Approximations for Customer-Viewed Delays in Multiprogrammed, Transaction- Oriented Computer Systems

The analysis of a multiprogramming computer system is greatly complicated by the requirement of an external queue to limit the level 1559 of multiprogramming (see Fig. la), and one is often led to approximation techniques. One common method for finding customer-experienced delays (such as the mean access time or mean response time) is to solve for the mean output rate from a closed (generally Markovian) model of the computer system with a fixed number of jobs resident equal to n = 1, 2, · · · , M (M is the maximum allowable multiprogramming level--see Fig. lb) and then approximate the entire system by a (Markovian) state-dependent server process (see Fig. lc) which can be analyzed for the quantities of interest. The accuracy of this approximation technique has been studied by Avi-Itzhak and Heyman1 for a certain class of models, and some specific error bounds are given there. Konheim and Reiser also consider briefly the accuracy question in Ref. 2, where they give an exact solution for a two-resource computer system. The conditions given to insure the accuracy of the state-dependent server approximation are essentially the same as those needed for decomposibility in the sense of Courtois3,4 as applied to the special class of systems considered in Refs. 1 and 2. While the state-dependent server model is often appliT O T A L SYSTEM