NewInput.OJN {queueing}

Define the inputs of an Open Jackson Network

Description

Define the inputs of an Open Jackson Network

Usage

NewInput.OJN(prob=NULL, ...)
NewInput2.OJN(prob=NULL, nodes)
NewInput3.OJN(vLambda, numNodes, vType, vVisit, vService, vChannel)

Arguments

prob

It is probability transition matrix or visit ratio vector. That is, the prob[i, j] is the transition probability of node i to node j, or prob[i] is the visit ratio to node i (the visit ratio values doesn't need to be probabilities, that is, a value greater than 1 can be used here. See the examples)

...

a separated by comma list of nodes of i_MM1, i_MMC or i_MMInf class

nodes

A list of nodes of i_MM1, i_MMC or i_MMInf class

vLambda

Vector with the arrivals rates to each node

numNodes

Number of nodes

vType

A vector with the type of server: "Q" for a queueing node, "D" for a delay node

vVisit

A vector with the visit ratios

vService

A vector with the services time of each node

vChannel

A vector with the number of channels of the node. The type of the server has to be "Q" to be inspected

Details

Define the inputs of an Open Jackson Network. For a operational use, NewInput3.OJN is recommended. For a more academic use, NewInput.OJN or NewInput2.OJN is recommended. Please, note that the different ways to create the inputs for a Open Jackson Network are equivalent to each other, and no validation is done at this stage. The validation is done calling CheckInput function.

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.

[Lazowska84] Edward D. Lazowska, John Zahorjan, G. Scott Graham, and Kenneth C. Sevcik (1984).
Quantitative System Performance: Computer System Analysis Using Queueing Network Models.
Prentice-Hall, Inc., Englewood Cliffs, New Jersey

See Also

QueueingModel.i_OJN

Examples

## See example 11.11 in reference [Sixto2004] for more details.
## create the nodes
n1 <- NewInput.MM1(lambda=8, mu=14, n=0)
n2 <- NewInput.MM1(lambda=0, mu=9, n=0)
n3 <- NewInput.MM1(lambda=6, mu=17, n=0)
n4 <- NewInput.MM1(lambda=0, mu=7, n=0)
m  <- c(0, 0.2, 0.56, 0.24, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)

# definition of the transition probabilities
prob <- matrix(data=m, nrow=4, ncol=4, byrow=TRUE)

ojn1 <- NewInput.OJN(prob, n1, n2, n3, n4)

## Using function NewInput2
## Not run: 
  ojn1 <- NewInput2.OJN(prob, list(n1, n2, n3, n4))

## End(Not run)


## Using visit ratios. Values taken from [Lazowska84], pag. 113.

## E[S] cpu = 0.005, Visit cpu = 121, D cpu = E[S] cpu * Visit cpu = 0.605
cpu <- NewInput.MM1(lambda=0.2, mu=1/0.005)

## E[S] disk1 = 0.030, Visit disk1 = 70, D disk1 = E[S] disk1 * Visit disk1 = 2.1
disk1 <- NewInput.MM1(lambda=0.2, mu=1/0.030)

## E[S] disk2 = 0.027, Visit disk2 = 50, D disk2 = E[S] disk2 * Visit disk2 = 1.35
disk2 <- NewInput.MM1(lambda=0.2, mu=1/0.027)

## In this example, to have the throughput per node, the visit ratios has to be given in this form.
## Please, don't use in the closed Jackson Network 
visit <- c(121, 70, 50)
net <- NewInput.OJN(visit, cpu, disk1, disk2)

## Using NewInput3
vLambda <- c(0.2, 0.2, 0.2)
vService <- c(0.005, 0.030, 0.027)
numNodes <- 3
vType <- c("Q", "Q", "Q")
vChannel <- c(1, 1, 1)
net2 <- NewInput3.OJN(vLambda, numNodes, vType, visit, vService, vChannel)