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.

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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.

  1. Firstly, it provides a collection of matrices on which different numerical solution methods may be tested and compared.
  2. 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.

  1. 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
  2. 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
  3. 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
  4. 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
  5. 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
  6. LEAKY: 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.


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