Numerical analysis of superposed GSPNs

• Published in: IEEE transactions on software engineering Vol. 22; no. 9; pp. 615 - 628
• Main Author: Kemper, P.
• Format: Journal Article Conference Proceeding
• Language: English
• Published: New York, NY IEEE 01.09.1996; Institute of Electrical and Electronics Engineers; IEEE Computer Society
• Subjects: Algebra; Algorithm design and analysis; Algorithmics. Computability. Computer arithmetics; Algorithms; Applied sciences; Automata. Abstract machines. Turing machines; Computer science; control theory; systems; Computer systems performance. Reliability; Exact sciences and technology; Iterative algorithms; Markov analysis; Numerical analysis; Petri nets; Restrictions; Software; Sparse matrices; State-space methods; Statistical analysis; Steady-state; Stochastic models; Stochastic processes; Studies; Systems analysis; Tensile stress; Theoretical computing; Process algebra; Numerical analysis; Petri nets; Markov processes; Stochastic approximation; Decomposition; Iterative methods; Reachability
• ISSN: 0098-5589; 1939-3520
• DOI: 10.1109/32.541433

The numerical analysis of various modeling formalisms profits from a structured representation for the generator matrix Q of the underlying continuous-time Markov chain, where Q is described by a sum of tensor (Kronecker) products of much smaller matrices. In this paper, we describe such a representation for the class of superposed generalized stochastic Petri nets (GSPNs), which is less restrictive than in previous work. Furthermore a new iterative analysis algorithm is proposed. It pays special attention to a memory-efficient representation of iteration vectors as well as to a memory-efficient structured representation of Q in consequence the new algorithm is able to solve models which have state spaces with several million states, where other exact numerical methods become impracticable on a common workstation.