(A) method of performance estimation using reduced timed petri nets

Abstract

Timed Petri net (TPN) has been widly used for the performance evaluation of a concurrent system. An approximate but highly accurate method for systematically converting a complicated TPN Into a simple net with a smaller state space is proposed in this thesis. It is based on reducible subnet and reduced reachability graph of it. A reducible subnet (RSN) is defined as a well formed place module in the complicated TPN. Even if the TPN has cycles, the rsn may have no cycles and no coupling with others outside it. The reachability grapho of a RSN is constructed and it is reduced to a simple form of a reachability graph defined as a reduced reachability graph (RRG). And from the RRG, a simple form of a TPN is deduced and defined as a reduced timed Petri net (RTN). The RSN is replaced by this resulting RTN and the same way is carried out on another RSN and so on, in the sequel, the complicated TPN can be converted into a simple TPN with a smaller state space. After this reduction, the remaining PTN with a samller state space is used for the performance evaluation of the modeled system by a conventional technique. The validity of the proposed method isshown by applying it to some example tasks to be runon hypercube multuprocessors, and it is used for the performance estimation of a hypercube multiprocessor designed in our laboratory.