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/** @author  John Miller
 *  @version 1.3
 *  @date    Wed Dec 30 15:13:32 EST 2009
 *  @see     LICENSE (MIT style license file).
 */

package apps.state

import scalation.state.MarkovC
import scalation.linalgebra.MatrixD

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/** The `MarkovQueue` object finds the steady-state solution and simulates a simple
 *  Markovian Queue (an M/M/1/2) where the arrival rate is 4 and the service rate is 5.
 *  Note, each diagonal value must make their row sum to 0.
 *  @see scalation.state.MarkovTest, scalation.state.MarkovCTest for example
 *  test code for discrete-time and continuous-time Markov chains, respectively.
 *  > run-main apps.state.MarkovQueue
 */
object MarkovQueue extends App
{
    /** The transition rate matrix
     */
    private val trMatrix = new MatrixD ((3, 3), -4.0,  4.0,  0.0,
                                                 5.0, -9.0,  4.0,
                                                 0.0,  5.0, -5.0)

    println ("\nTransition Rate Matrix trMatrix = " + trMatrix + "\n")

    /** The continuous-time Markov Chain
     */
    private val mc = new MarkovC (trMatrix)

    println ("\nContinuous-Time Markov Chain mc = " + mc + "\n")

    println ("\nContinuous-Time Markov Chain: steady-state solution:")
    println ("\njump matrix  \tj = " + mc.jump)
    println ("\nsteady-state \tp = " + mc.limit)

    println ("\nContinuous-Time Markov Chain: simulation:")
    mc.simulate (0, 100.0)

} // MarkovQueue object