應用馬可夫鏈於多原址多備援系統的容錯分析

Abstract

近年來分散式或網路系統已成為風尚，電腦更日趨小型化，加上成本的考 量，利用小型電腦來組成分散式的容錯系統是一個相當不錯的構想。 在1989年由Yennun Huang 和 Pankaj Jalote 兩人所發表的論文中，提到 了單原址多備援系統的容錯能力分析；本論文是將其模式延伸為多原址多 備援的容錯系統，然後利用馬可夫鏈中的birth -and-death 和 Primary- Sites Approach分別導出系統的可靠度、可用度、最佳備援電腦數目及最 佳檢核點的時間間隔的公式。由於分散式系統的架構相當多，本論文提出 兩個較具有代表性的系統，一是相依型系統，一是互補型系統，在舉一些 例子做為其間的比較分析，有興趣者亦可用類似方法推導其它型式的各項 公式。 Distributed systems using small computers and networking have provided alternatives to achieve high performance and fault tolerance. In reliability for systems with single primary site and multiple backups. This thesis extended the model into more general cases of multiple primary sites and multiple backups. Two types of systems were investigated; (1) systems in which primary nodes are dependent on one another, (2) systems in which primaries are complementary to one another. We derived formulas for the computations of availability, reliability, optimal chechpointing interval, and toptimal number of backup computers for each type of systems. Numerical examples were given. The readers of this report may derive formulas by themselves for other types of of systems by applying similar Markov chain and optimality analysis.