臺灣博碩士論文加值系統

派翠網路 (Petri Nets) 是一種用來描述並且分析系統行為的工具。
尤其是將時間引入派翠網路後，如隨機過程時間派翠網路，對於具有並行
性(concurrency) 、同步性 (synchronization) 和不確定性
(nondeterminism) 複雜行為的並行式/分散式系統 (Concurrent /
Distributed Systems)，不僅能發揮模組(model)的能力還增加了派翠網
路所不能做的效能評估 (performance evaluation)。從其底層
(underlying) 派翠網路做結構分析 (structrual property analysis)
尋找永不變特性 (invariant)，做為驗證安全及存活 (Safety&Liveness)
行為特性 (behavior properties) 的基礎；另外，應用其相對連續馬可
夫模式 (continuous-time Markov Chain) 的分析解 (analytical
solution) 則能有效地對所描述的系統做效能評估。 在這篇論文中，
我們以讀、寫問題 (Readers and Writers Problem) 引導出與分析解有
關的線性方程組 (Systems of Linear equations)。在分析解的求解上，
我們採用了傳統的高斯-約旦消去法 (Gauss-Jorden elimination)、以及
更適合稀疏矩陣 (sparse matrix) 的高斯-西斗法 (Gauss-Siedel
method)和傑寇比法 (Jacobi method)。在永不變特性的求解上，我們採
用J. Martinez的循序演算法 (sequential algorithm) 求取其解空間的
最小支持永不變特性(minimal support invariants)，並且據以提出兩個
在平行電腦架構 (parallel computers) 上的平行(parallel)演算法。

Petri Nets is a tool to describe and analyse systematic
behavior.Especially after time is led into Petri Nets,such as
Stochastic timed petri nets,the complicated behavior including
concurrency,synchronization and nondeterminism of Concurrent /
Distributed Systems can develop the modeling and evaluating
system than ever.We can make structural property analysis from
underlying Petri Net,and find out invariants being the basis of
verifying behavior properties including safety and liveness.In
addition,the analytical solution of relative continuous-time
Markov Chain applying for Stochastic Timed Petri Nets can make
performance evalution more efficiently for that system you
describe. In this thesis ,by means of Reader and Writers
problem,we lead systems of linear equations relative to
analytical solution .On finding answer of the analytical
solution,we adopt traditional Guass-Jorden elimination,and it is
better for us to adopt Guass-Siedel and Jacobi methods for
sparse matrix.On finding invariants,we adopt J.Martinez*s
sequencial algorithm to get minimal support invariants,and we
bring up the parallel algorithms under parallel computer
systems.