Graham Horton

Learn More
In this paper we introduce a new class of stochastic Petri nets in which one or more places can hold uid rather than discrete tokens. We deene a class of uid stochastic Petri nets in such a way that the discrete and continuous portions may aaect each other. Following this deenition we provide equations for their transient and steady-state behavior. We(More)
A new iterative algorithm, the <italic>multi-level</italic> algorithm, for the numerical solution of steady state Markov chains is presented. The method utilizes a set of recursively coarsened representations of the original system to achieve accelerated convergence. It is motivated by multigrid methods, which are widely used for fast solution of partial(More)
In this paper we introduce a new class of stochastic Petri nets in which one or more places can hold uid rather than discrete tokens. We de ne a class of uid stochastic Petri nets in such a way that the discrete and continuous portions may a ect each other. Following this de nition we provide equations for their transient and steady-state behavior. We(More)
A common approach for the quantitative analysis of a generalized stochastic Petri net GSPN is to gener ate its entire state space and then solve the correspond ing continuous time Markov chain CTMC numeri cally This analysis often su ers from two major prob lems the state space explosion and the sti ness of the CTMC In this paper we present parallel(More)
This paper combines two diierent extensions of the modeling power of stochastic Petri nets in one single framework. First, the ring times of transitions may be non-exponentially distributed. Second, certain places can hold a continuous ((uid), rather than discrete, number of tokens. Both extensions lead to a state space which is partially discrete and(More)
The advent of parallel computers has led to the development of new solution algorithms for time-dependent partial differential equations. Two recently developed methods, multigrid waveform relaxation and time-parallel multigrid, have been designed to solve parabolic partial differential equations on many time-levels simultaneously. This paper compares the(More)
Recently the Multi-Level algorithm was introduced as a general purpose solver for the solution of steady state Markov chains. In this paper we consider the performance of the Multi-Level algorithm for solving Nearly Completely Decomposable (NCD) Markov chains, for which special-purpose iterative aggregation/disaggregation algorithms such as the(More)