April 1974 - Vol. 17 No. 4
Features
A simple linear model of demand paging performance
Predicting the performance of a proposed automatically managed multilevel memory system requires a model of the patterns by which programs refer to the information stored in the memory. Some recent experimental measurements on the Multics virtual memory suggest that, for rough approximations, a remarkably simple program reference model will suffice. The simple model combines the effect of the information reference pattern with the effect of the automatic management algorithm to produce a single, composite statement: the mean number of memory references between paging exceptions increases linearly with the size of the paging memory. The resulting model is easy to manipulate, and is applicable to such diverse problems as choosing an optimum size for a paging memory, arranging for reproducible memory usage charges, and estimating the amount of core memory sharing.
Computation of page fault probability from program transition diagram
An algorithm is given for calculating page fault probability in a virtual memory system operating under demand paging with various memory sizes and replacement rules. A first order Markov model of program behavior is assumed, and a representation of the system based on memory states, control states, and memory substates is presented. The algorithm is general in the sense that the page fault probabilities can be calculated for nonpredictive replacement rules applied to any program represented by a one-step Markov chain. A detailed example is given to illustrate the algorithm for Random and Least Recently Used (LRU) replacement rules.
Execution characteristics of programs in a page-on-demand system
h show the execution characteristics of two types of commonly used programs in a large-scale, time-shared computer system. A software monitoring facility built into the supervisor was used for data collection during normal system operation. These data were analyzed, and results of this analysis are presented for a Fortran compiler and an interactive line file editor.
Probability distribution functions and other data are given for such things as CPU intervals, I/O intervals, and the number of such intervals during execution. Empirical distributions are compared with simple theoretical distributions (exponential, hyperexponential, and geometric). Other data show paging characteristics of tasks as a function of the number of pages those tasks have in core.
On Lion’s counter example for Gotlieb’s method for the construction of school timetables
The timetable problem is an essentially discrete problem. Although the discrete problem may have no feasible solution, there may exist a solution to the equivalent continuous problem. An example, is given, for which the nondiscrete solution can be interpreted as a set of timetables, differing from week to week, which together satisfy the long-term requirements of the timetable problem.
Copying list structures using bounded workspace
Two new algorithms are presented for list structure copying using bounded workspace. The first, of primarily theoretical interest, shows that without cell tag bits the task can be performed in time n2. The second algorithm, assuming one tag bit in each cell, delivers attractive practical speed. Any noncyclic structure is copied in linear speed, while cyclic structures are copied in average time less than n log n. No foreknowledge of cycle absence is necessary to achieve linear speed. A variation of the second algorithm solves an open problem concerning list structure marking. That result demonstrates that marking can be done in average time n log n without the aid of supplemental tag bits or stacks.
Two methods for employing parallelism in tape-sorting are presented. Method A is the natural way to use parallelism. Method B is new. Both approximately achieve the goal of reducing the processing time by a divisor which is the number of processors.
An improved program-synthesizing algorithm and its correctness
An improved program-synthesizing algorithm based on the algorithm proposed by Waldinger and Lee in 1969 is given. In the old algorithm, the program-synthesizing problem is translated into a theorem-proving problem, and a program is obtained by analyzing a proof. For the improved algorithm, the analysis is not necessary, and a program is obtained as soon as the proof is completed. This is achieved by using a modified variable tracing mechanism invented by Green in 1969. The correctness of the improved algorithm is also proved; i.e. the program thus obtained always satisfies the specification.
Scalar- and planar-valued curve fitting using splines under tension
The spline under tension was introduced by Schweikert in an attempt to imitate cubic splines but avoid the spurious critical points they induce. The defining equations are presented here, together with an efficient method for determining the necessary parameters and computing the resultant spline. The standard scalar-valued curve fitting problem is discussed, as well as the fitting of open and closed curves in the plane. The use of these curves and the importance of the tension in the fitting of contour lines are mentioned as application.
