moreover, queries requesting data as of a previous time are processed as rapidly as requests for current data. Access time is proportional to the logarithm of the number of current records in the database. Efficient methods for inserting, updating, and deleting records are described. Upper bounds for tree depth and for storage consumption are given and compared with results from simulation. It is concluded that, with rapidly improving storage technologies, indelible databases will become practical for many applications.

Cold-start vs. warm-start miss ratios

In a two-level computer storage hierarchy, miss ratio measurements are often made from a “cold start”, that is, made with the first-level store initially empty. For large capacities the effect on the measured miss ratio of the misses incurred while filling the first-level store can be significant, even for long reference strings. Use of “warm-start” rather than “cold-start” miss ratios cast doubt on the widespread belief that the observed “S-shape” of lifetime (reciprocal of miss ratio) versus capacity curve indicates a property of behavior of programs that maintain a constant number of pages in main storage. On the other hand, if cold-start miss ratios are measured as a function of capacity and measurement length, then they are useful in studying systems in which operation of a program is periodically interrupted by task switches. It is shown how to obtain, under simple assumptions, the cache miss ratio for multiprogramming from cold-start miss ratio values and how to obtain approximate cold-start miss ratios from warm-start miss ratios.

Design Choices for Selective-Repeat Retransmission Protocols

The design of selective-repeat retransmission protocols to provide reliable transfer of large data files is discussed. The transmission system is assumed capable of losing, distorting, or reordering the transmitted data frames and acknowledgment frames. The principle design considerations center on methods for managing the finite sequence number space and methods for managing the finite-sized receiver buffer. Under the assumption that there exists a maximum time from transmission of a frame to receipt of an acknowledgment for that frame, methods are described for safe reuse of frame sequence numbers. Previous results by Metzner and Morgan on buffer overflow control are extended to cover non-FIFO transmission systems. A two-dimensional space of design parameters is explored by way of Monte Carlo simulations. For appropriate designs, it is shown that significant increases in throughput over that achieved by the Go-Back- N protocol are possible on high-rate long-delay channels.

Model for interactive data base reference string

A particularly simple Markov chain model for a reference string is described. The model, which is only slightly more complicated than the independent reference model, generates strings that have a locality property and that have a specified probability distribution of references over pages. Expressions are obtained for expected working-set size and expected working-set miss ratio. The model is used in an examination of the effect of grouping pages into blocks and in a discussion of the problem of evaluating the effect of changes in the size of the data base. Predictions of the model are shown to agree closely with observations of a string of data base references generated by an interactive data base system having a large number of concurrent users.

Model for database reference strings based on behavior of reference clusters

The observation that references to a particular page are clustered (in time) in typical database reference strings is used as the intuitive motivation for a model of page reference activity in an interactive database system. The model leads to a two-parameter form for the (Denning) working-set functions associated with a page. Methods for estimating parameter values from measurements or from logical descriptions of applications are discussed. Results from the model are shown to agree well with measurements from two database systems.

Transient-free working-set statistics

Transient-free average working-set size and transient-free missing-page rate for a finite sample of a reference string are defined. Use of these statistics is appropriate if the contents of the working set at the start of the recorded string are unknown. If a certain stationarity condition holds, these statistics provide unbiased estimates of expected working-set sizes, missing-page probabilities, and interreference distance probabilities. Two other pairs of estimators are shown to be biased. Expressions for the transient-free statistics are obtained in terms of interval statistics. Several methods of computation are discussed, the usefulness of each depending on length of the sample, number of distinct references, and the amount of main storage available to the computer performing the calculations. In particular, methods are described for handling long strings containing many distinct page names.

The independence of miss ratio on page size

A theoretical justification is given to the empirical observation that in some computing systems with a paged, 2-level storage hierarchy, long-term miss ratio is roughly independent of page size. Let <italic>MISS</italic> be the expected working-set miss ratio in the independent reference model, with expected working set size <italic>CAP</italic> pages. Now form blocks, by combining the <italic>B</italic> pages with the highest probabilities of reference into one block, the <italic>B</italic> pages with the next-highest probabilities of reference into a second block, and so on. Let <italic>MISS</italic><supscrpt>*</supscrpt> be the expected working-set miss ratio when all data are moved in blocks and when the expected working set size is again <italic>CAP</italic> pages, that is, <italic>CAP</italic>/<italic>B</italic> = <italic>C</italic> blocks. It is proved that | <italic>MISS</italic> — <italic>MISS</italic><supscrpt>*</supscrpt> | < (2/<italic>C</italic>) + (33/<italic>C</italic><supscrpt>2</supscrpt>). Thus, if the expected working-set size (in blocks) is sufficiently large, then the miss ratios in the blocked and unblocked cases are approximately equal. This result is used to argue the approximate independence of miss ratio on page size in more realistic models of page references.

The Effect of a Capacity Constraint on the Minimal Cost of a Partition

A recent paper by Chandra and Wong considered the problem of finding a parti t ion of nonnegatlve numbers into m groups to minimize a certain cost, the sum of the squares of the group sums. One apphcatlon of thin problem is m allocation of data records to disks to minimize arm contention, under certain assumptions about record accessing behavior In the paper by Chandra and Wong it was assumed that the dmk capacltms were so large that capacity constraints could be ignored Consideration of the effect of such constraints, assuming equal-razed data records and equalsized dmks, leads to the problem of partitioning numbers (which represent access probabihtles) into m groups of at most k numbers each A practical method for par t l tmmng is shown to ymld a cost no more than } of the minimal cost without the constraint on group size (Cases are constructed that approach this limit asymptotically ) Therefore, within the context of the model, increasing the disk capacity (keeping the number of arms fixed) and arbitrarily changing the part i tmn cannot reduce the arm contention cost below 75 percent of that achieved on the existing system with the suggested partition The result also shows tha t the proposed partit ion has a cost for the constrained problem at most of the minimal cost for the constrained problem However, the exact worst-case performance is not yet known except in the case when the group size is 2. In that case, the proposed partit ion is actually optimal