queueing-package {queueing}

Analysis of Queueing Networks and Models.

Description

It provides a versatile tool for analysis of birth and death based Markovian Queueing Models and Single and Multiclass Product-Form Queueing Networks.

It implements the following basic markovian models:

M/M/1,	M/M/c,		M/M/Infinite,
M/M/1/K,	M/M/c/K,	M/M/c/c,
M/M/1/K/K,	M/M/c/K/K,	M/M/c/K/m,	M/M/Infinite/K/K

It also solves the following types of networks:

• Multiple Channel Open Jackson Networks.

• Multiple Channel Closed Jackson Networks.

• Single Channel Multiple Class Open Networks.

• Single Channel Multiple Class Closed Networks

• Single Channel Multiple Class Mixed Networks

Also it provides B-Erlang, C-Erlang and Engset calculators.

This work is dedicated to the memory of D. Sixto Rios Insua.

Details

All models are used in the same way:

1. Create inputs calling the appropiate NewInput.model. For example, x <- NewInput.MM1(lambda=0.25, mu=1, n=10) for a M/M/1 model. To know the exact acronymn model to use for NewInput function, you can search the html help or write help.search("NewInput") at the command line.

2. Optionally, as a help for creating the inputs, the CheckInput(x) function can be called

3. Solve the model calling y <- QueueingModel(x). In this step, the CheckInput(x) will be called. That is the reason that the previous step is optional

4. Finally, you can get a performance value as W(y), Wq(y) or a report of the principals performace values calling summary(y)

See the examples for more detailed information of the use.

Author(s)

Author, Maintainer and Copyright: Pedro Canadilla [e-mail]

References

[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.

Examples

## M/M/1 model
summary(QueueingModel(NewInput.MM1(lambda=1/4, mu=1/3, n=0)))

## M/M/1/K model
summary(QueueingModel(NewInput.MM1K(lambda=1/4, mu=1/3, k=3)))