A Oueueing Model Of A Rotational Position Sensing Disk System

Abstract

In this paper we present a general model of disk storage systems equipped with rotational position sensing (RPS). These systems are distinguished by sector scheduling at the channel. We show that the number of revolutions spent waiting for the channel due to the RPS feature is not geometrically distributed, as was assumed in most previous models. In place of the geometric assumption we give an approximate formula for the mean and variance of the number of revolutions required, and use this formula to develop an open, single queue model representing one disk module of the multi-module system. This model is then compared to simulations and to a previously developed analytic model. Finally, we develop a closed queueing network model using the single queue model as a component, and an approximate solution method is described by which to obtain performance measurements from the closed model.

Résumé

Nous présentons ici un modéle général pour une unité de disques capable de déceler la position rotationnelle. Dans ces systémes l’ordonnancement des secteurs est faite par les canaux. Nous démontrons que le nombre de révolutions où le canal doit attendre à cause du décèlement de position n’est pas distribué géométriquement, tel que supposé dans la plupart des modèles antérieurs. Nous remplaçons l’hypothèse géométrique par une formule approximative qui fournit la moyenne et la variance du nombre de révolutions requises. Cette formule sert alors à développer un modèle ouvert è file d’attente simple pour une unité de disques. Nous comparons ce modèle à un modèle analytique et à des simulations. Pour terminer, nous développons, basé sur le modèle à une seule file, un modèle comprenant un réseau fermé de files, et nous présentons une méthode approximative par laquelle on peut en obtenir des mesures de performance.

Additional information

Notes on contributors

John Zahorjan

JOHN ZAHORJAN received an sc B in Appljed Mathematics from Brown University (1975) and a Master of Science in Computer Science from the University of Toronto (1976). He is a PH D student at Toronto, whose work is concerned with queueing network models of computer systems.

J.N.P. Hume

J.N. PATTERSON HUME has been a pioneer in the field of computers. His physics interests in theoretical calculations of atomic wavefunctions led him to an early interest in computers in 1952. In 1954 he produced one of the first compilers, with its easy-to-learn programming language. In 1959 he coauthored one of the first books on data processing for business. Fie is (was?) a founding member of the Department of Computer Science at the University of Toronto and is now Professor and Chairman. His present interest is computer systems analysis.

K.C. Sevcik

KENNETH C. SEVCIK is an Associate Professor in the Department of Computer Science of the University of Toronto. His principal area of research is in modelling and predicting computer system performances. Other interest areas include file structure, data base systems and medical applications of computing. He recently completed a year of research leave, in which he worked in the Institutes of Informatics at Pontificia Universidade Catholica of Rio de Janeiro, IRIA LABORIA, in Paris and the University of Zurich.