Some Practical Results for Non-Exponential Models of Computer Performance Analysis PDF

Keywords

computers, non-exponential models, Markovian models

Abstract

Consistent measurements have shown that the service and interarrival time distributions for most computer resources are not exponential. The immediate consequence of this finding is that the popular Markovian models such as the M/M/I, M/M/C etc. do not accurately represent the underlying computer resources and therefore may not be totally reliable in the performance analysis of computer systems. Computer resources may be more appropriately represented by nonexponential models where both the service and interarrival times may be of a general type. Although this seems to be a natural resort, in practice analysis refrain from the use of non-exponential models because they are hard to solve and may not lead to useful solutions. This paper is an attempt to remove some of the difficulties associated with the analysis of non-exponential computer models. It is shown that the spectral solution of Lindley's integral equation with the help of Rouche's theorem may easily be used to obtain exact solutions for the non-exponential models of computer performance analysis. Several examples are used to illustrate the method. These include the E2/H2/I2, the H2/H2/I and E2/E2/I models for which exact performance measures are given for the first time, to the best of our knowledge.