#### Filter Results:

- Full text PDF available (71)

#### Publication Year

1950

2017

- This year (2)
- Last 5 years (15)
- Last 10 years (44)

#### Publication Type

#### Co-author

#### Journals and Conferences

#### Key Phrases

Learn More

- Graham Horton, Vidyadhar G. Kulkarni, David M. Nicol, Kishor S. Trivedi
- European Journal of Operational Research
- 1998

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)

- Graham Horton, Scott T. Leutenegger
- SIGMETRICS
- 1994

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)

- Graham Horton, Stefan Vandewalle
- SIAM J. Scientific Computing
- 1995

- Susann C. Allmaier, Markus Kowarschik, Graham Horton
- PNPM
- 1997

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)

- Katinka Wolter, Graham Horton, Graham Hortonyz, Reinhard German
- 1996

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)

- Claudia Isensee, Graham Horton
- SimVis
- 2004

This paper illustrates the current state of development of an algorithm for the steady state solution of continuous-time Markov chains. The so-called multi-level algorithm utilizes ideas from algebraic multigrid to provide an efficient alternative to the currently used Gauss-Seidel and successive overrelaxation methods. The multi-level method has been… (More)

- Graham Horton, Stefan Vandewalle, Patrick H. Worley
- SIAM J. Scientific Computing
- 1995

- Stefan Vandewalle, Graham Horton
- Computing
- 1995

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)