MARCA_Models is
A set of
subroutines and associated data files which may be used
to generate the transition rate matrices of a collection
of Markov chain models.
MARCA_Models:
A Collection of Markov Chain Models
William J. Stewart
MARCA_Models is a set of Fortran
subroutines and associated data files which may be used
to generate the transition rate matrices of a collection
of Markov chain models.
The purpose of the MARCA_Models
database is twofold.
- Firstly, it provides a collection of matrices on
which different numerical solution methods may be tested and
compared.
- Secondly, the models may prove to be useful to those
engaged in system modelling, for users can modify the model
parameters to obtain others that more closely correspond to
their own requirements.
Currently, the
MARCA_Models
collection consists of the following Markov chain models.
- NCD:
Model description and illustration.
A closed queueing network model of the central server type.
This model gives rise to a Nearly Completely Decomposable (NCD)
Markov chain. Hence its name.
Source code and data files for this model: ncd.tar.gz
- MUTEX:
Model description and illustration.
A "mutual-exclusion" model in which N processes seek to
share R resources.
Source code and data files for this model: mutex.tar.gz
- TwoD:
Model description and illustration.
A general 2D Markov chain model. Possible transitions from any
(nonboundary) state are to the North, South, East, West, North-East,
South-East, South-West and North-West. The specific model chosen is
a biological model:
the general epidemic model of Ridler-Rowe.
Source code and data files for this model: twoD.tar.gz
- TCOMM:
Model description and illustration.
A queueing network model of impatient telephone customers
on a computerized telephone exchange.
Source code and data files for this model: tcomm.tar.gz
- QNATM:
Model description and illustration.
A multi-class, finite-buffer, priority queueing network model
with applications to ATM.
Source code and data files for this model: qnatm.tar.gz
- LEAKY:
Model description and illustration.
A "leaky-bucket" model of the type used in telecommunication
modelling. This is basically a queueing system with a finite
buffer and two type of customers; the first arrive
according to a Poisson distribution and the second at fixed
intervals of time.
Source code and data files for this model: leaky.tar.gz
INSTRUCTIONS FOR USING MARCA_Models
To generate the transition rate matrix corresponding to an instance
of one of the above models, you must obtain the Fortran source
code and data files corresponding to the model.
The files that are needed for a specific
model are tar'd and gzip'd into a file named after the example
e.g., ncd.tar.gz, mutex.tar.gz, etc. When gunzip'd and untar'd each
produces a directory that bears the model's name. This directory
includes a Fortran source code file that
is specific to the model (ncd.f, mutex.f, etc.) and an input file
specific to the model (ncd_in, mutex_in, etc.).
For convenience, a Makefile is also included.
Additionally, the transition rate matrix corresponding to a selected
instance of the model (one that produces only a small set of states) is
usually available in this directory.
Finally, the file
generate.f containing Fortran source
code must be downloaded since it is used in all the models.
Once the files have been transferred to your system, you will need to
actually generate one or more transition matrices corresponding to
the model transferred. Instructions on how to do so are available
in:
Generating the matrix.
It is possible to alter the model, by modifying parameters
such as rates of transition, branching probabilities, number of customers
in a network, buffer sizes, and so on. This is achieved by changing
values in the source code file for the model and/or in its data file.
More information is available in:
Modifying a model.
Some information concerning the amount of memory needed to execute
the code for different values of the model parameters may be found in:
Memory requirements and matrix size.
Keywords for Search Engines
MARCA, Markov, Markov chain, Markov process, Markov model,
Testbed, collection, database,
NCD, 2D, mutual exclusion, leaky bucket, finite buffer,
priority queues, queueing network, two dimensional Markov chain,
compact storage, sparse, Harwell Boeing.