Stochastic High-level Petri Nets Research Articles

Wireless channel model using stochastic high‐level Petri nets for cross‐layer performance analysis in orthogonal frequency‐division multiplexing system

In this study, the authors form a wireless channel model for orthogonal frequency-division multiplexing (OFDM) systems with stochastic high-level Petri net (SHLPN) formalism in order to simplify the cross-layer performance analysis of modern wireless systems. Compared with existing finite state Markov channel model whose state space grows exponentially with the number of OFDM subchannels, the author's proposed SHLPN model uses state aggregation technique to deal with this problem. Closed-form expressions to calculate the transition probabilities among the compound markings of the SHLPN model are provided. When applied to derive the performance measures for OFDM system in terms of the average throughput, average delay and packet dropping probability, the SHLPN model can accurately capture the correlated time-varying nature of wireless channels. Simulation is performed to show that the numerical results offered by the proposed model are more accurate compared with other simplified channel models for avoiding state space complexity.

On the analysis of stochastic high level Petri net models

In this paper we review the Stochastic High Level Petri Nets, SHLPNs, introduced in [LiM86] and discuss the difficulties encountered in designing tools to automate the analysis of SHLPNs. Construction of net invariants and reachability trees for different classes of high level nets lead to open problems. We present High Level Petri Nets with marking variables and show that for this class of nets it is possible to construct efficiently the reachability tree. The algorithm is based upon equivalence and covering relations among marking variables. Then we discuss the compound token and token flow path concepts and present an algorithm to compute the S-invariants.

Stochastic high-level Petri nets and applications

A class of stochastic Petri nets called stochastic high-level Petri nets (SHLPNs) is proposed. SHLPNs are high-level Petri nets augmented with exponentially distributed firing times. SHLPNs generally lead to models with a smaller state space. A computer marking concept is introduced that allows a considerable reduction of the number of states and induces a correct grouping of states in the Markov-domain SHLPN models of multiprocessor systems. The main advantage of modeling homogeneous systems using SHLPNs is that the resulting models are simpler and more intuitive and have a smaller number of states, as shown by examples. >

Domain oriented analysis of PDE splitting algorithms

We consider the performance of Schwarz splitting algorithms for PDE problems on the hypothetical Multi- flex machine. The particular multi- flex considered consists of eight clusters of flex/32 multiprocessors. We introduce the concept of execution domains to model the three levels of memory on these machines: local, locally shared, and global. We apply the method of stochastic high level Petri nets (SHLPN) to model the performance of these PDE splitting algorithms on a Multi- flex machine. For very large, but realistic, applications we project potential speedup of 300 for 2D problems and more for 3D problems along with processor utilization of over 99 percent. Real computations on real machines can fall far short of this potential and still be very successful.