This thesis describes a scheme for providing a nearly constant response time in a multiple user on-line computer system. A holding state is introduced which does not release user tasks until they have spent the requisite elapsed time in the system. While such arrangement increases the mean response time, it reduces the processor utilization of the computer system. There are other compensating considerations which may make this an attractive possibility in a number of applications. The thesis presents a method for designing such systems, based on machine repair theory (i.e. the theory of finite-source M/G/l queues), and on the use of the heavy traffic approximation to determine the proportion of the responses which exceed the design response time.