Probability models are presented for computer systems with processor-shared (time-sliced) service discipline. The response (sojourn) time of an arriving job that requires T units of processing time is shown to be approximately Gaussian/normal under moderately heavy traffic conditions, e.g. when the number of terminals is large.

This paper presents an analysis of the performance of a special type of voice-data queueing system. The system consists of an integrated circuit-and packet-switched multiplexer resembling that found in the SENET network. A fluid-flow approximation for the data component is introduced to ease study of the voice loss rate and data packet waiting times. In this paper it is shown that very long data queues are possible, with the mean data queue length being proportional to the ratio of the holding time for voice to the holding time for data. The equilibrium distribution is determined, and aspects of the transient behavior are characterized. The question of how much bandwidth to reserve for exclusive use of data and how much to share between voice and data is addressed.

Probabilistic models are presented and investigated to describe the service furnished to messages sent via communications channels on which messages in progress may be "destroyed" by a new message demand. Retries by destroyed messages are modeled. The general approach utilizes diffusion approximations. The quality of the numerical results is evaluated by comparison with simulations, and is found to be satisfactory.

The purpose of the present paper is to study systems in which different job types are present at the various servers and are processed according to a variety of scheduling disciplines, in particular in “first-come, first-served” order. Our approach is numerical, and is applied to an example which is also analyzed by means of the Gordon and Newell (GN) model. Using a plausible method of fitting the latter provides a reasonably, satisfactory approximation to the “true” multitype system parameters.

This paper presents results of an approximation study of cyclic queueing phenomena that occur in multiprogrammed computer systems. Based on Wald’s identity and using ideas of diffusion, the objective is to develop convenient and nearly explicit formulas relating processor utilization in such systems to simple program parameters and the level of multiprogramming. Some numerical results to indicate the quality of the proposed approximation are given.

In a multiprogramming computer system modeled as a cyclic queue the number of program segments completed at the CPU in a period of time is discussed. It is shown that this number is approximately normally distributed as the time period becomes long. Parameters of the normal distribution are determined. Numerical examples illustrate the results.

Models are developed to describe delays and backlogs at remote terminals polled in turn by a single computer.The effects modeled include transmission delays caused by line noise, and the number and types of terminals (passive input, and active or two-way response).Use is made of the diffusion approximation to state variables, the latter being especially relevant when the system is heavily loaded.A limited amount of mathematical and stimulationgenerated evidence attests to the adequacy of this approximation.

This paper considers some of the issues that arise when messages or jobs inbound to a computer facility are buffered prior to being processed.Models are developed that describe (a) the results of blocking a single memory unit for the use of diverse messages, (b) the occupancy behavior of a buffer that is tied to a single message source, and (c) the occupancy of a buffer dynamically shared among many independent sources.

A probabilistic model is developed for a multiprogramming computer configuration, i.e., one in which several program segments are simultaneously in main memory (core). The model relates speed and number of input-output devices, core size, and central processor speed to central processor and system productivity. Incorporated in the model are parameters describing the statistical variability of input-output and central processor activities. Thus the model permits comparisons between systems loaded with different mixtures of job types (“scientific” vs. “business” applications). Numerical comparisons of various systems are provided.