Package jline.io

Class MAPQN2RENV

java.lang.Object
jline.io.MAPQN2RENV
public class MAPQN2RENV extends Object
Markov-modulated image of a network with MAP/MMPP/MMAP arrival or service processes as a queueing network in a random environment.

Every non-renewal process is a point process modulated by the CTMC with generator Q = D0 + D1, whose conditional intensity in phase k is lambda(k) = sum_j D1(k,j). The transformation freezes each phase into an environment stage in which the process is the Poisson process of that intensity, i.e. an exponential arrival or service time, and lets the environment switch stages at the rates of Q. With P modulated processes the stage set is the Cartesian product of their phase spaces and the environment generator is the Kronecker sum of the individual Q's, so only one process changes phase at a time, as in the original model.

The image is exact in structure for an MMPP (diagonal D1): the modulating chain, its stationary distribution and the phase-conditional intensities are all preserved. For a general MAP the phase jumps that occur AT an event epoch (off-diagonal D1) are aggregated into Q and their correlation with the event stream is lost, so the image matches the modulating chain and the conditional intensities but not the full inter-event autocorrelation.

Populations are carried across stage switches unchanged (identity reset), as a phase switch moves no job.

Mirrors matlab/src/io/map2renv.m.

  • Field Details

    • DEFAULT_MAX_STAGES

      public static final int DEFAULT_MAX_STAGES
      Default cap on the number of environment stages.
      See Also:

  • Constructor Details

    • MAPQN2RENV

      public MAPQN2RENV()

  • Method Details

    • mapqn2renv

      public static Environment mapqn2renv(Network model)
      Retained name for the transformation now implemented by map2renv(Network, SolverOptions), which generalizes it from a single MMPP2 service process to any number of MAP, MMPP2 or MMAP arrival and service processes of arbitrary phase order.
      Parameters:
      model - Network with at least one MAP/MMPP2/MMAP process
      Returns:
      Environment model with exponential rates modulated by the phases

    • map2renv

      public static Environment map2renv(Network model, SolverOptions options)
      Parameters:
      model - Network with at least one MAP/MMPP2/MMAP process
      options - solver options; config.map_env_maxstages caps the stage count
      Returns:
      Environment model with exponential rates modulated by the phases

    • map2renvImage

      public static MAPQN2RENV.RenvImage map2renvImage(Network model, SolverOptions options)
      Parameters:
      model - Network with at least one MAP/MMPP2/MMAP process
      options - solver options; config.map_env_maxstages caps the stage count
      Returns:
      the environment image and the shape of the transformation