# Define the inputs of a Closed Jackson Network ```r 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 - `n`: number of customers in the Network - `z`: 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 ## See Also `QueueingModel.i_CJN` ## Examples ```r ## 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)) ## End(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) ```

NewInput.CJN function