Predictive E-Mail Server Performability Analysis Based on Fuzzy Arithmetic

Abstract –The performability of disk arrays systems has been studied before. However, in the case of imprecise data, a fuzzy model can be the base for the performability analysis. This paper presents a performability analysis of an MSExchange-like e-mail server. The analysis is based on a Markov Reward model. The performability analysis is accomplished through the use of fuzzy arithmetic. Unlike traditional Markov Chains, Fuzzy Markov Chains can successfully handle uncertain, imprecise probabilities. In cases where the failure rates, repair rates, or the workload parameters are uncertain, Markov Chains enhanced with fuzzy arithmetic provide means for comprehensive predictive performability analysis of a system. This performability analysis provides a valuable guideline regarding required resources such as the number of mailboxes, and therefore, the number of users the mail server can support with regards to the reliability and performance of the disk array used by the mail server. The fuzzy arithmetic helps in better visualization and estimation of the range of number of users the mail server is capable of servicing over long periods of time. 1