The complexity of performance analysis in parallel algorithms and systems

The computational complexity of analyzing the performance of parallel algorithms and concurrent systems is addressed. The type and origin of this complexity are discussed, and the way to deal with it is investigated. Based on a symbolic notation of the large Markovian state-space, an approach is proposed which takes advantage of computer algebra and symbol-manipulation languages to collapse the state space, restructure it, and introduce efficient methods for a global balance equation solution, based on either closed-form or on low-cost Gaussian elimination techniques. The approach is compared to conventional methods for solving large Markovian systems, such as the decomposition and aggregation method and the stochastic Petri net method