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Quantitative analysis

Quantitative Analysis is pursued with the objective of assessing performance properties for a QPN. Different performance measures are offered for

ordinary places:
token population
timed places:
utilisation, throughput and token population

The calculation of performance measures can result in mean value, variance and distribution. They can be computed for all colours of a place separately or aggregated overall colours. They are easily specified by setting appropriate attributes of the corresponding place, see Fig. 5.

The employed analysis technique maps the specified QPN onto a corresponding Markov chain and subsequently analyses this chain with respect to its steady state distribution. The QPN's state space is fully explored causing quantitative analysis to be restricted to QPNs with a finite state space of acceptable size. For calculating a state descriptor for FCFS stations an upper bound of the queue length has to be determined. This is performed automatically during qualitative analysis by checking the reachability graph or an appropriate P-invariant.

QPN-Tool performs quantitative analysis based on Usenum. This is a tool developed at LS Informatik IV which is specially designed for numerical analysis of finite Markov chains, see [9]. Usenum's duties include three main steps:

  1. exploring state space
  2. computing steady state distribution
  3. calculating performance measures
It is able to handle state spaces with more than states and offers different algorithms for the calculation of the steady state distribution, e.g. Grassmann's algorithm, JOR, SOR.

Next: Comparison Up: Analysis techniques Previous: Qualitative analysis

Tue Jan 9 09:20:20 MET 1996