Analysis of catastrophic phenomena in a multiprogramming system

This paper presents a state analysis of multiprogramming, using the concept of cusp catastrophe in the theory of catastrophe. Based on the result, the catastrophic phenomena in the multiprogramming system are analyzed. It is shown first that the multiprogramming system exhibits two stable states, i.e., monostable and bistable states, for the change of job generation rate and the change of the maximum multiprogramming level. Then it is shown that a rapid change (catastrophe) of the performance of the multiprogramming system, such as the mean number of jobs in the system, throughput and response time, may occur with the change of the stable state of the system. Furthermore, it is shown that for any given job generation rate, there exists a maximum multiprogramming level which maximizes the throughput and minimizes the response time.