TY - JOUR
T1 - Computing Bounds for the Performance Indices of Quasi-Lumpable Stochastic Well-Formed Nets
AU - Fraoceschinis, Giuliana
AU - Muntz, Richard R.
N1 - Funding Information:
Manuscript received February, 1994; revised May 24, 1994. The work of G. Franceschinis was done while she was visiting the Department of Computer Science, University of Califomia at Los Angeles, with the support of the CNR Progetto Finalizzato Sistemi Informatici e Calcolo Parallelo and the Italian MURST 40% Project. The work of R.R. Muntz was supported by the National Science Foundation under Grant CCR-9215064. Recommended by G. Juanole. G. Franceschinis is with the Dipartimento di Informatica, Universitl di Torino, 10149 Torino, Italy; e-mail: [email protected]. R.R. Muntz is with the Department of Computer Science, University of Califomia at Los Angeles, CA 90024-1596 USA. IEEE Log Number 9403 191,
PY - 1994/7
Y1 - 1994/7
N2 - Structural symmetries in stochastic well-formed colored Petrinets (SWN's) lead to behavioral symmetries that can be exploited by using the symbolic reachability graph (SRG) construction algorithm. The SRG allows one to compute an aggregated reachability graph (RG) and a “lumped” continuous time Markov chain (CTMC) that contain all the information needed to study the qualitative properties and the performance of the modeled system, respectively. Some models exhibit qualitative behavioral symmetries that are not completely reflected at the CTMC level. We call them quasi-lumpable SWN models. In these cases, exact performance indices can be obtained by avoiding the aggregation of those markings that are qualitatively, but not quantitatively, equivalent. An alternative approach consists of aggregating all the qualitatively equivalent states and computing approximated performance indices. In this paper, a technique is proposed to compute bounds on the performance of SWN models of this kind, using the results we have presented elsewhere. The technique is based on the Courtois and Semal bounded aggregation method.
AB - Structural symmetries in stochastic well-formed colored Petrinets (SWN's) lead to behavioral symmetries that can be exploited by using the symbolic reachability graph (SRG) construction algorithm. The SRG allows one to compute an aggregated reachability graph (RG) and a “lumped” continuous time Markov chain (CTMC) that contain all the information needed to study the qualitative properties and the performance of the modeled system, respectively. Some models exhibit qualitative behavioral symmetries that are not completely reflected at the CTMC level. We call them quasi-lumpable SWN models. In these cases, exact performance indices can be obtained by avoiding the aggregation of those markings that are qualitatively, but not quantitatively, equivalent. An alternative approach consists of aggregating all the qualitatively equivalent states and computing approximated performance indices. In this paper, a technique is proposed to compute bounds on the performance of SWN models of this kind, using the results we have presented elsewhere. The technique is based on the Courtois and Semal bounded aggregation method.
KW - High-level Petri nets
KW - Markov chains
KW - bounds
KW - lumpability
KW - model symmetry
KW - performance evaluation
KW - symbolic reachability graph
UR - http://www.scopus.com/inward/record.url?scp=0028467935&partnerID=8YFLogxK
U2 - 10.1109/32.297940
DO - 10.1109/32.297940
M3 - Article
SN - 0098-5589
VL - 20
SP - 516
EP - 525
JO - IEEE Transactions on Software Engineering
JF - IEEE Transactions on Software Engineering
IS - 7
ER -