NewInput.CJN: Define the inputs of a Closed Jackson Network

Description

Define the inputs of a Closed Jackson Network

Usage

NewInput.CJN(prob=NULL, n=0, z=0, operational=FALSE, method=0, tol=0.001, ...)
NewInput2.CJN(prob=NULL, n=0, z=0, operational=FALSE, method=0, tol=0.001, nodes)
NewInput3.CJN(n, z, numNodes, vType, vVisit, vService, vChannel, method=0, tol=0.001)

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 (a probability, that is, a value between 0 and 1) to node i. Also, the visit ratio can express the number of times that a client visits the queueing center, in a more operational point of view. See the parameter operational

number of customers in the Network

think time of the client

operational

If prob is a vector with the visit ratios, operational equal to FALSE gives to the visit ratio a probability meaning, that is, as the stacionary values of the imbedded markov chain. If operational is equal to TRUE, the operational point of view is used: it is the number of visits that the same client makes to a node.

method

If method is 0, the exact MVA algorith is used. If method is 1, the Bard-Schweitzer approximation algorithm is used.

tol

If the parameter method is 1, this is the tolerance parameter of the algorithm.

…

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

numNodes

The number of nodes of the network

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. It represent visit counts to a center as if the parameter operational were TRUE

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 a Closed Jackson Network. For a operational use, NewInput3.CJN is recommended. For a more academic use, NewInput.CJN or NewInput2.CJN is recommended. Please, note that the different ways to create the inputs for a Closed 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

Examples

Run this code

# NOT RUN {
## See example 11.13 in reference [Sixto2004] for more details.
## create the nodes
n <- 2
n1 <- NewInput.MM1(lambda=0, mu=1/0.2, n=0)
n2 <- NewInput.MM1(lambda=0, mu=1/0.4, n=0)

## think time = 0
z <- 0

## operational value
operational <- FALSE

## definition of the transition probabilities
prob <- matrix(data=c(0.5, 0.5, 0.5, 0.5), nrow=2, ncol=2, byrow=TRUE)

cjn1 <- NewInput.CJN(prob, n, z, operational, 0, 0.001, n1, n2)

# }
# NOT RUN {
  cjn1 <- NewInput2.CJN(prob, n, z, operational, 0, 0.001, list(n1, n2))
# }
# NOT RUN {

## using visit ratios and service demands. See [Lazowska84] pag 117.
## E[S] cpu = 0.005, Visit cpu = 121, D cpu = E[S] cpu * Visit cpu = 0.605
cpu <- NewInput.MM1(mu=1/0.005)

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

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

## The visit ratios.
vVisit <- c(121, 70, 50)

operational <- TRUE

net <- NewInput.CJN(prob=vVisit, n=3, z=15, operational, 0, 0.001, cpu, disk1, disk2)

## Using the operational creation function
n <- 3
think <- 15
numNodes <- 3
vType <- c("Q", "Q", "Q")
vService <- c(0.005, 0.030, 0.027)
vChannel <- c(1, 1, 1)

net2 <- NewInput3.CJN(n, think, numNodes, vType, vVisit, vService, vChannel, method=0, tol=0.001)

# }