We evaluate a stochastic upper bound on the response time Probability Density Function (PDF) of complex workflows through an efficient and accurate compositional approach. Workflows consist of activities having generally distributed stochastic durations with bounded supports, composed through sequence, choice/merge, and balanced/unbalanced split/join operators, possibly breaking the structure of well-formed nesting. Workflows are specified using a formalism defined in terms of Stochastic Time Petri Nets (STPNs), that permits decomposition into a hierarchy of subworkflows with positively correlated response times, guaranteeing that a stochastically larger end-to-end response time PDF is obtained when intermediate results are approximated by stochastically larger PDFs and when dependencies are simplified by replicating activities appearing in multiple subworkflows. In particular, an accurate stochastically larger PDF is obtained by combining shifted truncated Exponential terms with positive or negative rates. Experiments are performed on sets of manually and randomly generated models with increasing complexity, illustrating under which conditions different decomposition heuristics work well in terms of accuracy and complexity, and showing that the proposed approach outperforms simulation having the same execution time.

我们通过高效准确的组合方法评估复杂工作流的响应时间概率密度函数 (PDF) 的随机上限。工作流由具有一般分布的随机持续时间和有限支持的活动组成，通过序列、选择/合并和平衡/不平衡拆分/连接运算符组成，可能会破坏结构良好的嵌套结构。使用根据随机时间 Petri 网 (STPN) 定义的形式来指定工作流，该形式允许分解为具有正相关响应时间的子工作流层次结构，当中间结果由随机较大的 PDF 近似时，以及通过复制出现在多个子工作流中的活动来简化依赖关系时，保证获得随机较大的端到端响应时间 PDF。特别是，通过将移位的截断指数项与正率或负率相结合，可以获得准确的随机较大的 PDF。对复杂性不断增加的手动和随机生成的模型集进行了实验，说明了在哪些条件下不同的分解启发式方法在准确性和复杂性方面表现良好，并表明所提出的方法优于具有相同执行时间的模拟。通过将移位截断指数项与正利率或负利率相结合，可以获得准确的随机较大的 PDF。对复杂性不断增加的手动和随机生成的模型集进行了实验，说明了在哪些条件下不同的分解启发式方法在准确性和复杂性方面表现良好，并表明所提出的方法优于具有相同执行时间的模拟。通过将移位截断指数项与正利率或负利率相结合，可以获得准确的随机较大的 PDF。对复杂性不断增加的手动和随机生成的模型集进行了实验，说明了在哪些条件下不同的分解启发式方法在准确性和复杂性方面表现良好，并表明所提出的方法优于具有相同执行时间的模拟。