The problem of multiprogram scheduling on a single processor is studied from the viewpoint of the characteristics peculiar to the program functions that need guaranteed service. It is shown that an optimum fixed priority scheduler possesses an upper bound to processor utilization which may be as low as 70 percent for large task sets. It is also shown that full processor utilization can be achieved by dynamically assigning priorities on the basis of their current deadlines. A combination of these two scheduling techniques is also discussed.

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Scheduling Algorithms for Multiprogramming in a Hard-Real-Time Environment

The Temporal Logic of Reactive and Concurrent Systems: Specification

J+=j

A hierarchical model of computer organizations is developed, based on a tree model using request/service type resources as nodes. Two aspects of the model are distinguished: logical and physical. General parallel- or multiple-stream organizations are examined as to type and effectiveness?especially regarding intrinsic logical difficulties. The overlapped simplex processor (SISD) is limited by data dependencies. Branching has a particularly degenerative effect. The parallel processors [single-instruction stream-multiple-data stream (SIMD)] are analyzed. In particular, a nesting type explanation is offered for Minsky's conjecture?the performance of a parallel processor increases as log M instead of M (the number of data stream processors). Multiprocessors (MIMD) are subjected to a saturation syndrome based on general communications lockout. Simplified queuing models indicate that saturation develops when the fraction of task time spent locked out (L/E) approaches 1/n, where n is the number of processors. Resources sharing in multiprocessors can be used to avoid several other classic organizational problems.

Some Computer Organizations and Their Effectiveness

Over the last decade, the Petr i net has gamed increased usage and acceptance as a basic model of systems of asynchronous concurrent computation. This paper surveys the basic concepts and uses of Petm nets. The structure of Petr i nets, thei r markings and execution, several examples of Petm net models of computer hardware and software, and research into the analysis of Petm nets are presented, as are the use of the reachabil i ty tree and the decidability and complexity of some Petr i net problems. Petr i net languages, models of computation related to Petm nets, and some extensions and subclasses of the Petri net model are also bmefly discussed

Petri Nets

A set of conditions are described which determine whether or not two successive portions of a given program can be performed in parallel and still produce the same results. The conditions are general and can be applied to sections of the program of arbitrary size. The conditions are interesting because of the light they shed on the structure of programs amenable to parallel processing and the memory organization of a multi-computer system.

Analysis of Programs for Parallel Processing

The following problem is considered: Given a data base which can be manipulated simultaneously by more than one process, what are the rules for synchronization which will maximize the amount of parallel activity allowed. It is assumed that the data base can be represented as a graph. An example of such a data base is a hierarchy of directories for an on-line file system. Methods for synchronization of processes are examined; their validity is discussed and their performance compared.

Synchronization in a parallel-accessed data base

The services received by a process from a time-sharing operating system can be characterized by a resource count ∑ wiRij where Rij is the number of units of service received by process j from resource i and wi is the cost per unit of the service. Each class of users can be characterized by a policy function which specifies the amount of service a user who belongs to this class should receive as a function of time. Priority changes dynamically as a function of the difference between the service promised to the user by the policy function and the service he actually receives.A scheduling and swapping algorithm which keeps the resource count of each process above its policy function will provide the specified level of service. Overhead can be reduced by avoiding swaps of processes which have received at least this level of service. The algorithm has been implemented in a general purpose operating system, and it has provided significantly better service to interactive and to batch jobs than the previous scheduler.

A policy-driven scheduler for a time-sharing system

A project is described whose purpose is to train selected black residents of the Albany-Schenectady area in computer programming and arrange for jobs for them in the computer field. Both the organization and curriculum of the course are discussed.

A. J. Bernstein

Papers

Analysis of Programs for Parallel Processing

Synchronization in a parallel-accessed data base

A policy-driven scheduler for a time-sharing system

A programmmer training project

Computer Group News